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Geometric and Semantic Coupling for Interaction Understanding in 3D Scenes
Hanyang Kong, Xingyi Yang
Intelligence
Status: succeeded | Model: Gemma-4-26B-A4B | Prompt: intel-v1 | Confidence: 94%
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Summary
The paper introduces Segment-Snap, a method for 3D interaction understanding that couples geometric and semantic information between movable parts and handles. It utilizes three predictors: a standalone part predictor, a dense handle predictor, and a joint part-handle predictor. A training-free geometric decoder uses handle locations to select hinge lines for rotational parts, while part motion classes refine handle labels. Experiments on Articulate3D show significant improvements in motion and handle accuracy by leveraging this bidirectional coupling.
Entities (10)
Relation Signals (7)
Segment-Snap → evaluatedon → Articulate3D
confidence 98% · On Articulate3D validation, handle guidance raises motion-gated AP from 13.74% to 40.98%
Segment-Snap → improves → motion-gated AP
confidence 96% · handle guidance raises motion-gated AP from 13.74% to 40.98%
Hanyang Kong → affiliatedwith → National University of Singapore
confidence 95% · Hanyang Kong 1 ... 1 National University of Singapore
Xingyi Yang → affiliatedwith → The Hong Kong Polytechnic University
confidence 95% · Xingyi Yang 2 ... 2 The Hong Kong Polytechnic University
Segment-Snap → uses → Geometric Decoder
confidence 95% · A geometric decoder uses planar and upright priors to constrain motion, then selects hinge lines using predicted handle locations
Articulate3D → basedon → ScanNet++
confidence 92% · Articulate3D extends interaction-oriented annotation to ScanNet++ reconstructions
USDNet → comparedwith → Segment-Snap
confidence 90% · USDNet jointly predicts movable parts... However, its motion decoder does not explicitly use the detected handle locations
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Abstract
Abstract:Interaction understanding in 3D scenes requires a joint description of movable parts, their motion, and the regions through which they can be operated. We present Segment-Snap, which connects these outputs through the physical relationship between parts and handles. Learned predictors identify broad part surfaces and small handles. A geometric decoder uses planar and upright priors to constrain motion, then selects hinge lines using predicted handle locations, without training a motion regressor. Conversely, a joint part-and-handle predictor supplies additional handle candidates, whose motion classes are refined using containing parts. Each information transfer is applied once, without iterative feedback. On Articulate3D validation, handle guidance raises motion-gated AP from 13.74% to 40.98% at fixed masks and axes. Additional handle candidates raise handle AP from 24.63% to 29.65%; part-based class correction adds 0.98 points, and full context reaches 30.99%. Repeated training, learned-decoder controls and paired visualizations establish the benefits and limitations of combining geometric and semantic evidence for interaction understanding.
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- Source: https://arxiv.org/abs/2609.25247v1
- Canonical: https://arxiv.org/abs/2609.25247v1
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Technical Report Geometric and Semantic Coupling for Interaction Understanding in 3D Scenes Hanyang Kong 1 , Xingyi Yang 2 1 National University of Singapore, 2 The Hong Kong Polytechnic University Abstract Interaction understanding in 3D scenes requires a joint description of movable parts, their motion, and the regions through which they can be operated. We present Segment–Snap, which connects these outputs through the physical relationship between parts and handles. Learned predictors identify broad part surfaces and small handles. A geometric decoder uses planar and upright priors to constrain motion, then selects hinge lines using predicted handle locations, without training a motion regressor. Conversely, a joint part-and-handle predictor supplies additional handle candidates, whose motion classes are refined using containing parts. Each information transfer is applied once, without iterative feedback. On Articulate3D validation, handle guidance raises motion-gated AP from 13.74% to 40.98% at fixed masks and axes. Additional handle candidates raise handle AP from 24.63% to 29.65%; part-based class correction adds 0.98 points, and full context reaches 30.99%. Repeated training, learned-decoder controls and paired visualizations establish the benefits and limitations of combining geometric and semantic evidence for interaction understanding. Correspondence: Xingyi Yang (xingyi.yang@polyu.edu.hk) Author email: Hanyang Kong (hanyang.k@u.nus.edu) Date: September 9, 2026 Keywords: 3D interaction understanding, part-handle coupling, part segmentation, motion estimation Project Page: https://hyokong.github.io/segment-snap-page/ axis hinge (a) RGB input static indoor scan (b) Parts + motion Part predictor + fixed geometric decoder (c) Handles Dense + joint part-handle predictors Measured RGB scan One scene, coupled predictions Masks + classes + motion Fixed geometric decoder Dense handles Extra joint handles +5.01 p handle AP Dense + joint handles dense unchanged; joint children corrected Motion ← handles +27.25 p motion AP Parts → handles +0.98 p handle AP Refine joint handle classes Figure 1. Coupled part and handle understanding. From a static RGB scene (a), we recover movable parts and their motion (b) together with handles (c). Handles guide motion (orange arrow): handle locations select the opposite hinge side, improving motion AP by 27.25 points. Parts refine handles (teal arrow): part motion classes correct the joint predictor’s handle labels, improving handle AP by 0.98 points with part-only context. The joint predictor also uses its own internal part features to propose extra handles (blue, +5.01 points). Full class correction additionally consults dense-handle labels, gaining 1.34 points instead of 0.98. Only the added handles’ classes change; dense detections remain unchanged. Each transfer runs once, with no feedback from final handles to motion. Gains are validation-wide (Table 2); the dashed door indicates rotation. 1 arXiv:2609.25247v1 [cs.CV] 21 Sep 2026 Coupled Part-Handle ReasoningTechnical Report 1 Introduction Understanding a 3D scene for interaction requires more than recognizing its objects. For a cabinet, we need to identify which surfaces are movable, where they can be operated, and how they move: does a panel rotate about a hinge or translate like a drawer? Recent benchmarks formulate these questions as the prediction of movable parts, their motion parameters, and small interactable regions from static scene observations [3,5]. We call these interactable regions handles, including annotated operating regions that need not have a conventional handle shape. Our goal is to recover this interaction structure from an RGB point cloud, without observing motion or executing an action. Two ambiguities make this task difficult. The first concerns scale and context: a door occupies a broad surface, whereas its handle may contain only a few observed points. Grouping points into large regions helps delineate the door but can absorb its handle into the surrounding surface. Conversely, a small handle crop may reveal where to interact without revealing whether the associated part rotates or translates. The second ambiguity concerns motion geometry. Even a well-segmented, closed door may be compatible with a hinge on either side. Its surface constrains the possible motion but does not, by itself, identify the attachment side. Better part masks alone therefore need not yield better motion estimates, just as accurate handle locations alone do not determine their motion class. Existing methods address these issues through different forms of scene representation. USDNet jointly predicts movable parts, interactable regions and motion, combining part-instance features with dense pointwise motion predictions [5]. However, its motion decoder does not explicitly use the detected handle locations to choose a hinge. Functional scene graphs represent which interactive element controls which object [15], but this semantic association does not specify a metric motion axis or origin. Object- reconstruction methods infer articulation from completed geometry and geometric rules [7,16], under different input and reconstruction assumptions. We investigate a complementary route: using the predicted relationship between movable parts and handles to resolve ambiguities in both outputs. Movable parts and handles are physically linked: a handle is attached to a part and moves with it. On many upright doors, the handle lies away from the hinge, so its position can distinguish two otherwise plausible attachment sides. In the other direction, the surrounding part gives meaning to the handle: a region on a hinged door is associated with rotation, whereas one on a drawer is associated with translation. The full part also offers a larger visual context from which to predict its small operating region. These observations motivate two distinct uses of the relationship: handle locations guide part motion, while part features and motion classes guide handle prediction. We introduce Segment–Snap, with three independently trained predictors that receive the same scene point cloud (Figures 1 and 2). The part predictor segments movable surfaces and classifies each as rotating or translating; it supplies the final parts, but does not estimate their axes or hinge locations. The dense handle predictor classifies individual points and groups foreground points into handle instances, providing an initial set of handles. The joint part-handle predictor offers a complementary way to find handles: it detects its own parts, then uses each part’s feature to predict an associated handle mask. Its parts serve as internal context; only its handle predictions enter the final outputs. The two handle sources thus localize operating regions in complementary ways: directly from pointwise predictions or conditioned on a predicted parent part. We combine these predictions to recover a joint description of interaction. For part motion, the part predictor supplies surface geometry and a rotation/translation class, while the dense handle predictor supplies handle locations. A fixed geometric decoder fits the part surface, constructs candidate hinge lines under an upright-door prior, and uses a nearby handle to choose the opposite attachment side. For a translating part, the fitted surface’s thin direction supplies the motion axis. This is why motion decoding is training-free: axes and origins are computed from predicted masks and geometric rules, not produced by a trained motion-regression head. For handle detection, we retain the dense detections and add the joint predictor’s handles. Each added handle initially inherits its joint-model parent’s rotation/translation class. A confident containing part from the separate part predictor can correct this label, with dense-handle labels providing a fallback (Section 4.5). This changes only the added handles’ classes, leaving their masks and scores, and all dense detections, unchanged. Final parts therefore come from the part predictor and geometric decoder; final handles combine both handle sources. These handles are not fed back into motion decoding. On Articulate3D’s public validation split, handle-guided hinge selection raises motion-gated AP from 2 Coupled Part-Handle ReasoningTechnical Report 13.74 to 40.98 (+27.25 percentage points) while keeping part masks, scores, classes and axes fixed. Adding the part-associated handle candidates raises handle AP from 24.63 to 29.65. Correcting their classes using parts alone adds 0.98 points; the full rule, including the dense-handle fallback, reaches 30.99. Repeated training runs support the hinge-guidance and added-proposal gains, while showing greater variability in the benefit of class correction. Fixed-input ablations, learned alternatives and qualitative comparisons examine when each source of evidence is useful for the joint scene description. Our contributions are: 1. A part-handle coupling strategy for 3D interaction understanding: handle locations help recover part motion, while part-associated predictions and part motion classes improve handle detection. 2.A geometric motion decoder that combines predicted part support, explicit axis priors and handle-guided hinge selection, without training a motion regressor. 3. A controlled study of both information transfers, with fixed-input ablations, learned-decoder compar- isons, repeated training runs and qualitative failure analysis that establish where the coupling helps and where its assumptions break down. 2 Related work Interaction-oriented scene understanding. SceneFun3D studies fine-grained functional elements, affor- dance grounding and motion estimation in real scenes [3]. Articulate3D extends interaction-oriented annotation to ScanNet++ reconstructions, including movable and interactable parts and motion param- eters [5,13]. Its USDNet baseline extends query-based instance segmentation [11] with dense motion prediction. Our work shares the goal of recovering these outputs, but changes how evidence reaches the motion decoder: predicted handle instances explicitly determine hinge selection. SceneFun3D uses ARK- itScenes assets and a different annotation domain; its results are not interchangeable with Articulate3D validation scores. Articulation from geometry and reconstruction. Real2Code reconstructs and completes articulated-object parts from multiview observations, then generates executable joint code from geometric representations [16]. S2O augments static container meshes with openable parts, articulation and interior geometry [7]. Its released door operator already uses box edges opposite a geometry-derived handle proxy [9]. We build on the same physical intuition, rather than claiming the opposite-handle primitive as new: the distinctive input here is an independently detected scene handle, and the reverse part-to-handle transfer is part of the same inference system. REACT3D addresses the broader scene-to-simulation problem, combining perception, articulation recovery and completion [6]. These systems motivate geometric structure, but their reconstruction requirements differ from our fixed-scan prediction setting. Our learned-decoder experiments isolate an internal design choice on frozen features; they are not end-to-end comparisons against these pipelines. Instance scale and functional relations. Mask3D and SPFormer provide query-based instance grouping, with SPFormer decoding over superpoint features [11,12]. We retain this structure for broad movable surfaces and use dense point/voxel support for small interaction regions. This is a scale-specific use of existing representations, not a new backbone. OpenFunGraph predicts directed functional relations between interactive elements and objects from posed RGB-D observations [15]. Its graph makes the interaction relation explicit at a semantic level; our relation additionally determines a metric hinge and transfers a part’s motion class to a handle. Metric articulation could complement such graphs as input to downstream reasoning and interaction systems, although we do not evaluate that integration here. 3 Problem formulation We study interaction understanding in 3D scenes: recovering what can move, how it moves, and where it can be operated from a static observation. Given an RGB point cloudX=(x i , c i , n i ) N i=1 , with position, color and normal at every point, we seek a joint description of movable parts, their motion and their handles. These are related components of one scene-understanding task. A movable-part prediction comprises an instance mask, confidence, rotation/translation class, unit motion axis ˆ aand representative origin ˆ o. A handle prediction comprises an instance mask, confidence and the motion class of the associated part. Here a handle means the local region through which a part is operated, not necessarily a conventional mechanical handle. A rotational axis and origin specify a hinge 3 Coupled Part-Handle ReasoningTechnical Report line; the origin is a representative point on that line, not a unique physical pivot. Translation is described by its direction. The outputs characterize possible interaction from observation; they do not include an executed action, a motion trajectory or a completed simulation asset. The part-handle relationship supplies information in both directions. A handle’s position can disambiguate a part’s motion geometry, while the part’s extent and motion class provide context for locating and interpreting a handle. Our method uses these complementary cues within the joint prediction problem. Dataset-specific annotation and scoring conventions are introduced with the experimental protocol in Section 5.1. 4 Method Segment–Snap recovers interaction structure by exchanging explicit geometric and semantic evidence between movable parts and handles. We first define the prediction interface, then describe part and handle perception, handle-guided motion decoding, and the reverse transfer to handle proposals and labels. Figure 2 illustrates the operations on concrete scene geometry. 4.1 Prediction interface and information flow Our pipeline first predicts movable parts and handles from the scene, then combines their geometric and semantic evidence using fixed rules (Figure 2). Three independently trained networks take the same point cloud X from Section 3: f part (X) =P, f dense (X) =H d , f joint (X) = (Q,H c ).(1) Standalone part and handle predictions. The part predictor returnsP=(M i ,s i ,y i ), whereM i is a movable-part mask,s i its confidence, andy i ∈rot, transits motion class. These predictions supply all final movable-part instances. The dense handle predictor groups pointwise labels into handle instances H d =(H d k ,s d k ,y d k ). Their locations guide motion decoding, and their masks, scores and classes are retained in the final handle output. Joint part-handle predictions. The joint part-handle predictor provides a complementary source of handles by modelling them together with their supporting parts. It processes the scene independently and decodes its own movable partsQand associated handlesH c from shared features. The part predictions determine which handle candidates are retained and provide their initial motion labels. These parts remain internal to the joint model; the standalone part predictor supplies the final movable-part instances. The additional handles complement the dense detections, with their labels subsequently refined using standalone part context. Section 4.4 describes the architecture, training and candidate selection. Preparing part geometry and confidence. Before coupling, we identify the largest spatially connected componentS i ⊆ M i for geometric fitting and recalibrates i to ̄s i using the mask’s connectivity (Section 4.3 and Equation (4)). The fitting subset limits the influence of stray points; the confidence adjustment downweights fragmented predictions. Neither operation replaces the output maskM i or changes its class y i . We collect these quantities asP =(M i ,S i , ̄s i ,y i ). These deterministic operations prepare the part geometry and confidence for the reasoning stage in Figure 2. Final part motion and handle instances. The training-free decoderDfits geometry toS i using the coordinates inX, applies the motion-class axis prior, and uses dense-handle locations to select a rotational hinge line (Section 4.3). It augments each prepared part with an axis ˆ a i and origin ˆ o i : M = D(X,P,H d ) =(M i , ̄s i ,y i , ˆ a i , ˆ o i ).(2) The final part records therefore retain the original masks and classes, use calibrated scores, and add geometric motion parameters. The fitting subsetsS i are internal; they are not substituted for the output masks. For handles, a separate fixed ruleCcorrects only the joint children’s motion classes. It consults the masks, calibrated confidence and classes inP, with dense-handle labels as a fallback (Section 4.5); it does not use S i or the decoded axes and origins. Writing e H c for these class-corrected children, the final handle set is e H c = C(H c ; P,H d ), H =H d ∪ e H c .(3) 4 Coupled Part-Handle ReasoningTechnical Report hingehandle INPUTINDEPENDENT PREDICTORSTRAINING-FREE REASONINGOUTPUTS Scene point cloud RGB + normals Same input to all three models Part predictor Dense handle predictor Joint part-handle predictor Part masks + motion classes final part instances Point labels → handle instances dense detections feature internal partsextra handles part context location dense detections retained label fallback children Motion decoder Training-free · physical priors choose opposite side Final parts mask · class axis · origin Child-class correction e.g. rotation → translation mask + score unchanged Final handles dense child One pass per transfer No feedback from final handles + Figure 2. From scene perception to coupled interaction understanding. The same RGB point cloud and normals feed three independently trained predictors. The part predictor produces movable-part masks and rotation/translation classes; the dense handle predictor groups pointwise labels into handle instances. Their outputs enter a training-free motion decoder: it fits the part surface and applies physical priors, using an upright axis and the hinge line farthest from a nearby handle for rotation, or the fitted surface’s thin direction for translation. No motion-regression head is trained. The top view illustrates handle-guided hinge selection; purple marks the final axis and origin. In parallel, the joint part-handle predictor uses its own internal part features to propose extra handles. The standalone part predictions provide class context (teal), complemented by dense-label fallback (dashed orange), to correct only these added handles’ rotation/translation classes; their masks and scores stay fixed. Corrected children are concatenated with unchanged dense detections (+). Each information transfer is applied once; final handles do not feed back into motion decoding. Correction leaves child masks and scores fixed, and the union concatenates detections rather than merging masks. Dense detections remain unchanged throughout. These equations distinguish the two information transfers: handle locations guide hinge placement, whereas part context refines handle classes. Each transfer is applied once. The final handle setHis not fed back intoD, and changing a decoded hinge alone cannot change handle labels. A second motion pass is evaluated only as a separate variant in Section 5. 4.2 Part and handle perception All three components use a Volt-B voxel Transformer initialized from ScanNet++ pretraining [14]. Input features comprise measured RGB and surface normals on a 2 cm voxel grid, with 5×5×5 voxel patches. Coordinates preserve the scene’s upright reference frame for downstream motion decoding. We choose the prediction support according to the target scale: superpoint grouping for broad movable surfaces and fine point/voxel fields for small interaction regions. Movable-part instances. A SPFormer decoder attends to features pooled over graph-partitioned super- points [4,12]. Its 200 queries predict instance masks, rotation/translation classes and confidence. Parent supervision uses Hungarian assignment with classification, mask binary cross-entropy (BCE), Dice and score terms. At inference each standalone query emits its highest-scoring class, followed by the predictor’s instance filtering. This per-query selection avoids treating two class hypotheses from one query as two distinct parts. It is held fixed in motion-decoder comparisons, since changing query selection changes the mask set. Dense handle instances. A separate network predicts pointwise probabilities for background, rotation handles and translation handles. Class-weighted cross-entropy, label smoothing and multiclass Lovász loss supervise this field [2]. We assign each point its maximum-probability class and form class-wise connected components on a radius graph with radius 2.5 cm. Components with at least three points become instances; their confidence is the mean probability of the assigned class over the component. This path does not pool handle targets by superpoint majority, and its small component threshold preserves tiny candidates. The resulting detections are both the initial handle output and the spatial evidence supplied to D. 5 Coupled Part-Handle ReasoningTechnical Report 4.3 Handles to parts: geometric motion decoding A static planar surface constrains motion without uniquely determining it. We separate this problem into support estimation, an axis prior, and handle-guided selection of a hinge line. The decoder is training-free; the masks and handle locations on which it operates are learned predictions. Stable geometric support. For a predicted maskM i , we retain its largest connected component under a 5 cm radius graph as supportS i . The originalM i remains the output mask. From the support covariance we obtain a PCA plane normal, project the points into that plane, and fit a minimum-area rectangle over their convex hull. The resulting box has orthonormal directionsb 1 , b 2 , b 3 , ordered by decreasing extent ℓ 1 ≥ ℓ 2 ≥ ℓ 3 , and reference centrec i , the support-point mean. This is a planar rectangle fit, not a general minimum-volume box. Support cleanup and confidence calibration are distinct. We use the same connected component to rescale confidence, ̄s i = s i |S i | |M i | γ , γ = 1,(4) which downweights fragmented predictions without changing their extent. Cleanup affects the fitted geometry; rescoring affects ranking. Their separate and combined effects are measured in the component controls. Motion-axis prior. The axis depends on the predicted motion class: ˆ a i = ( e z , y i = rot, b 3 , y i = trans. (5) Rotational axes therefore use a constant world-vertical prior, appropriate to many upright doors. Transla- tion axes use the fitted thinnest direction, appropriate to drawers moving approximately normal to their front. In particular, the rotational axis is not selected from the box and is not learned. Horizontal hinges and tilted mechanisms are limitations of this prior, rather than cases resolved by the handle cue. Associating a handle. For every dense handle instance, leth k be its point centroid. We choose the centroid nearest the part’s geometric support: k ∗ = arg min k min j∈S i ∥h k − x j ∥ 2 .(6) The association is accepted only if this distance is below 0.5 m. It uses the handle’s location, not its motion label. Thus the handle model’s classification quality and its utility as a hinge cue need not vary together. If no handle passes the gate, the origin falls back to c i . Selecting the hinge side. For a rotational part with an associated handle, identify the box direction most parallel to ˆ a i . Letu,vindex the other two box directions. Four anchors define axis-parallel candidate lines: b στ = c i + σℓ u 2 b u + τℓ v 2 b v , L στ =b στ + t ˆ a i : t∈ R, σ,τ ∈−1, 1.(7) These are box-derived lines, not necessarily literal box edges when the vertical axis and the box orientation differ. For a thin door, the four lines form two physical sides, with a front/back pair on each side. The handle primarily disambiguates these attachment sides. WritingQ i =I− ˆ a i ˆ a T i for perpendicular projection, we select the candidate farthest from the handle and project the support centroid onto that line: L ∗ = arg max L στ ∥Q i (h k ∗ − b στ )∥ 2 , ˆ o i = b ∗ + ˆ a i ˆ a T i (c i − b ∗ ).(8) Hereb ∗ is the selected anchor. The origin is a representative point on a hinge line; it is not claimed to be a unique physical pivot. Translation origins are emitted as the support centroid but are not scored by the motion-origin metric. Opposite-handle geometric reasoning has precedent in S2O [7,9]; its role here is to transfer independently predicted scene-handle evidence into the part’s metric motion estimate. 4.4 Parts to handles: complementary proposals Dense localization and part-associated prediction expose different failure modes. The dense path identifies foreground locally, while a part query represents a larger movable surface to which a small interaction region belongs. We retain both proposal sources and evaluate their complementarity, rather than assuming one representation subsumes the other. 6 Coupled Part-Handle ReasoningTechnical Report Parent-associated child masks. The joint model attaches a voxel-level child head to each parent query. For query q j and voxel feature f v , learned projections g q ,g v produce p jv = σ g q (q j ) T g v (f v ) .(9) The query carries parent context while the voxel field preserves fine spatial support. Parent-only Hungarian assignment associates a predicted query with its ground-truth movable instance; the child term does not change that assignment. A child’s target consists of interactable points belonging to the assigned parent. Boolean max pooling marks a voxel positive if it contains any target child point, avoiding the disappearance of a small target under majority pooling. For each matched query, the child loss is L child =L BCE +L Dice + 2L Tv , L Tv = 1− TP + ε TP + 0.7 FP + 0.3 FN + ε ,(10) where TP, FP and FN are soft sums computed fromp jv and the binary target [10]. The larger false-positive weight penalizes spreading a small handle mask over its parent. This is a design motivation; the separate loss contribution is not inferred from the union gain. Selection, association and union. The joint parent decoder uses its own top-kclass-query selection and non-maximum suppression. For each retained parent we retrieve the child field by the originating query index, preserving that identity through reordering. The child mask contains all points whose voxel probability exceeds 0.30; it is neither split into connected components nor clipped to the predicted parent. This keeps an imperfect parent boundary from truncating a localized child. Its initial class and confidence come from that parent, with confidence scaled by 0.05 before concatenation with dense detections. The dense masks, labels and scores are retained unchanged. In the reference outputs, appended children also rank below every dense incumbent globally within each class; the matching and ranking-prefix checks are reported in Section 5. This is a verified property of those outputs, not a general monotonic-AP guarantee for arbitrary appended proposals. The matched unconditioned experiment separately tests whether query conditioning, as opposed to the additional source and its association, explains the gain. 4.5 Parts to handles: contextual motion labels The child inherits a motion class from its own joint-model parent, but another part prediction may provide better evidence. For a child mask H and a candidate containing mask A, define r(H,A) = |H ∩ A| |H| .(11) Among standalone part predictions withr(H,M i )≥0.9 and ̄s i ≥0.3, select the highest-confidence part and denote its class byy P . If it differs from the child’s initial labely 0 , adopt it. Otherwise—including when no qualifying part exists—the dense incumbent with greatest containment supplies a fallback label y D if its containment is at least 0.9. With ∅ denoting an unavailable label, ̃y(H) = y P , y P ̸= ∅ and y P ̸= y 0 , y D , y D ̸= ∅, y 0 , otherwise. (12) The second case is reached only when the first does not apply: agreement with a part can still permit an incumbent override. The fallback uses the original dense incumbents, not previously corrected children. This operation changes only child labels. It does not move a handle, alter its confidence, or correct a dense detection. The part-based case assigns the child’s motion class from a confident containing part. Parts-only and dense-only ablations distinguish this part-to-handle transfer from the handle-based fallback; their improvements are overlapping effects, not additive shares of the full rule. 4.6 Training and inference protocol The three perception components are optimized independently with AdamW [8]; joint parent-child supervision occurs only within the third component. All use a 400-epoch schedule, peak learning rate 3×10 −4 , cosine one-cycle scheduling, a batch of two with eight-step gradient accumulation, and exponential- moving-average weights with decay 0.999. Weight decay is 0.1 for the part and joint models and 0.05 for 7 Coupled Part-Handle ReasoningTechnical Report dense handles. Training uses spatial crops, rotations, scaling and color augmentation; the dense model additionally uses flips, jitter and elastic distortion. For dense-handle training, foreground targets are dilated by 0.10 m during the first half of training, 0.04 m during the next 30%, and zero during the final 20%. This schedule specifies the training targets; inference uses the pointwise predictions described above. The reference part predictor is selected by validation motion-gated AP at 70% of its schedule. The dense branch uses its segmentation-selected checkpoint, while the joint child branch uses its final weights. These are different selection rules, not three instances of the same metric-based choice. Validation-based model and hyperparameter selection is disclosed in Section 5. No motion-regression loss trains the geometric decoder. At inference, we compute standalone parts, dense handles and joint-model children, construct stable part supports, then evaluate the two outputs in Equations (2) and (3). Handles guide part motion once, and part context guides child labels once. The final handle set is an output, not a new decoder input. These explicit boundaries let the ablations change one information source while preserving the other predictions. 5 Experiments We evaluate three questions: can predicted handles resolve part motion, can part-associated proposals recover additional handles, and can part semantics improve their motion labels? We then examine the fixed geometric decoder, training variability and the failure modes of the resulting interaction description. 5.1 Dataset and evaluation protocol We use Articulate3D [5], whose annotations cover movable parts, motion parameters and interactable regions. All perception models are trained on its 195 training scenes, and all component studies use the 42 public validation scenes. These are development-set comparisons: model and hyperparameter choices have consulted validation data, and the results are not an untouched generalization estimate. Test annotations are withheld; only final public leaderboard metrics are reported for that split. Metrics. For movable-part and handle instances, we report macro-averagedAP 50 over rotation and translation, with IoU greater than 0.5 required for an instance match. For movable parts, we additionally use motion-gated average precision. A full motion match must satisfy the mask criterion and a sign- invariant axis error below 15 ◦ . For rotations, the displacement between the predicted and annotated representative origins must also be below 0.25 m when projected perpendicular to each of the predicted and annotated axes. Translation origins are not evaluated. We denote mask AP byAP 50 , axis-gated AP by AP A 50 , the origin-only diagnostic by AP O 50 , and jointly gated AP by AP AO 50 . The latter corresponds to the benchmark’s MAO-ST score; its rotational origin check uses both axes, unlike the one-sided origin-only diagnostic. Scores are percentages; differences are reported in percentage points (p) and computed before rounding displayed scores. Because the translation-origin clause is omitted, the primary motion score decomposes as AP AO 50 = 1 2 AP AO 50,rot + AP A 50,trans .(13) An origin-only intervention therefore changes only the rotation term. We retain the macro score for the benchmark comparison and report the class breakdown to show which population benefits. Where available, class-specific intervals are computed separately; uncertainty estimated for the macro score is not transferred to a class-specific claim. For the published-number comparison only, we additionally report the evaluator’s Euclidean-origin variant, which thresholds the full displacement between representative origins instead of perpendicular line distances and also applies an origin check to translations. It is not interchangeable withAP AO 50 . Reporting both conventions avoids assigning an unspecified implementation to a published baseline; all internal motion comparisons use the line-distance convention above. Uncertainty notation. Brackets [L,U] give the lower and upper bounds of an approximate 95% confidence interval for the stated difference in AP, in percentage points. We use a paired scene jackknife: omit one validation scene at a time and recompute both configurations on the same remaining scenes. The interval is the full-validation difference plus or minus 1.96 jackknife standard errors, not the minimum and maximum omitted-scene results. An interval entirely above zero supports a positive change under 8 Coupled Part-Handle ReasoningTechnical Report this analysis; an interval containing zero leaves its sign unresolved, rather than demonstrating no effect. Model predictions are fixed, so these intervals describe scene-sampling variability, not retraining variability. Training-seed ranges are reported separately as descriptive statistics. 5.2 Reference results Table 1. Published benchmark results and our validation reference. USDNet values are transcribed from Tables 2–4 of Halacheva et al.[5]; our values use the public challenge validation split. Both evaluations contain 42 Articulate3D scenes, but their scene-list identity has not been verified. This is a contextual comparison, not a matched-system experiment. All scores are percentages. MethodMovable partsHandles AP 50 +Axis † +Origin † Joint motion † AP 50 USDNet (published)41.834.631.425.031.1 Ours (public validation)47.9343.7543.1138.99 / 40.9830.99 †Gated columns retain each source’s reported convention; equivalent origin-diagnostic implementations are not verified. The published protocol specifies IoU>0.5, a 15 ◦ axis threshold and a 0.25 m origin threshold, but does not disambiguate the evaluator’s two joint-origin implementations. For ours, the joint entries report Euclidean-origin AP (38.99) and the line-distance MAO-ST convention used throughout our ablations (40.98), respectively. Training resources and complete split equivalence are not controlled. Handle AP is numerically similar (31.1 versus 30.99); the challenge test score is not substituted for our validation result. The reference configuration combines the three independently trained predictors with geometric motion decoding and contextual child labels. It achieves 47.93 movable-part AP, 40.98 motion-gated AP and 30.99 handle AP on public validation (Table 1). Its published-number comparison with USDNet provides benchmark context: part scores are numerically higher and handle AP is similar, but the scene-list identity, training resources and complete evaluator implementations are not matched. The following controlled comparisons establish which information transfers improve our own system. 5.3 Contributions of part-handle coupling Table 2. Three measured mechanisms in coupled part-handle inference. All results use the public validation split. The mechanisms act once in an acyclic graph and address different outputs; their gains must not be added. Scores and parenthesized differences are percentages and percentage points, respectively. Differences are computed before rounding the displayed endpoints. DirectionMeasured interventionMetricResult Handles→partsDense handle selects a box-derived hinge lineAP AO 50 13.74→ 40.98 (+27.25) Parts→handlesAppend query-associated child proposals to dense handles AP 50 24.63→ 29.65 (+5.01) Parts→handlesPart context only for child labelsAP 50 29.65→ 30.63 (+0.98) Parts + dense→handles Reference contextual rule for child labelsAP 50 29.65→ 30.99 (+1.34) The first row fixes movable masks, classes, scores, and axes. The child-union gain is evidence for a complementary proposal source, not a causal estimate of parent conditioning: the matched conditioning control is reported separately (Table 15). The parts-only and full-vote gains overlap, so the +0.98 is not an additive “share” of +1.34. Dense incumbents are never relabelled. 9 Coupled Part-Handle ReasoningTechnical Report Table 3. Per-class localization of the directed effects. The evaluator macro-averages rotation and translation classes. Absolute rows are scores (%); difference rows are p. Each bracket gives the lower and upper bounds of the paired 95% scene-jackknife confidence interval (CI) for the difference immediately above it, in the same class or macro column. Interval endpoints are p, not absolute AP scores. Configuration or differenceRotationTranslationMacro Part-motion centroid origin1.8825.5913.74 Part-motion dense-handle origin56.3725.5940.98 Dense-handle minus centroid+54.49+0.00+27.25 95% paired CI[+43.71, +65.27][0.00, 0.00] [+21.86, +32.63] Handle child union48.5610.7429.65 Handle contextual vote48.5413.4530.99 Vote minus union−0.02+2.71+1.34 95% paired CI[−0.15, +0.10] [+0.80, +4.62][+0.37, +2.31] Origin is not evaluated for translations, so the handle-origin change acts only on rotations; the zero translation interval reflects identical outputs in every paired scene omission. Conversely, the contextual vote’s macro improvement is concentrated on translation handles. The class-resolved intervals describe these populations and do not substitute for a generalization claim beyond this split. Handle locations resolve hinge ambiguity. Fixing part masks, classes, scores and axes isolates the origin rule. Replacing the centroid origin with a handle-guided hinge raisesAP AO 50 from 13.74 to 40.98, a 27.25-p gain (Tables 2 and 16). Mask AP and axis-gated AP remain unchanged. The class breakdown in Table 3 places this gain on rotational parts, whose motion AP rises from 1.88 to 56.37. Translation scores are unchanged because their origins are not evaluated. Parts supply complementary handles and motion context. Appending query-associated children raises handle AP from 24.63 to 29.65. Holding the resulting masks and scores fixed, parts-only class correction adds 0.98 p; the full rule with dense-handle fallback adds 1.34 p (Table 2). The two label gains overlap and must not be summed. The class-resolved result shows a +2.71-p translation-handle gain with a positive paired interval, while the−0.02-p rotation-handle change is unresolved (Table 3). Thus, the net label benefit is concentrated on translation handles, although the rule can relabel either class. Two directed transfers in one inference pass. Table 14 enables handle guidance and contextual labels separately and together, with the child union fixed. Each retains its own benefit when both are enabled: handles change part origins, whereas parts change child classes. These distinct outputs yield zero interaction in this control, consistent with the acyclic one-pass dependency structure. 10 Coupled Part-Handle ReasoningTechnical Report 5.4 Training-free motion decoding Table 4. Matched learned motion decoders on frozen part inputs. Learned rows report minimum–maximumAP AO 50 scores (%) over three training seeds and receive the same predicted handle evidence when marked. All rows retain AP 50 = 47.93 because masks are fixed. The bracket in the note gives lower and upper bounds of a paired 95% scene-jackknife confidence interval for the closest learned head minus the rule (p); it is distinct from the three-seed score ranges. Motion decoderHandle cueAP AO 50 (three-seed range) Reference training-free rule✓40.98 Box-axis rule with recomputed origin✓41.20 Continuous regression–17.24–18.24 Continuous regression✓29.61–31.30 Learned candidate selection–25.38–28.32 Learned candidate selection✓37.27–38.63 Learned selection, box axes only–25.07–27.84 Learned selection, box axes only✓37.11–38.78 Rule axis + learned edge–25.36–28.75 Rule axis + learned edge✓37.69–39.36 These heads consume frozen query features and geometry, not jointly trained backbones. Discrete learned selection exceeds continuous regression with identical handle evidence, but neither establishes an improvement over the training-free rule. The box-axis variant changes the axis and recomputes the origin; it is not an axis-only control. The closest learned row has paired jackknife 95% interval [−4.31, +1.05] p relative to the rule. The decoder combines a world-Zrotational-axis prior, a thin-box translation direction and handle-guided hinge selection. On frozen part inputs, discrete learned selection has higher point estimates than continuous regression at the same handle-cue availability (Table 4). The training-free rule reaches 40.98, compared with at most 39.36 for the displayed learned heads on the reference part model. The two-part-model comparison in Table 17 retains this ordering, but its paired intervals include zero. These results support an effective decoder without motion-regression training, not a statistically resolved or general advantage over learned motion estimation. The separate box-axis rule scores 41.20 while also recomputing origins; it is not an axis-only comparison. Table 5. Component changes measured from both ends of the part-motion pipeline. “Add gain” applies one component to the naive pipeline; “removal loss” is full decoder minus the result after removing that component. Their difference is a two-end non-additivity diagnostic, not a unique causal interaction. Values are changes in AP AO 50 (p). The final row’s bracket gives the lower and upper bounds of the paired 95% scene-jackknife confidence interval for the full-minus-naive change, also in p. ComponentAdd gainRemoval lossTwo-end difference Per-query argmax selection+0.13+0.19+0.06 Largest-C support cleanup−0.11+2.95+3.07 Dense-handle origins+23.79+27.25+3.45 Connectivity rescoring+1.49+1.60+0.11 Full versus naive pipeline+28.74 p; 95% CI [+22.12, +35.37] The naive and referenceAP AO 50 values are 12.24 and 40.98. Cleanup and handle origins leave mask AP exactly unchanged, as required by their fixed-mask implementation. Cleanup is slightly negative alone but useful in the full decoder, demonstrating non-additivity rather than a contradictory result. Table 5 measures each component both when added to the naive pipeline and when removed from the full decoder. The complete configuration improves motion AP from 12.24 to 40.98, with a paired gain interval of [+22.12,+35.37] p. Support cleanup is most useful when combined with handle-guided geometry: it changes the fitted box and candidate lines, costs 2.95 p when removed from the full decoder, but gives a −0.11-p change when added alone. This two-ended comparison shows why isolated component gains cannot simply be added. 11 Coupled Part-Handle ReasoningTechnical Report 5.5 Complementary proposals and contextual labels Table 6. Complementary handle localization. Each configuration appends a child source below the same dense-handle detections without label correction. The corrupted-mask controls preserve child count, mask size and confidence while disrupting localization. Scores are validation AP 50 percentages. Proposal sourceHandle AP 50 Dense detections only24.63 Dense + spatially permuted child masks24.63 Dense + random size-matched child masks24.63 Dense + query-associated child proposals29.65 The real child union retains all 140 GT handles matched by dense incumbents and adds 53 matches, while preserving the incumbent TP/FP ranking prefix. Its gain demonstrates complementary localization, not an isolated effect of parent conditioning; Table 15 separates conditioning from the readout used to associate children. The proposal controls in Table 6 test whether the extra source contributes localized handles rather than merely extending the ranked detection list. Spatially permuted and random size-matched children return exactly the dense-only AP. Real children preserve the dense detections’ matching prefix and recover 53 additional GT handles, increasing AP by 5.01 p. This demonstrates complementary localization. A separate conditioning/readout control in Table 15 does not isolate a reliable benefit of parent conditioning itself, so we attribute the gain to the implemented proposal source rather than conditioning alone. Table 7. Contextual child-label controls. Child masks and scores are fixed; only labels of appended children can change. Scores are validation AP 50 percentages. Label rulePart cueDense cueAP 50 ∆ No correction–29.65– Parts only✓–30.63 +0.98 Dense incumbents only–✓30.66 +1.01 Full contextual rule✓30.99+1.34 Fallback only when no part speaks✓30.99 +1.34 Part classes permuted within scenecorrupted✓28.62 −1.03 Part classes randomizedcorrupted✓28.90 −0.75 The two cues are complementary but overlap: their individual gains must not be summed. Restricting fallback changes one child and is AP-identical on this split. In the last two rows, masks and scores are frozen and only the part-class channel is corrupted; dense labels remain intact. They relabel more children than the reference rule, but lower AP below the no-correction union, so relabel count alone is not evidence of useful context. Dense incumbents themselves are never relabelled. Table 7 isolates the source of child-label evidence. Part context and dense-incumbent context each improve AP by about one point; their combination reaches 30.99. Corrupting only the part-class channel instead reduces AP below the uncorrected union, despite changing more labels. Useful semantic evidence, rather than the number of corrections, explains the benefit. The alternative fallback policy has identical AP on this split. All rows preserve child masks and scores and leave dense detections unchanged. 12 Coupled Part-Handle ReasoningTechnical Report centroid 0.42 m FAIL (i-median) 61adef · gt 1003 handle-guided origin passes, centroid fails — median centroid line error 0.42 m centroid 0.58 m FAIL (i-p90) e91722 · gt 1016 handle-guided origin passes, centroid fails — 90th percentile centroid error 0.58 m centroid 0.01 m PASS (i) 8890d0 · gt 1062 both pass — smallest centroid error 0.01 m centroid 0.86 m FAIL (i) 38d58a · gt 1019 non-vertical hinge (>15° from world-Z) — median axis error among the covered 0.86 m centroid 0.28 m FAIL (iv) 88627b · gt 1158 no handle in reach, centroid fallback fired — median origin error 0.28 m centroid 0.56 m FAIL (v) bcd243 · gt 1039 no instance has handle-guided failing where centroid passes; showing the largest handle-guided error instead 0.56 m handle-guided 0.05 m PASS 0.05 m handle-guided 0.13 m PASS 0.13 m handle-guided 0.05 m PASS 0.05 m handle-guided 0.85 m FAIL 0.85 m handle-guided 0.28 m FAIL 0.28 m handle-guided 1.13 m FAIL 1.13 m Paired hinge gallery — same masks, same view; only the origin rule changes. Black line: GT hinge. Coloured segment: the perpendicular distance the 0.25 m gate tests. Specimens by stated quantile rank within named strata (fig_select_specimens.py). Of 186 covered GT rotations: 121 where the handle rule passes and the centroid fails, 37 where both pass, 28 where both fail, and 0 where the centroid passes and the handle rule does not. Median centroid error 90th-percentile centroid error Both rules pass Non-vertical hinge Missing-handle fallback Largest handle- guided error Figure 3. Paired hinge-origin cases on validation scenes. Each column fixes the predicted part mask and camera; only the origin rule changes. Black denotes the ground-truth hinge, and the colored segment depicts the perpendicular origin error. The first two columns are centroid-error ranks 61 and 109 among 121 rotations for which handle guidance passes but the centroid fails (median and 90th percentile). The remaining selections are the smallest centroid error among 37 both-pass cases, median axis error among 12 non-vertical hinges, median origin error among 19 missing-handle fallbacks, and the largest handle-guided error among 186 covered rotations. No case has a passing centroid but failing handle-guided origin in this population; the last column retains a large residual failure instead. 5.6 Stability and geometric coverage Table 8. Observed variation of the directed effects. All values are AP changes in p. “Seed span” is the maximum minus minimum paired gain acrossntraining draws, not a confidence interval. Brackets give the lower and upper bounds of the paired 95% scene-jackknife confidence interval (CI) for the reference gain. A CI containing zero leaves the direction of change unresolved. MechanismReference gainSeed span95% scene CI Dense handles → hinge origin+27.25 2.11 (n = 4) [+21.86, +32.63] Child proposals appended to dense handles+5.01 1.08 (n = 3) [+1.47, +8.56] Contextual child-label vote+1.34 1.15 (n = 3) [+0.37, +2.31] The child family varies the part-associated child predictor with dense incumbents fixed. Its append increments are 5.01/4.89/3.94 p; its vote increments are 1.34/0.19/0.38 p. The append interval compares the reference child union against dense detections alone; the gain remains positive in every leave-one-scene-out evaluation. This supports a complementary proposal source, not an isolated conditioning effect. The three reference gains have positive paired scene intervals (Table 8). Handle guidance remains beneficial across four part-model draws. Appending children improves handle AP by 3.94–5.01 p across three child-model draws, and its reference scene interval is [+1.47,+8.56] p; the gain is positive under every single-scene omission. Contextual correction also improves all three draws, but varies more relative to its gain, from 0.19 to 1.34 p (Table 13). We therefore distinguish the reference label gain from its smaller repeated-training gains. The source-configuration comparisons in Table 11 show both transfers remain useful with weaker pre- dictors. Table 12 additionally varies the dense-handle model while fixing the other predictors: proposal augmentation and label correction improve handle AP in all four draws. These comparisons test the listed configurations, not an isolated pretraining effect or a universal relationship between detector AP and hinge quality. The candidate construction covers 94.4% of matched rotational predictions, with 88.3% correct selection among those covered (Table 18). This supports a compact physical search space for the represented mechanisms. The broader limitation is instance coverage: of 390 GT parts, 139 lack a matching mask, while 14 more fail the axis gate and another 14 fail the origin gate (Table 19). A hinge selector cannot recover an undetected part. The complete coverage analysis and population definitions are in Section A.4. 13 Coupled Part-Handle ReasoningTechnical Report (i-a) dense success, median GT handle size 2e7481 · rota · 21 pts prediction GT handle (i-b) dense success, just above the median 5eb318 · rota · 21 pts (i-a) child-only recovery, median GT size 8a20d6 · tran · 27 pts (i-b) child-only recovery, smallest GT size f8062c · rota · 7 pts (i) over-extended dense prediction, largest size ratio 565409 · rota · 15 pts · 2× GT (iv) child relabelled by a containing part — median size among those with a GT match 1ae9e5 · rota · 28 pts translation → rotation (v) relabelled child matching NO GT — the caveat, median size among them bcd243 · rota · 21 pts translation → rotation Complementarity — black: GT handle, coloured: the prediction that matches it (red where the dense prediction is over-extended) Specimens by stated quantile rank within named strata. Of 388 GT handles the dense model matches 141 at IoU > 0.5 and the union 196; 55 are recovered only by the union, 55 of them by an appended child. Panels (iv) and (v) are the class vote: it fixes 453 children the evaluator can score and relabels 432 it cannot — both are shown. Dense success median size Dense success above median Child-only median size Child-only smallest size Over-extended dense mask Contextual label update Unmatched relabeled child Figure 4. Dense and child handle complementarity on validation scenes. The selected strata show dense successes, handles recovered only after appending child proposals, an over-extended dense prediction, and contextual child- label updates. The final panel is deliberately a relabeled child without an IoU>0.5 ground-truth match, making explicit that label accuracy is only directly assessable for the matched subset. Specimens are deterministic quantile selections within their stated strata. 5.7 Qualitative comparisons Figure 3 holds each predicted mask and camera fixed while comparing origins. The paired successes show how handle location resolves the hinge side; the non-vertical-axis, missing-handle and residual-error cases expose the decoder’s physical limits. Figure 4 shows complementary child detections and contextual label changes. Its over-extended mask and unmatched relabelled child illustrate why correct class context cannot repair poor localization. Additional galleries in Section B connect component ablations to changed geometric support, compare weaker prediction sources and illustrate the failure census. Cases are selected deterministically within stated strata; they explain the mechanisms rather than estimate their frequency. 5.8 Public test-set results Our Articulate3D challenge submission (team TnG) achieved the highest published scores for movable-part motion and handle detection: 48.28%AP AO 50 and 34.46%AP 50 , respectively. Tables 9 and 10 reproduce every public team entry and every metric exposed by the official board as accessed on September 6, 2026. These are challenge standings, not matched-resource comparisons. Test annotations are not public; all component studies above use public validation. Table 9. Challenge leaderboard: movable-part motion result. All 11 public team entries and all four published metrics. Scores are percentages; ranking is by AP AO 50 . RankTeamAP 50 AP A 50 AP O 50 AP AO 50 1TnG (ours)55.3852.3449.7648.28 2 coreMany46.6843.1543.2840.56 3 teamzb47.2044.9938.5537.11 4 core44.4441.0539.5536.89 5 Z47.7244.8137.7735.72 6 linxii43.5241.3535.4733.60 7 coreN43.7040.6035.9433.38 8 ZeroR39.5337.2530.1428.61 9 wwwjh43.6637.9831.5426.34 10 ShinNam!35.5233.7329.0424.67 11 t30.5828.3825.9924.00 Source: official Articulate3D leaderboard [1], accessed September 6, 2026. Superscripts A, O, and AO denote axis, origin, and joint motion checks, respectively. 14 Coupled Part-Handle ReasoningTechnical Report Table 10. Challenge leaderboard: handle-detection result. All eight public team entries. The board providesAP 50 only; scores are percentages. RankTeamAP 50 1TnG (ours)34.46 2coreMany32.86 3core32.60 4teamzb31.10 5Z30.69 6coreN28.86 7ZeroR25.71 8moon24.80 Same source and access date as Table 9. The public movable-part-motion and handle-detection boards contain different participant sets. 6 Discussion and limitations What coupling contributes. Handles and parts provide different forms of evidence: handle locations constrain a part’s attachment side, while part-associated proposals and motion classes improve handle detection and interpretation. The fixed-input and label-source controls separate these roles (Tables 7 and 16). No iterative refinement is required because the two directions read and update different attributes. Within the geometric decoder, however, support estimation and origin selection remain interdependent, as the two-ended component ablation shows (Table 5). Physical and perceptual limits. The decoder assumes approximately planar parts and upright rotational axes. Horizontal hinges, tilted or curved mechanisms, missing handles and fragmented support can violate these assumptions; proximity-based association can also select a neighboring handle (Figures 3 and 10). High hinge-candidate coverage does not resolve missing instances or incorrect motion classes. The coverage and failure census instead motivate better part detection and more general axis hypotheses alongside improved hinge selection (Tables 18 and 19). Scope of the measured benefits. The proposal gain demonstrates complementary localization, not a separately established advantage of parent conditioning (Table 15). Label correction improves the reference configuration, but its magnitude changes across child-training draws (Table 13). Likewise, the frozen-feature decoder comparisons support the effectiveness of training-free geometry in this setting, without ruling out stronger jointly learned representations (Table 17). These distinctions define which aspects of the method are supported by the present controls. 7 Conclusion We presented Segment–Snap for recovering movable parts, motion and handles as a joint description of interaction in static 3D scenes. Predicted handles guide training-free hinge selection; part-associated proposals expand handle coverage, and part context refines their motion labels. Fixed-input comparisons, repeated training and paired visualizations demonstrate the value of these directed information transfers. The results support geometric and semantic coupling as a useful strategy for 3D interaction understanding, with further progress requiring better instance coverage and motion models beyond upright planar mechanisms. References [1]Articulate3D Organizers. Articulate3D Challenge Public Leaderboard, 2026. URL https://art3d-challenge.m o.com/web/challenges/challenge-page/1/leaderboard/. Accessed September 6, 2026; public test standings and metric columns. 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Volume transformer: Revisiting vanilla transformers for 3d scene understanding. In European Conference on Computer Vision, 2026. URL https://github.com/YilmazKadir/Volt. [15]Chenyangguang Zhang, Alexandros Delitzas, Fangjinhua Wang, Ruida Zhang, Xiangyang Ji, Marc Pollefeys, and Francis Engelmann. Open-vocabulary functional 3d scene graphs for real-world indoor spaces. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, 2025. URL https: //arxiv.org/abs/2503.19199. [16]Mandi Zhao, Yijia Weng, Dominik Bauer, and Shuran Song. Real2Code: Reconstruct articulated objects via code generation. In International Conference on Learning Representations, 2025. URL https://openreview.n et/forum?id=CAssIgPN4I. 16 Coupled Part-Handle ReasoningTechnical Report A Additional quantitative analysis These controls detail the prediction sources, motion decoder and geometric coverage underlying the main results. All use the public validation split. Alternative configurations are identified explicitly and do not replace the reference system. A.1 Prediction sources and training variability Table 11. Coupling under source-configuration perturbations. The complementary cue is held fixed within each row. Random-initialization rows also use a longer training schedule, so they are configuration comparisons rather than isolated pretraining effects. Scores are validation percentages. Output and source configuration Fixed complementary cueWithout cueWith cue Part motion: reference part model Dense handles13.7440.98 Part motion: joint part headDense handles12.2637.33 Part motion: random-init part model Dense handles5.8625.42 Handle detection: reference dense model Frozen child union24.6329.65 Handle detection: random-init dense model Frozen child union1.7513.63 The upper block reports part-motionAP AO 50 ; the lower block reports handleAP 50 . These controls show that the measured transfers persist for the listed source configurations, but they do not establish a monotonic relation between source quality and coupling gain. Table 11 changes the target predictor while fixing its complementary cue. Handle guidance improves the reference, joint-head and random-initialization part configurations; the same child source improves both reference and weak dense-handle configurations. Random-initialization runs also use a different training schedule, so these are source-configuration comparisons rather than isolated tests of pretraining. Table 12. Dense-handle model repeats with fixed child and part sources. All columns are validation percentages. The first three columns are handle AP; the final column is part-motionAP AO 50 when that dense field supplies the handle cue. Dense-model drawDense APUnion APFull-context APPart motion AP Reference24.6329.6530.9940.98 Repeat 123.7627.6828.8140.66 Repeat 222.8327.6728.9040.46 Repeat 325.1629.7030.8239.51 The same released child predictor, part predictions, and post-processing are fixed in every row. Appending children and applying contextual labels each increase handle AP in all four draws. Dense-handle AP and part-motion AP need not order the draws identically: the decoder uses handle position, not the detector’s entire mask-and-class ranking. Table 13. Child-training sensitivity of handle proposals and label correction. Dense incumbents and the part-voting input are fixed; only the child model’s training draw changes. The append gain is relative to the frozen dense baseline; the vote gain is relative to that draw’s own union. Entries are validation AP 50 gains (p). Child training drawAppend child proposalsContextual vote Reference child+5.01+1.34 Child seed A+4.89+0.19 Child seed B+3.94+0.38 The union increment remains positive across the three child draws (range 1.08 p). The vote increment ranges by 1.15 p, including much smaller values for both repeats. This descriptive family does not replace a formal uncertainty analysis; the reference configuration’s reported score remains 30.99. 17 Coupled Part-Handle ReasoningTechnical Report Table 12 varies the dense predictor with both the part and child sources fixed. Child proposals and label correction each improve handle AP in all four rows. The ordering of dense AP differs from that of part-motion AP because a handle’s local position and its complete detection quality are different quantities. Table 13 instead varies only the child predictor, with dense incumbents and part context fixed. Proposal gains remain positive across all three draws; contextual gains are also positive but substantially smaller for the two repeats. These distinct training families describe sensitivity to different prediction sources and are not pooled into one uncertainty estimate. A.2 Information flow and child association Table 14. Orthogonal one-pass coupling controls. The child-proposal union is fixed in every cell; the factorial switches only dense-handle guidance for part origins and contextual child-label voting for handles. Scores are validation percentages. Brackets in the note give lower and upper bounds of paired 95% scene-jackknife confidence intervals for each signal’s on-minus-off AP change, in p. Switched signalRanking metric ConfigurationHandle-guided originContext votePart motion AP AO 50 Handle AP 50 Neither signal–13.7429.65 Handle-guided hinge only✓–40.9829.65 Contextual vote only–✓13.7430.99 Both signals (reference)✓40.9830.99 Handles change part-motion AP by +27.25 p (paired scene jackknife 95% interval [+21.86,+32.63]); voting changes handle AP by +1.34 p ([+0.37,+2.31]). The measured interaction is exactly zero on both metrics: handle guidance changes origins only, while voting reads masks and classes. This is a factorial control of two directed transfers, not evidence of iterative refinement. Table 15. Separating child conditioning from association. The shared-field rows differ in parent conditioning under a matched readout; the reference instead associates child masks by query index. Dense detections and contextual label rules are fixed. Scores are validationAP 50 percentages. Brackets in the note are paired 95% scene-jackknife confidence intervals for conditioned minus unconditioned AP (p). Child predictor and readoutUnionAfter label correction Unconditioned, shared-field readout28.0729.78 Conditioned, shared-field readout28.4129.26 Reference query-associated children29.6530.99 Within the shared-field pair, conditioning changes union AP by +0.34 p (95% CI [−0.99,+1.66]) and corrected AP by −0.52 p ([−2.66,+1.62]); both intervals include zero. Query-associated readout gives a separate +1.24-p union difference from conditioned shared-field readout. These comparisons distinguish the implemented proposal source from a causal claim about conditioning alone. Table 14 verifies output ownership: dense-handle guidance affects part origins, and contextual labels affect handles. The child union is fixed throughout, so this is a control of the two exchanged signals, not all three proposal-and-correction mechanisms. Its zero interaction is consistent with the one-pass dependency structure. Table 15 distinguishes the role of the additional predictor from parent conditioning and the readout used to associate children. The matched shared-field pair gives opposite-signed union and corrected-output differences, with both scene intervals including zero. Query-associated readout yields a separate 1.24-p union difference. Together with the localization controls, this supports the implemented proposal source without identifying conditioning alone as the cause of its gain. 18 Coupled Part-Handle ReasoningTechnical Report A.3 Motion-decoder controls Table 16. Fixed-input handle-origin control. Part masks, classes, scores, and axes are identical in both rows; only the origin rule changes. Scores are validation percentages. Origin ruleAP 50 AP A 50 AP O 50 AP AO 50 Centroid origin (no handle cue)47.93 43.75 14.37 13.74 Hinge guided by dense handles47.9343.7543.1140.98 Equal mask and axis columns are an implementation check: handles enter this comparison only through the representative origin. Table 17. Matched learned heads on two part-model training draws. Each learned entry uses the best head seed for that backbone with predicted-handle evidence. A cell listsAP AO 50 (%) followed by the lower and upper bounds of the paired 95% scene-jackknife confidence interval for that head minus its column’s training-free rule (p). Thus, brackets describe uncertainty in the AP change, not the absolute score or a range across seeds. Learned headReference part modelSecond part-model draw Training-free rule40.9839.45 Learned candidate selection38.63 [−5.35, +0.63]38.63 [−4.54, +2.91] Learned selection, box axes only38.78 [−5.33, +0.92]39.39 [−4.44, +4.31] Rule axis + learned edge39.36 [−4.31, +1.05]37.64 [−4.66, +1.04] The displayed learned heads have lower point estimates than their own rule on both part-model draws, but every scene interval includes zero. These frozen-feature comparisons support the effectiveness of the training-free rule without establishing a statistically resolved advantage over the learned heads. Table 16 isolates handle guidance by preserving masks, classes, scores and axes; equal mask and axis AP confirm that only the origin rule changes. Table 17 compares the training-free rule with matched learned heads on two fixed part-model draws, reporting the best head seed for each family. The rule has the higher point estimates, while the paired intervals leave the differences unresolved. The comparison concerns decoding from frozen features, not jointly trained representations. A.4 Coverage and failure populations Table 18. Coverage and selection diagnostics on validation. Coverage asks whether a valid candidate exists; selection asks whether the reference rule chooses it. These are different populations and are not end-to-end AP. Population / diagnosticnCoverageSelection given coverage Movable parts matched by a predicted mask390 64.4%– Matched rotations: a passing hinge candidate1,423 94.4%88.3% Ground-truth rotations: a passing hinge candidate236 95.8%88.1% Ground-truth handles matched by the child union388 49.7%– On predicted movable-part masks, 57.2% of ground-truth instances satisfy the joint motion criterion; 64.4% are reachable by mask overlap alone. For the four hinge candidates, absence (5.6% of matched rotations) and wrong edge selection (11.0%) are reported separately. Candidate coverage does not establish a learned selector’s performance. 19 Coupled Part-Handle ReasoningTechnical Report Table 19. Where validation instances are lost. The movable-part census assigns each of 390 GT instances to the first applicable bucket: missing mask, axis failure, origin failure, or all gates passed. Counts are not AP or additive oracle gains. Movable-part outcomeRotationTranslationTotal No mask with IoU > 0.55089139 Covered; axis gate fails12214 Covered; axis passes; origin fails14014 All motion gates passed16063223 GT population236154390 The union of dense and child handles covers 193 of 388 GT handles. By GT-size quartile, coverage is 22/97, 53/99, 63/96 and 55/96; the smallest quartile has at most 11 points and the largest more than 29. These descriptive bins use the validation population and were not used as training targets. Table 18 separates mask reachability, hinge-candidate availability and selection. Matched-prediction statistics may include several predictions for one GT rotation; the GT-mask diagnostic instead uses one mask per annotated rotation. Candidate coverage is high on both populations, at 94.4% and 95.8%, respectively, with conditional selection rates of 88.3% and 88.1%. These instance fractions are not class-macro AP. Table 19 assigns each GT part to its first failure: missing mask, axis, or origin. Missing masks account for the largest group, including 89 translations and 50 rotations. Handle coverage is lowest in the smallest size quartile, while the middle quartiles show that size alone does not determine detection success. Counts describe the available predictions, not additive or recoverable AP gains. B Additional qualitative analysis B.1 Coverage and geometric components Figure 5 visualizes the census in Table 19: missing instances limit the gains available to motion decoding, and small handles remain difficult. Figure 6 compares the naive and full configurations on common GT instances, including a case where the naive origin is closer and a newly covered instance whose origin still fails. The predicted instance sets can differ between these configurations. Figure 7 illustrates the component dependence measured in Table 5. Removing disconnected support can substantially change the fitted box and hinge, while a typical instance changes little. The two examples connect a population-level ablation to its geometric action without implying uniform improvement. 0.00.20.40.60.81.0 fraction of the 390 GT movable instances not covered 139 · 35.6% axis gate 14 (3.6%) origin gate 14 (3.6%) scored 223 · 57.2% MAO_ST 0.410 AP50 0.479 Track 1: coverage is the largest loss, the motion decode the smallest 0.00.10.20.30.40.50.60.7 AP / fraction of GT reachable Track 1 AP50 Track 1 MAO_ST Track 2 AP50 −16 pts −16 pts −20 pts selection: what the ranking converts ceiling = coverageachieved AP ≤11 pts12–1819–29>29 pts GT handle size (quartiles) 0 20 40 60 80 covered at IoU > 0.5 (%) 22.7% 53.5% 65.6% 57.3% all handles 49.7% Track 2: small handles are the coverage problem Movable-part coverageCoverage and APHandle coverage Part AP50 Part motion AP Handle AP50 coverage fraction and AP shown on a common 0--1 scale Figure 5. Coverage and selection limits on the public validation split. Left: the movable-part census assigns each ground-truth instance to coverage, axis, origin, or fully scored outcomes. Centre: each metric’s macro AP is juxtaposed with a pooled instance-coverage fraction on a common 0–1 scale. These coverage fractions are diagnostic reachability statistics, not strict AP ceilings or quantities subtractable from AP. Right: handle coverage by ground-truth size quartile. 20 Coupled Part-Handle ReasoningTechnical Report naive 0.36 m FAIL axis 0.0° (i) 61adef · gt 1025 · rot · arms 1.0000 · vs GT 0.91 covered by both — median naive line error naive 0.63 m FAIL axis 0.0° (i) b20a26 · gt 1019 · rot · arms 1.0000 · vs GT 0.92 covered by both — 90th percentile naive line error naive: no prediction covers this GT (i') e39868 · gt 1018 · rot · vs GT 0.54 ROTATION the released arm covers and the naive arm does not — median GT size (stratum (i) as specified is empty: no translation differs in coverage) naive 0.01 m PASS axis 0.0° (iv) 8890d0 · gt 1062 · rot · arms 1.0000 · vs GT 0.56 both arms pass the origin gate — smallest naive error full 0.03 m PASS axis 0.0° full 0.08 m PASS axis 0.0° full 0.35 m FAIL axis 0.0° full 0.05 m PASS axis 0.0° ground truth hinge line ground truth hinge line ground truth hinge line ground truth hinge line G1 — the naive pipeline against the released geometric decode, on the same GT part and the same camera. Black line: the GT hinge. Coloured segment: the perpendicular distance the 0.25 m origin gate tests. Specimens by stated quantile rank within named strata. Of 390 GT instances, 183 rotations are covered by both arms, 0 translations by the released arm only, and 38 covered rotations pass the origin gate in both. The arms share most instances — 209 of the covered GT are covered by the same prediction id in both, coverage differs on 3 rotations and 0 translations — so what AP50 sees is the rescoring and the selection rule reordering and trimming the same instances (the rule alone +0.005, F1), and what the ranked column sees is the origin. The 'arms' figure is how much the two arms' matched predictions overlap EACH OTHER: it is 1.0000 for 244 of 248 covered GT (median 1.0000, min 0.5778) because the same instance usually survives into both arms, while the prediction matrices themselves are elementwise equal in 0 of 42 scenes. Agreement with GT is a different and lower number — the evaluator's own IoU over the covering rotation matches has median 0.8301 and maximum 0.9771; no mask is superpoint-exact against GT. Median naive- origin error 90th-percentile naive-origin error Full-model-only coverage Naive origin is better Figure 6. Naive versus full geometric decoding. The top and bottom rows compare the naive and full decoders against the same ground-truth part and camera; black denotes the annotated hinge. The first two columns are naive-error ranks 92 and 165 among 183 rotations covered by both configurations. The third is the median-size instance among three rotations covered only by the full configuration; its origin still fails. The last has the smallest naive-origin error among 38 both-pass cases, and the naive origin is closer. No translation is covered by only one configuration in the selection population. The gallery retains these exceptions rather than estimating their frequency. No support cleanup Centroid origin Stock query selection Reference decoder Ground-truth hinge Largest cleanup-induced change (rank 183/183) drop_c no largest-C cleanup MAO_ST 0.38032 origin 6.04 m off panel drop_c 6.04 m FAIL axis 0.0° · IoU 0.68 (i) 27d4d · gt 1071 · 977 pts · rank 183 of 183 — the LARGEST change in line error between drop_c and full (rank: max). drop_c 6.04 m → full 0.06 m drop_c 0.32 m FAIL axis 90.0° · IoU 0.80 (i) 9859de · gt 1026 · 1209 pts · rank 92 of 183 — the MEDIAN change in line error between drop_c and full, which is exactly zero — the cleanup is inert on most parts and decisive on a few. drop_c 0.32 m → full 0.32 m drop_hnd no handle guidance (centroid origin) MAO_ST 0.13739 drop_hnd 0.27 m FAIL axis 0.0° · IoU 0.68 drop_hnd 0.32 m FAIL axis 90.0° · IoU 0.80 drop_sel no selection rule MAO_ST 0.40795 drop_sel 0.06 m PASS axis 0.0° · IoU 0.68 drop_sel 0.32 m FAIL axis 90.0° · IoU 0.80 full the released decode MAO_ST 0.40984 full 0.06 m PASS axis 0.0° · IoU 0.68 full 0.32 m FAIL axis 90.0° · IoU 0.80 ground truth ground truth hinge line ground truth hinge line G2 — one GT part decoded by each rung of the component ladder, on one camera per column. Dark: the GT part. Pale red: that arm's own matched prediction. Coloured segment: the perpendicular distance the 0.25 m origin gate tests, green if the arm clears MAO_ST. Each arm is re-scored here from its own prediction file and must return its committed metrics.json on all five motion keys before a specimen is chosen; all four did. Dropping one component at a time from the released decode costs +0.02952 (cleanup), +0.27245 (handle guidance) and +0.00189 (selection rule) on MAO_ST_ap50 — which sum to +0.30385 against a release at 0.40984 over a naive 0.12241, a total of +0.28743. The parts do not add because they act on each other: the cleanup moves the box, the box moves the edges the origin is placed on, and the edges only matter once the selection rule chooses among them. drop_sel is a DIFFERENT prediction set (5556 instances against 6285), so a part is drawn only where all four arms cover it (183 GT rotations of the 42-scene validation split) and each panel shows that arm's own matched prediction with its IoU against the GT. The figure's own axis is concentrated: of the 183 parts, the cleanup changes the line error not at all on 120 (the median change is 0.0000 m, which is why column (i) is four identical panels), by more than the 0.25 m gate on 25, and by 5.98 m at most — the same shape as the min_points scenes, a handful of carriers rather than a broad shift. Specimens by stated rank on the drop_c → full change; ties break by scene id then instance id. drop_c no largest-C cleanup MAO_ST 0.38032 origin 6.04 m off panel drop_c 6.04 m FAIL axis 0.0° · IoU 0.68 (i) 27d4d · gt 1071 · 977 pts · rank 183 of 183 — the LARGEST change in line error between drop_c and full (rank: max). drop_c 6.04 m → full 0.06 m drop_c 0.32 m FAIL axis 90.0° · IoU 0.80 (i) 9859de · gt 1026 · 1209 pts · rank 92 of 183 — the MEDIAN change in line error between drop_c and full, which is exactly zero — the cleanup is inert on most parts and decisive on a few. drop_c 0.32 m → full 0.32 m drop_hnd no handle guidance (centroid origin) MAO_ST 0.13739 drop_hnd 0.27 m FAIL axis 0.0° · IoU 0.68 drop_hnd 0.32 m FAIL axis 90.0° · IoU 0.80 drop_sel no selection rule MAO_ST 0.40795 drop_sel 0.06 m PASS axis 0.0° · IoU 0.68 drop_sel 0.32 m FAIL axis 90.0° · IoU 0.80 full the released decode MAO_ST 0.40984 full 0.06 m PASS axis 0.0° · IoU 0.68 full 0.32 m FAIL axis 90.0° · IoU 0.80 ground truth ground truth hinge line ground truth hinge line G2 — one GT part decoded by each rung of the component ladder, on one camera per column. Dark: the GT part. Pale red: that arm's own matched prediction. Coloured segment: the perpendicular distance the 0.25 m origin gate tests, green if the arm clears MAO_ST. Each arm is re-scored here from its own prediction file and must return its committed metrics.json on all five motion keys before a specimen is chosen; all four did. Dropping one component at a time from the released decode costs +0.02952 (cleanup), +0.27245 (handle guidance) and +0.00189 (selection rule) on MAO_ST_ap50 — which sum to +0.30385 against a release at 0.40984 over a naive 0.12241, a total of +0.28743. The parts do not add because they act on each other: the cleanup moves the box, the box moves the edges the origin is placed on, and the edges only matter once the selection rule chooses among them. drop_sel is a DIFFERENT prediction set (5556 instances against 6285), so a part is drawn only where all four arms cover it (183 GT rotations of the 42-scene validation split) and each panel shows that arm's own matched prediction with its IoU against the GT. The figure's own axis is concentrated: of the 183 parts, the cleanup changes the line error not at all on 120 (the median change is 0.0000 m, which is why column (i) is four identical panels), by more than the 0.25 m gate on 25, and by 5.98 m at most — the same shape as the min_points scenes, a handful of carriers rather than a broad shift. Specimens by stated rank on the drop_c → full change; ties break by scene id then instance id. drop_c no largest-C cleanup MAO_ST 0.38032 origin 6.04 m off panel drop_c 6.04 m FAIL axis 0.0° · IoU 0.68 (i) 27d4d · gt 1071 · 977 pts · rank 183 of 183 — the LARGEST change in line error between drop_c and full (rank: max). drop_c 6.04 m → full 0.06 m drop_c 0.32 m FAIL axis 90.0° · IoU 0.80 (i) 9859de · gt 1026 · 1209 pts · rank 92 of 183 — the MEDIAN change in line error between drop_c and full, which is exactly zero — the cleanup is inert on most parts and decisive on a few. drop_c 0.32 m → full 0.32 m drop_hnd no handle guidance (centroid origin) MAO_ST 0.13739 drop_hnd 0.27 m FAIL axis 0.0° · IoU 0.68 drop_hnd 0.32 m FAIL axis 90.0° · IoU 0.80 drop_sel no selection rule MAO_ST 0.40795 drop_sel 0.06 m PASS axis 0.0° · IoU 0.68 drop_sel 0.32 m FAIL axis 90.0° · IoU 0.80 full the released decode MAO_ST 0.40984 full 0.06 m PASS axis 0.0° · IoU 0.68 full 0.32 m FAIL axis 90.0° · IoU 0.80 ground truth ground truth hinge line ground truth hinge line G2 — one GT part decoded by each rung of the component ladder, on one camera per column. Dark: the GT part. Pale red: that arm's own matched prediction. Coloured segment: the perpendicular distance the 0.25 m origin gate tests, green if the arm clears MAO_ST. Each arm is re-scored here from its own prediction file and must return its committed metrics.json on all five motion keys before a specimen is chosen; all four did. Dropping one component at a time from the released decode costs +0.02952 (cleanup), +0.27245 (handle guidance) and +0.00189 (selection rule) on MAO_ST_ap50 — which sum to +0.30385 against a release at 0.40984 over a naive 0.12241, a total of +0.28743. The parts do not add because they act on each other: the cleanup moves the box, the box moves the edges the origin is placed on, and the edges only matter once the selection rule chooses among them. drop_sel is a DIFFERENT prediction set (5556 instances against 6285), so a part is drawn only where all four arms cover it (183 GT rotations of the 42-scene validation split) and each panel shows that arm's own matched prediction with its IoU against the GT. The figure's own axis is concentrated: of the 183 parts, the cleanup changes the line error not at all on 120 (the median change is 0.0000 m, which is why column (i) is four identical panels), by more than the 0.25 m gate on 25, and by 5.98 m at most — the same shape as the min_points scenes, a handful of carriers rather than a broad shift. Specimens by stated rank on the drop_c → full change; ties break by scene id then instance id. drop_c no largest-C cleanup MAO_ST 0.38032 origin 6.04 m off panel drop_c 6.04 m FAIL axis 0.0° · IoU 0.68 (i) 27d4d · gt 1071 · 977 pts · rank 183 of 183 — the LARGEST change in line error between drop_c and full (rank: max). drop_c 6.04 m → full 0.06 m drop_c 0.32 m FAIL axis 90.0° · IoU 0.80 (i) 9859de · gt 1026 · 1209 pts · rank 92 of 183 — the MEDIAN change in line error between drop_c and full, which is exactly zero — the cleanup is inert on most parts and decisive on a few. drop_c 0.32 m → full 0.32 m drop_hnd no handle guidance (centroid origin) MAO_ST 0.13739 drop_hnd 0.27 m FAIL axis 0.0° · IoU 0.68 drop_hnd 0.32 m FAIL axis 90.0° · IoU 0.80 drop_sel no selection rule MAO_ST 0.40795 drop_sel 0.06 m PASS axis 0.0° · IoU 0.68 drop_sel 0.32 m FAIL axis 90.0° · IoU 0.80 full the released decode MAO_ST 0.40984 full 0.06 m PASS axis 0.0° · IoU 0.68 full 0.32 m FAIL axis 90.0° · IoU 0.80 ground truth ground truth hinge line ground truth hinge line G2 — one GT part decoded by each rung of the component ladder, on one camera per column. Dark: the GT part. Pale red: that arm's own matched prediction. Coloured segment: the perpendicular distance the 0.25 m origin gate tests, green if the arm clears MAO_ST. Each arm is re-scored here from its own prediction file and must return its committed metrics.json on all five motion keys before a specimen is chosen; all four did. Dropping one component at a time from the released decode costs +0.02952 (cleanup), +0.27245 (handle guidance) and +0.00189 (selection rule) on MAO_ST_ap50 — which sum to +0.30385 against a release at 0.40984 over a naive 0.12241, a total of +0.28743. The parts do not add because they act on each other: the cleanup moves the box, the box moves the edges the origin is placed on, and the edges only matter once the selection rule chooses among them. drop_sel is a DIFFERENT prediction set (5556 instances against 6285), so a part is drawn only where all four arms cover it (183 GT rotations of the 42-scene validation split) and each panel shows that arm's own matched prediction with its IoU against the GT. The figure's own axis is concentrated: of the 183 parts, the cleanup changes the line error not at all on 120 (the median change is 0.0000 m, which is why column (i) is four identical panels), by more than the 0.25 m gate on 25, and by 5.98 m at most — the same shape as the min_points scenes, a handful of carriers rather than a broad shift. Specimens by stated rank on the drop_c → full change; ties break by scene id then instance id. drop_c no largest-C cleanup MAO_ST 0.38032 origin 6.04 m off panel drop_c 6.04 m FAIL axis 0.0° · IoU 0.68 (i) 27d4d · gt 1071 · 977 pts · rank 183 of 183 — the LARGEST change in line error between drop_c and full (rank: max). drop_c 6.04 m → full 0.06 m drop_c 0.32 m FAIL axis 90.0° · IoU 0.80 (i) 9859de · gt 1026 · 1209 pts · rank 92 of 183 — the MEDIAN change in line error between drop_c and full, which is exactly zero — the cleanup is inert on most parts and decisive on a few. drop_c 0.32 m → full 0.32 m drop_hnd no handle guidance (centroid origin) MAO_ST 0.13739 drop_hnd 0.27 m FAIL axis 0.0° · IoU 0.68 drop_hnd 0.32 m FAIL axis 90.0° · IoU 0.80 drop_sel no selection rule MAO_ST 0.40795 drop_sel 0.06 m PASS axis 0.0° · IoU 0.68 drop_sel 0.32 m FAIL axis 90.0° · IoU 0.80 full the released decode MAO_ST 0.40984 full 0.06 m PASS axis 0.0° · IoU 0.68 full 0.32 m FAIL axis 90.0° · IoU 0.80 ground truth ground truth hinge line ground truth hinge line G2 — one GT part decoded by each rung of the component ladder, on one camera per column. Dark: the GT part. Pale red: that arm's own matched prediction. Coloured segment: the perpendicular distance the 0.25 m origin gate tests, green if the arm clears MAO_ST. Each arm is re-scored here from its own prediction file and must return its committed metrics.json on all five motion keys before a specimen is chosen; all four did. Dropping one component at a time from the released decode costs +0.02952 (cleanup), +0.27245 (handle guidance) and +0.00189 (selection rule) on MAO_ST_ap50 — which sum to +0.30385 against a release at 0.40984 over a naive 0.12241, a total of +0.28743. The parts do not add because they act on each other: the cleanup moves the box, the box moves the edges the origin is placed on, and the edges only matter once the selection rule chooses among them. drop_sel is a DIFFERENT prediction set (5556 instances against 6285), so a part is drawn only where all four arms cover it (183 GT rotations of the 42-scene validation split) and each panel shows that arm's own matched prediction with its IoU against the GT. The figure's own axis is concentrated: of the 183 parts, the cleanup changes the line error not at all on 120 (the median change is 0.0000 m, which is why column (i) is four identical panels), by more than the 0.25 m gate on 25, and by 5.98 m at most — the same shape as the min_points scenes, a handful of carriers rather than a broad shift. Specimens by stated rank on the drop_c → full change; ties break by scene id then instance id. 6.04 m0.27 m0.06 m0.06 m Median cleanup-induced change (rank 92/183; zero change) drop_c no largest-C cleanup MAO_ST 0.38032 origin 6.04 m off panel drop_c 6.04 m FAIL axis 0.0° · IoU 0.68 (i) 27d4d · gt 1071 · 977 pts · rank 183 of 183 — the LARGEST change in line error between drop_c and full (rank: max). drop_c 6.04 m → full 0.06 m drop_c 0.32 m FAIL axis 90.0° · IoU 0.80 (i) 9859de · gt 1026 · 1209 pts · rank 92 of 183 — the MEDIAN change in line error between drop_c and full, which is exactly zero — the cleanup is inert on most parts and decisive on a few. drop_c 0.32 m → full 0.32 m drop_hnd no handle guidance (centroid origin) MAO_ST 0.13739 drop_hnd 0.27 m FAIL axis 0.0° · IoU 0.68 drop_hnd 0.32 m FAIL axis 90.0° · IoU 0.80 drop_sel no selection rule MAO_ST 0.40795 drop_sel 0.06 m PASS axis 0.0° · IoU 0.68 drop_sel 0.32 m FAIL axis 90.0° · IoU 0.80 full the released decode MAO_ST 0.40984 full 0.06 m PASS axis 0.0° · IoU 0.68 full 0.32 m FAIL axis 90.0° · IoU 0.80 ground truth ground truth hinge line ground truth hinge line G2 — one GT part decoded by each rung of the component ladder, on one camera per column. Dark: the GT part. Pale red: that arm's own matched prediction. Coloured segment: the perpendicular distance the 0.25 m origin gate tests, green if the arm clears MAO_ST. Each arm is re-scored here from its own prediction file and must return its committed metrics.json on all five motion keys before a specimen is chosen; all four did. Dropping one component at a time from the released decode costs +0.02952 (cleanup), +0.27245 (handle guidance) and +0.00189 (selection rule) on MAO_ST_ap50 — which sum to +0.30385 against a release at 0.40984 over a naive 0.12241, a total of +0.28743. The parts do not add because they act on each other: the cleanup moves the box, the box moves the edges the origin is placed on, and the edges only matter once the selection rule chooses among them. drop_sel is a DIFFERENT prediction set (5556 instances against 6285), so a part is drawn only where all four arms cover it (183 GT rotations of the 42-scene validation split) and each panel shows that arm's own matched prediction with its IoU against the GT. The figure's own axis is concentrated: of the 183 parts, the cleanup changes the line error not at all on 120 (the median change is 0.0000 m, which is why column (i) is four identical panels), by more than the 0.25 m gate on 25, and by 5.98 m at most — the same shape as the min_points scenes, a handful of carriers rather than a broad shift. Specimens by stated rank on the drop_c → full change; ties break by scene id then instance id. drop_c no largest-C cleanup MAO_ST 0.38032 origin 6.04 m off panel drop_c 6.04 m FAIL axis 0.0° · IoU 0.68 (i) 27d4d · gt 1071 · 977 pts · rank 183 of 183 — the LARGEST change in line error between drop_c and full (rank: max). drop_c 6.04 m → full 0.06 m drop_c 0.32 m FAIL axis 90.0° · IoU 0.80 (i) 9859de · gt 1026 · 1209 pts · rank 92 of 183 — the MEDIAN change in line error between drop_c and full, which is exactly zero — the cleanup is inert on most parts and decisive on a few. drop_c 0.32 m → full 0.32 m drop_hnd no handle guidance (centroid origin) MAO_ST 0.13739 drop_hnd 0.27 m FAIL axis 0.0° · IoU 0.68 drop_hnd 0.32 m FAIL axis 90.0° · IoU 0.80 drop_sel no selection rule MAO_ST 0.40795 drop_sel 0.06 m PASS axis 0.0° · IoU 0.68 drop_sel 0.32 m FAIL axis 90.0° · IoU 0.80 full the released decode MAO_ST 0.40984 full 0.06 m PASS axis 0.0° · IoU 0.68 full 0.32 m FAIL axis 90.0° · IoU 0.80 ground truth ground truth hinge line ground truth hinge line G2 — one GT part decoded by each rung of the component ladder, on one camera per column. Dark: the GT part. Pale red: that arm's own matched prediction. Coloured segment: the perpendicular distance the 0.25 m origin gate tests, green if the arm clears MAO_ST. Each arm is re-scored here from its own prediction file and must return its committed metrics.json on all five motion keys before a specimen is chosen; all four did. Dropping one component at a time from the released decode costs +0.02952 (cleanup), +0.27245 (handle guidance) and +0.00189 (selection rule) on MAO_ST_ap50 — which sum to +0.30385 against a release at 0.40984 over a naive 0.12241, a total of +0.28743. The parts do not add because they act on each other: the cleanup moves the box, the box moves the edges the origin is placed on, and the edges only matter once the selection rule chooses among them. drop_sel is a DIFFERENT prediction set (5556 instances against 6285), so a part is drawn only where all four arms cover it (183 GT rotations of the 42-scene validation split) and each panel shows that arm's own matched prediction with its IoU against the GT. The figure's own axis is concentrated: of the 183 parts, the cleanup changes the line error not at all on 120 (the median change is 0.0000 m, which is why column (i) is four identical panels), by more than the 0.25 m gate on 25, and by 5.98 m at most — the same shape as the min_points scenes, a handful of carriers rather than a broad shift. Specimens by stated rank on the drop_c → full change; ties break by scene id then instance id. drop_c no largest-C cleanup MAO_ST 0.38032 origin 6.04 m off panel drop_c 6.04 m FAIL axis 0.0° · IoU 0.68 (i) 27d4d · gt 1071 · 977 pts · rank 183 of 183 — the LARGEST change in line error between drop_c and full (rank: max). drop_c 6.04 m → full 0.06 m drop_c 0.32 m FAIL axis 90.0° · IoU 0.80 (i) 9859de · gt 1026 · 1209 pts · rank 92 of 183 — the MEDIAN change in line error between drop_c and full, which is exactly zero — the cleanup is inert on most parts and decisive on a few. drop_c 0.32 m → full 0.32 m drop_hnd no handle guidance (centroid origin) MAO_ST 0.13739 drop_hnd 0.27 m FAIL axis 0.0° · IoU 0.68 drop_hnd 0.32 m FAIL axis 90.0° · IoU 0.80 drop_sel no selection rule MAO_ST 0.40795 drop_sel 0.06 m PASS axis 0.0° · IoU 0.68 drop_sel 0.32 m FAIL axis 90.0° · IoU 0.80 full the released decode MAO_ST 0.40984 full 0.06 m PASS axis 0.0° · IoU 0.68 full 0.32 m FAIL axis 90.0° · IoU 0.80 ground truth ground truth hinge line ground truth hinge line G2 — one GT part decoded by each rung of the component ladder, on one camera per column. Dark: the GT part. Pale red: that arm's own matched prediction. Coloured segment: the perpendicular distance the 0.25 m origin gate tests, green if the arm clears MAO_ST. Each arm is re-scored here from its own prediction file and must return its committed metrics.json on all five motion keys before a specimen is chosen; all four did. Dropping one component at a time from the released decode costs +0.02952 (cleanup), +0.27245 (handle guidance) and +0.00189 (selection rule) on MAO_ST_ap50 — which sum to +0.30385 against a release at 0.40984 over a naive 0.12241, a total of +0.28743. The parts do not add because they act on each other: the cleanup moves the box, the box moves the edges the origin is placed on, and the edges only matter once the selection rule chooses among them. drop_sel is a DIFFERENT prediction set (5556 instances against 6285), so a part is drawn only where all four arms cover it (183 GT rotations of the 42-scene validation split) and each panel shows that arm's own matched prediction with its IoU against the GT. The figure's own axis is concentrated: of the 183 parts, the cleanup changes the line error not at all on 120 (the median change is 0.0000 m, which is why column (i) is four identical panels), by more than the 0.25 m gate on 25, and by 5.98 m at most — the same shape as the min_points scenes, a handful of carriers rather than a broad shift. Specimens by stated rank on the drop_c → full change; ties break by scene id then instance id. drop_c no largest-C cleanup MAO_ST 0.38032 origin 6.04 m off panel drop_c 6.04 m FAIL axis 0.0° · IoU 0.68 (i) 27d4d · gt 1071 · 977 pts · rank 183 of 183 — the LARGEST change in line error between drop_c and full (rank: max). drop_c 6.04 m → full 0.06 m drop_c 0.32 m FAIL axis 90.0° · IoU 0.80 (i) 9859de · gt 1026 · 1209 pts · rank 92 of 183 — the MEDIAN change in line error between drop_c and full, which is exactly zero — the cleanup is inert on most parts and decisive on a few. drop_c 0.32 m → full 0.32 m drop_hnd no handle guidance (centroid origin) MAO_ST 0.13739 drop_hnd 0.27 m FAIL axis 0.0° · IoU 0.68 drop_hnd 0.32 m FAIL axis 90.0° · IoU 0.80 drop_sel no selection rule MAO_ST 0.40795 drop_sel 0.06 m PASS axis 0.0° · IoU 0.68 drop_sel 0.32 m FAIL axis 90.0° · IoU 0.80 full the released decode MAO_ST 0.40984 full 0.06 m PASS axis 0.0° · IoU 0.68 full 0.32 m FAIL axis 90.0° · IoU 0.80 ground truth ground truth hinge line ground truth hinge line G2 — one GT part decoded by each rung of the component ladder, on one camera per column. Dark: the GT part. Pale red: that arm's own matched prediction. Coloured segment: the perpendicular distance the 0.25 m origin gate tests, green if the arm clears MAO_ST. Each arm is re-scored here from its own prediction file and must return its committed metrics.json on all five motion keys before a specimen is chosen; all four did. Dropping one component at a time from the released decode costs +0.02952 (cleanup), +0.27245 (handle guidance) and +0.00189 (selection rule) on MAO_ST_ap50 — which sum to +0.30385 against a release at 0.40984 over a naive 0.12241, a total of +0.28743. The parts do not add because they act on each other: the cleanup moves the box, the box moves the edges the origin is placed on, and the edges only matter once the selection rule chooses among them. drop_sel is a DIFFERENT prediction set (5556 instances against 6285), so a part is drawn only where all four arms cover it (183 GT rotations of the 42-scene validation split) and each panel shows that arm's own matched prediction with its IoU against the GT. The figure's own axis is concentrated: of the 183 parts, the cleanup changes the line error not at all on 120 (the median change is 0.0000 m, which is why column (i) is four identical panels), by more than the 0.25 m gate on 25, and by 5.98 m at most — the same shape as the min_points scenes, a handful of carriers rather than a broad shift. Specimens by stated rank on the drop_c → full change; ties break by scene id then instance id. drop_c no largest-C cleanup MAO_ST 0.38032 origin 6.04 m off panel drop_c 6.04 m FAIL axis 0.0° · IoU 0.68 (i) 27d4d · gt 1071 · 977 pts · rank 183 of 183 — the LARGEST change in line error between drop_c and full (rank: max). drop_c 6.04 m → full 0.06 m drop_c 0.32 m FAIL axis 90.0° · IoU 0.80 (i) 9859de · gt 1026 · 1209 pts · rank 92 of 183 — the MEDIAN change in line error between drop_c and full, which is exactly zero — the cleanup is inert on most parts and decisive on a few. drop_c 0.32 m → full 0.32 m drop_hnd no handle guidance (centroid origin) MAO_ST 0.13739 drop_hnd 0.27 m FAIL axis 0.0° · IoU 0.68 drop_hnd 0.32 m FAIL axis 90.0° · IoU 0.80 drop_sel no selection rule MAO_ST 0.40795 drop_sel 0.06 m PASS axis 0.0° · IoU 0.68 drop_sel 0.32 m FAIL axis 90.0° · IoU 0.80 full the released decode MAO_ST 0.40984 full 0.06 m PASS axis 0.0° · IoU 0.68 full 0.32 m FAIL axis 90.0° · IoU 0.80 ground truth ground truth hinge line ground truth hinge line G2 — one GT part decoded by each rung of the component ladder, on one camera per column. Dark: the GT part. Pale red: that arm's own matched prediction. Coloured segment: the perpendicular distance the 0.25 m origin gate tests, green if the arm clears MAO_ST. Each arm is re-scored here from its own prediction file and must return its committed metrics.json on all five motion keys before a specimen is chosen; all four did. Dropping one component at a time from the released decode costs +0.02952 (cleanup), +0.27245 (handle guidance) and +0.00189 (selection rule) on MAO_ST_ap50 — which sum to +0.30385 against a release at 0.40984 over a naive 0.12241, a total of +0.28743. The parts do not add because they act on each other: the cleanup moves the box, the box moves the edges the origin is placed on, and the edges only matter once the selection rule chooses among them. drop_sel is a DIFFERENT prediction set (5556 instances against 6285), so a part is drawn only where all four arms cover it (183 GT rotations of the 42-scene validation split) and each panel shows that arm's own matched prediction with its IoU against the GT. The figure's own axis is concentrated: of the 183 parts, the cleanup changes the line error not at all on 120 (the median change is 0.0000 m, which is why column (i) is four identical panels), by more than the 0.25 m gate on 25, and by 5.98 m at most — the same shape as the min_points scenes, a handful of carriers rather than a broad shift. Specimens by stated rank on the drop_c → full change; ties break by scene id then instance id. 0.32 m0.32 m0.32 m0.32 m Figure 7. Geometric component changes on fixed validation specimens. Each row fixes the camera and ground-truth part; columns show four decoder variants and the annotated hinge. Dark points denote ground truth, pale red the matched prediction, and the colored segment the perpendicular origin error reported below each panel. The upper row has the largest cleanup-induced change among 183 jointly covered rotations; the lower row has the median change, which is zero. The large origin error in the first panel lies outside the view and is explicitly marked. Selection can change the matched mask; the other columns do not imply a fixed instance set across configurations. B.2 Weaker prediction sources Figure 8 fixes the predicted mask within each centroid-versus-handle comparison while varying the part model between rows. It illustrates the source-configuration results in Table 11. Figure 9 holds the scene 21 Coupled Part-Handle ReasoningTechnical Report crop fixed and compares dense-handle fields from the reference and random-initialization models. It shows how the dense source fragments; the aggregate table, rather than this pre-union view, measures the benefit of adding children. released centroid 0.51 m FAIL axis 0.0° (i) f8062c · gt 1005 covered by all three — median RELEASED line error handle 0.06 m PASS axis 0.0° released centroid 0.27 m FAIL axis 0.0° (i) 4a1a3a · gt 1016 covered by all three — 90th percentile RELEASED error handle 0.17 m PASS axis 0.0° joint (K4) centroid 0.52 m FAIL axis 0.0° handle 0.06 m PASS axis 0.0° joint (K4) centroid 0.25 m FAIL axis 0.0° handle 0.06 m PASS axis 0.0° random init centroid 0.55 m FAIL axis 0.0° handle 0.07 m PASS axis 0.0° random init centroid 0.32 m FAIL axis 0.0° handle 0.12 m PASS axis 0.0° G4 — the same coupling on three Track-1 sources. Within a row the two panels are the SAME prediction decoded twice from the SAME released handles: only the origin rule changes. Across rows the parts model changes. Black line: the GT hinge. Specimens by stated quantile rank among the 122 GT rotations covered by all three sources. Per-class context: the handle effect is +0.54490 on rotations and exactly 0.00000 on translations, so the mechanism lives here. Coverage per source: released 186 · joint (K4) 171 · random init 147. Median reference-origin error90th-percentile reference-origin error Reference parts Joint-model parts Random initialization Reference parts Joint-model parts Random initialization Figure 8. Handle guidance across part-source strength. Within each row, the same part prediction is decoded with centroid and handle-guided origins using the same dense handle field; across rows, the part source changes. Columns use reference-origin-error ranks 61 and 110 among 122 rotations covered by all three sources (median and 90th percentile). The comparison shows the handle cue on reference, joint and random-initialized part predictions, without treating masks from different rows as matched. 22 Coupled Part-Handle ReasoningTechnical Report pretrained (released) · single 14 components in this scene · 342 over validation random init (D2') · single 35 components in this scene · 1195 over validation whole scenewhole scene G4, Track-2 half — what removing the pretrain does to the dense field. Colour is the predicted component id; the camera is the same in both panels. Scene 4422722c49 chosen by GT-handle count quantile 0.50 -> index 21 of 42 (6 handles). Validation-wide component counts are printed in each panel: the random-init field fragments the same scenes into far more, far smaller pieces — 342 components over validation against 1195 — which is D2'-T2's mechanism: fragmentation, not calibration. Crop: the 2.5 m window centred on the random-init arm's densest component neighbourhood (23 components within 1.25 m), ties by (x, y); the same window in both panels. Bottom row: the whole scene, same colouring. The union stage is not drawn; its component counts are read from each stage's metrics.json: union 4471 and 5324, so union minus single is 4129 in both arms — the appended child is identical, checked. Figure 9. Dense-handle fields under source variation. The same validation crop and camera compare the reference and random-initialization configurations from Table 11. Their training schedules also differ, so the comparison does not isolate pretraining. The scene has the median ground-truth-handle count (21st of 42 scenes). The random-initialized field emits more fragmented components (35 versus 14 in this scene; 1,195 versus 342 over validation). These are dense predictions before child augmentation. B.3 Representative failures Figure 10 illustrates the categories in Table 19: missing parts, a violation of the upright-axis prior, an origin-selection error, and small or over-extended handle predictions. Each gallery uses deterministic cases from a stated population; the examples explain the error types, not their prevalence. 23 Coupled Part-Handle ReasoningTechnical Report Uncovered rotation Median size, rank 25/50 Uncovered translation Median size, rank 45/89 Axis-gate failure Median axis error, rank 7/14 (a) uncovered rotation — 9071e1 · gt 1011 · 1131 pts rank 25 of 50 by n_gt | nothing reaches IoU 0.5 (best 0.43); drawn: the largest overlapping prediction, 2215 pts = 2.0× the GT at IoU 0.42 (b) uncovered translation — 88627b · gt 2076 · 224 pts rank 45 of 89 by n_gt | nothing reaches IoU 0.5 (best 0.11); drawn: the largest overlapping prediction, 5270 pts = 23.5× the GT at IoU 0.03 (c) axis gate — 1366d5 · gt 1009 · 1442 pts rank 7 of 14 by axis_err | drawn: the highest-confidence covering prediction, IoU 0.73 · axis 89.5° > 15° gate (d) origin gate — e91722 · gt 1012 · 2390 pts rank 7 of 14 by axp_line | drawn: the highest-confidence axis- passing prediction, IoU 0.78 · axis 0.0° PASS · origin 0.32 m > 0.25 m gate (e) Track 2 — smallest-quartile miss — 55b2bf · handle 35 · 8 pts rank 38 of 75 by n_gt | nothing reaches IoU 0.5 (best 0.12); drawn: the largest overlapping prediction, 349 pts = 43.6× the GT at IoU 0.02 (f) Track 2 — oversized prediction — 5e7c2 · handle 14 · 46 pts rank 19 of 37 by ratio | nothing reaches IoU 0.5 (best 0.16); drawn: the largest overlapping prediction, 188 pts = 4.1× the GT at IoU 0.16 G8 — one specimen per failure bucket of the released outputs, at the median of each bucket's own statistic. Dark: the GT part the evaluator scored. Red: the one prediction each panel names. Black line: the GT motion axis; dashed red: the predicted axis; red segment: the distance the origin gate tests. Denominators, reproduced from the dumps by this producer and asserted against RESULTS_e_census_released.md before drawing: of 390 GT movable instances, 139 (35.6 %) are never covered at IoU 0.5 — 50 rotations of 236 and 89 translations of 154 — against 14 charged to the axis gate and 14 to the origin gate, and 223 scored. Coverage is the whole story and it is a translation story, and panels (a) and (b) are why: the median uncovered rotation still reaches IoU 0.30 on its best prediction, the median uncovered translation only 0.10 — drawers are not near misses. Both motion buckets are near misses instead: ALL 12 of the axis bucket's rotations are non- vertical hinges against a rule that emits world-Z (its other 2 members are translations, whose GT axes are also off-vertical), and 12 of the 14 origin failures lie between 0.26 and 0.41 m against a 0.25 m gate. On Track 2, 193 of 388 GT handles are covered; the smallest quartile (≤ 11 pts) is covered 22.7 % of the time and 38 of its 75 misses have no overlapping prediction at all, while the largest quartile drops back to 57.3 % with 37 of 96 carrying an overlapping prediction at least 2× their size. Specimen ranks are stated per panel; ties break by scene id then instance id. (a) uncovered rotation — 9071e1 · gt 1011 · 1131 pts rank 25 of 50 by n_gt | nothing reaches IoU 0.5 (best 0.43); drawn: the largest overlapping prediction, 2215 pts = 2.0× the GT at IoU 0.42 (b) uncovered translation — 88627b · gt 2076 · 224 pts rank 45 of 89 by n_gt | nothing reaches IoU 0.5 (best 0.11); drawn: the largest overlapping prediction, 5270 pts = 23.5× the GT at IoU 0.03 (c) axis gate — 1366d5 · gt 1009 · 1442 pts rank 7 of 14 by axis_err | drawn: the highest-confidence covering prediction, IoU 0.73 · axis 89.5° > 15° gate (d) origin gate — e91722 · gt 1012 · 2390 pts rank 7 of 14 by axp_line | drawn: the highest-confidence axis- passing prediction, IoU 0.78 · axis 0.0° PASS · origin 0.32 m > 0.25 m gate (e) Track 2 — smallest-quartile miss — 55b2bf · handle 35 · 8 pts rank 38 of 75 by n_gt | nothing reaches IoU 0.5 (best 0.12); drawn: the largest overlapping prediction, 349 pts = 43.6× the GT at IoU 0.02 (f) Track 2 — oversized prediction — 5e7c2 · handle 14 · 46 pts rank 19 of 37 by ratio | nothing reaches IoU 0.5 (best 0.16); drawn: the largest overlapping prediction, 188 pts = 4.1× the GT at IoU 0.16 G8 — one specimen per failure bucket of the released outputs, at the median of each bucket's own statistic. Dark: the GT part the evaluator scored. Red: the one prediction each panel names. Black line: the GT motion axis; dashed red: the predicted axis; red segment: the distance the origin gate tests. Denominators, reproduced from the dumps by this producer and asserted against RESULTS_e_census_released.md before drawing: of 390 GT movable instances, 139 (35.6 %) are never covered at IoU 0.5 — 50 rotations of 236 and 89 translations of 154 — against 14 charged to the axis gate and 14 to the origin gate, and 223 scored. Coverage is the whole story and it is a translation story, and panels (a) and (b) are why: the median uncovered rotation still reaches IoU 0.30 on its best prediction, the median uncovered translation only 0.10 — drawers are not near misses. Both motion buckets are near misses instead: ALL 12 of the axis bucket's rotations are non- vertical hinges against a rule that emits world-Z (its other 2 members are translations, whose GT axes are also off-vertical), and 12 of the 14 origin failures lie between 0.26 and 0.41 m against a 0.25 m gate. On Track 2, 193 of 388 GT handles are covered; the smallest quartile (≤ 11 pts) is covered 22.7 % of the time and 38 of its 75 misses have no overlapping prediction at all, while the largest quartile drops back to 57.3 % with 37 of 96 carrying an overlapping prediction at least 2× their size. Specimen ranks are stated per panel; ties break by scene id then instance id. (a) uncovered rotation — 9071e1 · gt 1011 · 1131 pts rank 25 of 50 by n_gt | nothing reaches IoU 0.5 (best 0.43); drawn: the largest overlapping prediction, 2215 pts = 2.0× the GT at IoU 0.42 (b) uncovered translation — 88627b · gt 2076 · 224 pts rank 45 of 89 by n_gt | nothing reaches IoU 0.5 (best 0.11); drawn: the largest overlapping prediction, 5270 pts = 23.5× the GT at IoU 0.03 (c) axis gate — 1366d5 · gt 1009 · 1442 pts rank 7 of 14 by axis_err | drawn: the highest-confidence covering prediction, IoU 0.73 · axis 89.5° > 15° gate (d) origin gate — e91722 · gt 1012 · 2390 pts rank 7 of 14 by axp_line | drawn: the highest-confidence axis- passing prediction, IoU 0.78 · axis 0.0° PASS · origin 0.32 m > 0.25 m gate (e) Track 2 — smallest-quartile miss — 55b2bf · handle 35 · 8 pts rank 38 of 75 by n_gt | nothing reaches IoU 0.5 (best 0.12); drawn: the largest overlapping prediction, 349 pts = 43.6× the GT at IoU 0.02 (f) Track 2 — oversized prediction — 5e7c2 · handle 14 · 46 pts rank 19 of 37 by ratio | nothing reaches IoU 0.5 (best 0.16); drawn: the largest overlapping prediction, 188 pts = 4.1× the GT at IoU 0.16 G8 — one specimen per failure bucket of the released outputs, at the median of each bucket's own statistic. Dark: the GT part the evaluator scored. Red: the one prediction each panel names. Black line: the GT motion axis; dashed red: the predicted axis; red segment: the distance the origin gate tests. Denominators, reproduced from the dumps by this producer and asserted against RESULTS_e_census_released.md before drawing: of 390 GT movable instances, 139 (35.6 %) are never covered at IoU 0.5 — 50 rotations of 236 and 89 translations of 154 — against 14 charged to the axis gate and 14 to the origin gate, and 223 scored. Coverage is the whole story and it is a translation story, and panels (a) and (b) are why: the median uncovered rotation still reaches IoU 0.30 on its best prediction, the median uncovered translation only 0.10 — drawers are not near misses. Both motion buckets are near misses instead: ALL 12 of the axis bucket's rotations are non- vertical hinges against a rule that emits world-Z (its other 2 members are translations, whose GT axes are also off-vertical), and 12 of the 14 origin failures lie between 0.26 and 0.41 m against a 0.25 m gate. On Track 2, 193 of 388 GT handles are covered; the smallest quartile (≤ 11 pts) is covered 22.7 % of the time and 38 of its 75 misses have no overlapping prediction at all, while the largest quartile drops back to 57.3 % with 37 of 96 carrying an overlapping prediction at least 2× their size. Specimen ranks are stated per panel; ties break by scene id then instance id. Origin-gate failure Median line error, rank 7/14 Smallest-quartile handle miss Median size, rank 38/75 Over-extended handle Median size ratio, rank 19/37 (a) uncovered rotation — 9071e1 · gt 1011 · 1131 pts rank 25 of 50 by n_gt | nothing reaches IoU 0.5 (best 0.43); drawn: the largest overlapping prediction, 2215 pts = 2.0× the GT at IoU 0.42 (b) uncovered translation — 88627b · gt 2076 · 224 pts rank 45 of 89 by n_gt | nothing reaches IoU 0.5 (best 0.11); drawn: the largest overlapping prediction, 5270 pts = 23.5× the GT at IoU 0.03 (c) axis gate — 1366d5 · gt 1009 · 1442 pts rank 7 of 14 by axis_err | drawn: the highest-confidence covering prediction, IoU 0.73 · axis 89.5° > 15° gate (d) origin gate — e91722 · gt 1012 · 2390 pts rank 7 of 14 by axp_line | drawn: the highest-confidence axis- passing prediction, IoU 0.78 · axis 0.0° PASS · origin 0.32 m > 0.25 m gate (e) Track 2 — smallest-quartile miss — 55b2bf · handle 35 · 8 pts rank 38 of 75 by n_gt | nothing reaches IoU 0.5 (best 0.12); drawn: the largest overlapping prediction, 349 pts = 43.6× the GT at IoU 0.02 (f) Track 2 — oversized prediction — 5e7c2 · handle 14 · 46 pts rank 19 of 37 by ratio | nothing reaches IoU 0.5 (best 0.16); drawn: the largest overlapping prediction, 188 pts = 4.1× the GT at IoU 0.16 G8 — one specimen per failure bucket of the released outputs, at the median of each bucket's own statistic. Dark: the GT part the evaluator scored. Red: the one prediction each panel names. Black line: the GT motion axis; dashed red: the predicted axis; red segment: the distance the origin gate tests. Denominators, reproduced from the dumps by this producer and asserted against RESULTS_e_census_released.md before drawing: of 390 GT movable instances, 139 (35.6 %) are never covered at IoU 0.5 — 50 rotations of 236 and 89 translations of 154 — against 14 charged to the axis gate and 14 to the origin gate, and 223 scored. Coverage is the whole story and it is a translation story, and panels (a) and (b) are why: the median uncovered rotation still reaches IoU 0.30 on its best prediction, the median uncovered translation only 0.10 — drawers are not near misses. Both motion buckets are near misses instead: ALL 12 of the axis bucket's rotations are non- vertical hinges against a rule that emits world-Z (its other 2 members are translations, whose GT axes are also off-vertical), and 12 of the 14 origin failures lie between 0.26 and 0.41 m against a 0.25 m gate. On Track 2, 193 of 388 GT handles are covered; the smallest quartile (≤ 11 pts) is covered 22.7 % of the time and 38 of its 75 misses have no overlapping prediction at all, while the largest quartile drops back to 57.3 % with 37 of 96 carrying an overlapping prediction at least 2× their size. Specimen ranks are stated per panel; ties break by scene id then instance id. (a) uncovered rotation — 9071e1 · gt 1011 · 1131 pts rank 25 of 50 by n_gt | nothing reaches IoU 0.5 (best 0.43); drawn: the largest overlapping prediction, 2215 pts = 2.0× the GT at IoU 0.42 (b) uncovered translation — 88627b · gt 2076 · 224 pts rank 45 of 89 by n_gt | nothing reaches IoU 0.5 (best 0.11); drawn: the largest overlapping prediction, 5270 pts = 23.5× the GT at IoU 0.03 (c) axis gate — 1366d5 · gt 1009 · 1442 pts rank 7 of 14 by axis_err | drawn: the highest-confidence covering prediction, IoU 0.73 · axis 89.5° > 15° gate (d) origin gate — e91722 · gt 1012 · 2390 pts rank 7 of 14 by axp_line | drawn: the highest-confidence axis- passing prediction, IoU 0.78 · axis 0.0° PASS · origin 0.32 m > 0.25 m gate (e) Track 2 — smallest-quartile miss — 55b2bf · handle 35 · 8 pts rank 38 of 75 by n_gt | nothing reaches IoU 0.5 (best 0.12); drawn: the largest overlapping prediction, 349 pts = 43.6× the GT at IoU 0.02 (f) Track 2 — oversized prediction — 5e7c2 · handle 14 · 46 pts rank 19 of 37 by ratio | nothing reaches IoU 0.5 (best 0.16); drawn: the largest overlapping prediction, 188 pts = 4.1× the GT at IoU 0.16 G8 — one specimen per failure bucket of the released outputs, at the median of each bucket's own statistic. Dark: the GT part the evaluator scored. Red: the one prediction each panel names. Black line: the GT motion axis; dashed red: the predicted axis; red segment: the distance the origin gate tests. Denominators, reproduced from the dumps by this producer and asserted against RESULTS_e_census_released.md before drawing: of 390 GT movable instances, 139 (35.6 %) are never covered at IoU 0.5 — 50 rotations of 236 and 89 translations of 154 — against 14 charged to the axis gate and 14 to the origin gate, and 223 scored. Coverage is the whole story and it is a translation story, and panels (a) and (b) are why: the median uncovered rotation still reaches IoU 0.30 on its best prediction, the median uncovered translation only 0.10 — drawers are not near misses. Both motion buckets are near misses instead: ALL 12 of the axis bucket's rotations are non- vertical hinges against a rule that emits world-Z (its other 2 members are translations, whose GT axes are also off-vertical), and 12 of the 14 origin failures lie between 0.26 and 0.41 m against a 0.25 m gate. On Track 2, 193 of 388 GT handles are covered; the smallest quartile (≤ 11 pts) is covered 22.7 % of the time and 38 of its 75 misses have no overlapping prediction at all, while the largest quartile drops back to 57.3 % with 37 of 96 carrying an overlapping prediction at least 2× their size. Specimen ranks are stated per panel; ties break by scene id then instance id. (a) uncovered rotation — 9071e1 · gt 1011 · 1131 pts rank 25 of 50 by n_gt | nothing reaches IoU 0.5 (best 0.43); drawn: the largest overlapping prediction, 2215 pts = 2.0× the GT at IoU 0.42 (b) uncovered translation — 88627b · gt 2076 · 224 pts rank 45 of 89 by n_gt | nothing reaches IoU 0.5 (best 0.11); drawn: the largest overlapping prediction, 5270 pts = 23.5× the GT at IoU 0.03 (c) axis gate — 1366d5 · gt 1009 · 1442 pts rank 7 of 14 by axis_err | drawn: the highest-confidence covering prediction, IoU 0.73 · axis 89.5° > 15° gate (d) origin gate — e91722 · gt 1012 · 2390 pts rank 7 of 14 by axp_line | drawn: the highest-confidence axis- passing prediction, IoU 0.78 · axis 0.0° PASS · origin 0.32 m > 0.25 m gate (e) Track 2 — smallest-quartile miss — 55b2bf · handle 35 · 8 pts rank 38 of 75 by n_gt | nothing reaches IoU 0.5 (best 0.12); drawn: the largest overlapping prediction, 349 pts = 43.6× the GT at IoU 0.02 (f) Track 2 — oversized prediction — 5e7c2 · handle 14 · 46 pts rank 19 of 37 by ratio | nothing reaches IoU 0.5 (best 0.16); drawn: the largest overlapping prediction, 188 pts = 4.1× the GT at IoU 0.16 G8 — one specimen per failure bucket of the released outputs, at the median of each bucket's own statistic. Dark: the GT part the evaluator scored. Red: the one prediction each panel names. Black line: the GT motion axis; dashed red: the predicted axis; red segment: the distance the origin gate tests. Denominators, reproduced from the dumps by this producer and asserted against RESULTS_e_census_released.md before drawing: of 390 GT movable instances, 139 (35.6 %) are never covered at IoU 0.5 — 50 rotations of 236 and 89 translations of 154 — against 14 charged to the axis gate and 14 to the origin gate, and 223 scored. Coverage is the whole story and it is a translation story, and panels (a) and (b) are why: the median uncovered rotation still reaches IoU 0.30 on its best prediction, the median uncovered translation only 0.10 — drawers are not near misses. Both motion buckets are near misses instead: ALL 12 of the axis bucket's rotations are non- vertical hinges against a rule that emits world-Z (its other 2 members are translations, whose GT axes are also off-vertical), and 12 of the 14 origin failures lie between 0.26 and 0.41 m against a 0.25 m gate. On Track 2, 193 of 388 GT handles are covered; the smallest quartile (≤ 11 pts) is covered 22.7 % of the time and 38 of its 75 misses have no overlapping prediction at all, while the largest quartile drops back to 57.3 % with 37 of 96 carrying an overlapping prediction at least 2× their size. Specimen ranks are stated per panel; ties break by scene id then instance id. Figure 10. Different failure mechanisms on validation. Dark points show ground truth and pale red the displayed prediction; black denotes the annotated hinge where applicable. Each panel is a deterministic median-rank specimen of its named stratum. Missed rotations and translations have different overlap patterns; the horizontal hinge violates the rotational axis prior; a covered panel can still fail the origin gate. Small and over-extended handle failures illustrate distinct localization problems. The gallery explains mechanisms rather than estimating their frequency. 24