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A Functional Pilot for Certified Freshness-Aware Semantic--Spatial Range Retrieval

Taimoor Ahmad

Year: 2026Venue: arXiv preprintArea: cs.DBType: PreprintEmbeddings: 63

Intelligence

Status: succeeded | Model: Gemma-4-26B-A4B | Prompt: intel-v1 | Confidence: 91%

Last extracted: 9/23/2026, 3:43:07 AM

Summary

The paper introduces FRESH-GEORANGE, a semantic-spatial range retrieval system designed to provide certified completeness for geographic queries with semantic thresholds. Unlike approximate top-k systems, it ensures all qualifying objects within a radius and similarity threshold are returned, distinguishing between source-watermark freshness and record age. The system uses geographic cells, semantic microblocks, and an ANN graph for verification ordering, supporting both exact mode (100% recall) and certified mode (deterministic recall lower bound). A CPU pilot demonstrates feasibility but highlights performance trade-offs, noting that certified mode is slower than exact baselines.

Entities (10)

FRESH-GEORANGE · system · 100%Certified Mode · feature · 95%Exact Mode · feature · 95%HNSW · algorithm · 90%OpenFlights · dataset · 90%Semantic Microblocks · data-structure · 90%Visibility Watermark · concept · 90%LIST · system · 85%Mesh · system · 85%WISK · system · 85%

Relation Signals (9)

Certified Mode → achievesrecall → 99.91%

confidence 95% · The 95-percent mode achieved 99.91% empirical mean recall

Exact Mode → achievesrecall → +10,000%

confidence 95% · Exact mode achieved 100.00% set recall on every query.

FRESH-GEORANGE → supports → Exact Mode

confidence 95% · Exact mode scans every nonprunable block and the delta overlay.

FRESH-GEORANGE → supports → Certified Mode

confidence 95% · Certified mode may stop early and reports a deterministic query-specific recall lower bound

FRESH-GEORANGE → uses → Semantic Microblocks

confidence 95% · Geographic cells and semantic microblocks provide admissible pruning bounds

FRESH-GEORANGE → evaluateson → OpenFlights

confidence 90% · A reproducible CPU pilot uses 2,500 real OpenFlights airport records

HNSW → foundationfor → ANN Systems

confidence 90% · HNSW supplies the graph-search foundation used by many ANN systems

Mesh → comparedto → FRESH-GEORANGE

confidence 85% · Mesh directly combines a true spatial range with vector ANN... making it the closest integrated vector baseline

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Abstract

Abstract:Geographic applications need every object inside a radius that satisfies a semantic threshold, yet embedding indexes return approximate top-ranked lists and may omit qualifying records silently. We present FRESH-GEORANGE, a semantic- spatial range design that separates source-watermark freshness from optional record age. Geographic cells and semantic mi- croblocks provide admissible pruning bounds; a graph proposes verification order but supplies no correctness evidence. Exact mode scans every nonprunable block and the delta overlay. Certified mode may stop early and reports a deterministic query- specific recall lower bound from verified answers and unresolved records. A reproducible CPU pilot uses 2,500 real OpenFlights airport records, a 2,000-record base, and 740 simulated insert, delete, and text-revision events; it evaluates 180 unique queries over five seeds. Exact mode achieved 100.00% set recall on every query. The 95-percent mode achieved 99.91% empirical mean recall with a 99.41% reported mean certificate and no observed bound violation. However, its 7.24 ms median latency was 5.85 times the 1.24 ms spatial-first exact baseline, and full-history delta replay became slower than rebuilding at larger batches. The prototype therefore validates the completeness mechanism, not performance superiority or production freshness. Submission- scale evaluation requires real map diffs, official recent baselines, and truly incremental versioned maintenance.

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A Functional Pilot for Certified Freshness-Aware Semantic–Spatial Range Retrieval Taimoor Ahmed †thanks: Superior University Lahore, Pakistan Abstract Geographic applications need every object inside a radius that satisfies a semantic threshold, yet embedding indexes return approximate top-ranked lists and may omit qualifying records silently. We present FRESH-GEORANGE, a semantic-spatial range design that separates source-watermark freshness from optional record age. Geographic cells and semantic microblocks provide admissible pruning bounds; a graph proposes verification order but supplies no correctness evidence. Exact mode scans every nonprunable block and the delta overlay. Certified mode may stop early and reports a deterministic query-specific recall lower bound from verified answers and unresolved records. A reproducible CPU pilot uses 2,500 real OpenFlights airport records, a 2,000-record base, and 740 simulated insert, delete, and text-revision events; it evaluates 180 unique queries over five seeds. Exact mode achieved 100.00% set recall on every query. The 95-percent mode achieved 99.91% empirical mean recall with a 99.41% reported mean certificate and no observed bound violation. However, its 7.24 ms median latency was 5.85 times the 1.24 ms spatial-first exact baseline, and full-history delta replay became slower than rebuilding at larger batches. The prototype therefore validates the completeness mechanism, not performance superiority or production freshness. Submission-scale evaluation requires real map diffs, official recent baselines, and truly incremental versioned maintenance. Index Terms: semantic–spatial retrieval, range reporting, freshness watermark, certified recall, dynamic index, exact verification I Introduction Location-aware search increasingly depends on meanings beyond literal keyword overlap. A request for “emergency treatment for a severe allergic reaction” should retrieve a nearby facility advertising “anaphylaxis services.” Learned systems support such matches by embedding queries and points of interest (POIs). LIST couples learned routing with embedding relevance [1, 2], while Mesh integrates geographic range constraints with high-dimensional approximate nearest-neighbor (ANN) search [3]. Both target a ranked top-k list. Operational tasks such as emergency-resource discovery and regulatory auditing instead need threshold enumeration—every active object inside a stated radius whose semantic similarity reaches a threshold. The caller must know whether the returned list is exhaustive, rather than merely well ranked; an incomplete top-k list cannot safely represent that set [4]. For top-k, ANN may stop after collecting enough competitive candidates. Under a threshold, cardinality is unknown and every skipped partition could hide an answer. Exact rescoring removes false positives but cannot recover unseen positives; it certifies precision, not completeness. A valid certificate must therefore account for partitions that heuristic traversal never reaches, not infer completeness from the retrieved candidates. Range-complete foundations include Boolean radius engines [5], WISK’s learned partitions for exact region-and-keyword processing [6], and geographic-radius enumeration under a Jaccard threshold [7]. Word2Vec has also been used for continuous spatial range processing [8, 2, 9]. These interfaces do not jointly define dense-semantic threshold enumeration, versioned visibility, and a query-specific completeness certificate. Mutability creates a second gap. POI catalogs receive insertions, deletions, and text revisions continually, so an answer may be correct for an old index but wrong for the promised version. Per-edit rebuilding is costly; periodic rebuilding hides new resources and can resurrect deleted ones between rebuilds. Dynamic spatial–keyword systems maintain queries as objects change [10, 11, 12], while vector systems support streaming or incremental maintenance [13, 14, 15]. LIST is not purely static: it supports cluster-assigned insertion, deletion, and index-only retraining after sustained inserts or distribution shift [1, 16]. It nevertheless remains top-k and supplies no radius-plus-threshold completeness contract. We therefore distinguish an update-visibility watermark, a correctness promise about reflected commits, from optional record-age semantics, an application predicate over old observations. A recent observation can be absent behind a stale watermark, while an old observation can be fully visible; treating both as one “freshness” value obscures correctness. FRESH-GEORANGE addresses this conjunction. Its query specifies a location, radius, semantic vector, similarity threshold, and maximum visibility lag. The index combines geographic cells, semantic microblocks with admissible cosine bounds, an ANN graph used only to order work, and a latest-write delta overlay for inserts, replacements, and tombstones. A watermark identifies the visible snapshot. Exact mode visits every non-prunable spatially relevant block and scans the entire visible delta. Certified mode may stop earlier, but conservatively counts unresolved physical records and derives a deterministic per-query recall lower bound from that count and the verified positives. Tombstones and replacements suppress superseded base versions, and the delta and watermark are published atomically. Approximation therefore changes cost and certificate tightness, not the truth of the bound. The closest adjacent field is range-filtered ANN (RFANN), which restricts dense-vector top-k search by an interval on one ordered attribute. SeRF and iRangeGraph optimize static filters [17, 18, 19]; Dynamic RFANNS, DIGRA, RangePQ, and WoW add dynamic or incremental maintenance [20, 21, 22, 23]. Yet an interval is not a two-dimensional geodesic disk, and approximate top-k is not threshold enumeration. Mapping a disk to longitude intervals or a space-filling key introduces different selectivity and boundary behavior. Vector-radius retrieval approximately reports all vectors within an embedding distance but lacks a geographic predicate and mutable snapshot [24]. ConANN provides a distribution-free conformal risk guarantee for ANN [25]; our target is instead deterministic, bound-based accounting for one declared snapshot. We claim novelty only for this conjunction, not for any ingredient alone. We refer to this setting as semantic–spatial range retrieval, where the objective is not to return a fixed number of highly ranked objects, but to enumerate the complete set of objects satisfying both a geographic range constraint and a semantic-similarity threshold [24]. This distinction is important because the number of qualifying objects is unknown before execution: a query may have no matches, a few matches, or hundreds of matches within the same radius. Consequently, conventional approximate nearest-neighbor search can miss qualifying objects that were never examined, even when all retrieved candidates are subsequently verified exactly [9, 26, 27, 28]. We therefore use completeness to mean that every object satisfying the declared predicates is represented in the returned set. Dynamic data introduce an additional dimension, because completeness must be defined relative to a particular visible database state. We call the latest committed source position reflected by the index the visibility watermark, while record age describes the age of an individual stored observation; the two notions are intentionally separate. Finally, a recall certificate denotes a deterministic, query-specific lower bound on the fraction of qualifying objects that have been returned when execution terminates before exhaustive verification. In our CPU pilot, exact mode attains 100.00% mean recall and certified mode attains 99.91% with a 99.41% mean lower bound; however, certified retrieval costs 5.85× the median latency of spatial-first exact scanning. This negative result supports feasibility of the guarantee, not deployment superiority. This paper makes three contributions: • We formalize fresh semantic–spatial range enumeration: all visible POIs inside a geodesic radius and above a dense-similarity threshold, under an explicit update-watermark contract that distinguishes visibility lag from record age. • We design a dual spatial–semantic index with a latest-write delta overlay, atomic watermark publication, and safe geometric and cosine bounds. Its ANN component only prioritizes verification; exact mode exhausts every non-prunable block, while certified mode returns a sound query-specific recall lower bound after exact delta scanning. • We provide a reproducible CPU pilot that evaluates set recall and precision, certificate validity and tightness, tail latency, complete-history replay cost, staleness, scripted drift instrumentation, selectivity, and ablations under deterministic insertion, deletion, and text-revision streams, and we state the evidence still required for a submission-scale claim. The remainder of the paper is organized as follows. Section I positions the problem against spatial–textual, filtered-vector, and dynamic indexes. Section I formulates the query and presents the index, update contract, and certification argument. Section IV describes the reproducible pilot and reports its results and limitations. Section V concludes. I Related Work Spatial–textual retrieval. Classical structures combine a spatial hierarchy with an inverted text index. The IR-tree is a representative design for geographic document search [29]; later main-memory processing supports point-plus-radius Boolean queries with perfect result recall [5]. WISK learns workload-aware spatial partitions while preserving exact keyword-query processing and buffers insertions before localized retraining [6]. Tampakis et al. are especially close because their filter–refine index returns every object inside a radius whose keyword-set Jaccard similarity exceeds a threshold [7]. FRESH-GEORANGE changes the semantic predicate from a sparse token-set measure to dense cosine similarity and couples it to a mutable-snapshot certificate; it does not treat threshold range completeness itself as new. Embedding-aware spatial retrieval has mainly evolved around ranking. The S2RS^2R-tree uses semantic pivots for spatial keyword search [30], DrW develops neural relevance modeling [31], and LIST jointly learns object/query representations, cluster routing, and spatial relevance for embedding-based top-k spatial keyword queries [1]. LIST explicitly supports insertion, deletion, and index-only retraining; calling it static would erase a material capability. What it does not offer is all-object output under both a geographic radius and a similarity threshold, nor a per-query lower bound that accounts for work not visited. Mesh directly combines a true spatial range with vector ANN [3], making it the closest integrated vector baseline, but still returns approximate top-k results. Oh et al. maintain Word2Vec-based range results over moving objects [8]; FAST, Salgado et al., and Dong et al. likewise establish that continuous and dynamic spatial–keyword processing is mature [10, 12, 11]. Their motion, Boolean, or top-k semantics differ from versioned POI create/delete/text-replace operations with a declared visibility watermark. TABLE I: Closest-work landscape. “All” means threshold/range enumeration rather than a fixed top-k list; guarantees are characterized by what the cited interface establishes. FRESH-GEORANGE’s proposed novelty is the conjunction in the last row. System Spatial filter Semantic model Output Update model Recall/completeness evidence Lee et al. [5] 2-D point radius Boolean keywords All Not central Perfect result recall Tampakis et al. [7] 2-D radius Jaccard threshold All Static Exact filter–refine Oh et al. [8] 2-D range Word2Vec Range results Moving objects No query certificate established WISK [6] 2-D region Boolean keywords All Buffered inserts; local retraining Exact keyword processing Dong et al. [11] Spatial proximity Keyword relevance Top-k Dynamic objects Maintained top-k semantics LIST [1] Learned spatial relevance Dense embeddings Top-k Insert; delete; index-only retraining Empirical top-k effectiveness Mesh [3] 2-D spatial range Dense vectors Approximate top-k Static Empirical ANN recall Vector-radius retrieval [24] None Vector-distance radius Approximate all Static Empirical reporting recall SeRF [17] Scalar interval Dense vectors Approximate top-k Static Empirical ANN recall iRangeGraph [18] Scalar interval Dense vectors Approximate top-k Static Empirical ANN recall Dynamic RFANNS [20] Scalar interval Dense vectors Approximate top-k Dynamic Empirical ANN recall DIGRA [21] Scalar interval Dense vectors Approximate top-k Dynamic graph Empirical ANN recall RangePQ [22] Scalar interval Dense vectors Approximate top-k Dynamic quantization index Empirical ANN recall WoW [23] Scalar window Dense vectors Approximate top-k Incremental insert-from-empty Empirical ANN recall FRESH-GEORANGE 2-D geodesic radius Dense threshold All / certified Versioned insert, delete, replace Exact mode or deterministic per-query lower bound Filtered and range-reporting vector search. Filtered-DiskANN demonstrates graph search with categorical filters [32]; SeRF, iRangeGraph, UNIFY, and window-filter methods exploit ordered filter structure [17, 18, 33, 34]. More recent work makes the filtered index mutable: Dynamic RFANNS, DIGRA, and RangePQ address changing data [20, 21, 22], while WoW is a fully incremental insert-from-empty design but leaves frequent deletion and in-place update as open concerns [23]. These methods inform graph routing, segment organization, and update engineering. Their conventional query asks for the nearest k vectors satisfying a one-dimensional range, however; adapting longitude or a space-filling key to that interface does not faithfully represent a circular geographic predicate. Manohar et al. instead study approximate reporting of every vector within a vector-distance radius [24], which is the direct threshold-output precedent, but lacks a geographic constraint, snapshot visibility, and deterministic accounting of missed objects. Freshness, drift, and guarantees. HNSW supplies the graph-search foundation used by many ANN systems [35], but benchmark recall remains an empirical aggregate. SPFresh performs incremental in-place vector-index updates [13]; VStream addresses distributed streaming search [14]; and Quake adapts partitioning and predicts parameters for requested recall levels under changing workloads [15]. These systems motivate delta maintenance and drift-triggered consolidation, not the certificate itself. ConANN provides an important formal counterpoint by controlling ANN risk with distribution-free conformal methods [25]. Its statistical guarantee and assumptions differ from a deterministic statement about one radius-and-threshold result set. In FRESH-GEORANGE, admissible block bounds and a conservative count of every unresolved visible record yield the certificate; learned routing and ANN traversal may reduce work but are never trusted as proof. Table I summarizes why no individual ingredient is unprecedented and why the proposed contribution must be evaluated as a conjunction. I Method I-A Problem Formulation Unlike top-k search, our threshold query must return every live object that passes its spatial, semantic, and freshness predicates. Define xi x_i =(i,νi,pi,vi,ai,oi), =(i, _i,p_i,v_i,a_i,o_i), (1) Q Q =(ℓ,r,q,τ,tq,Amax,Δmax,ρreq). =( ,r,q,τ,t_q,A_ , _ , _ req). where pip_i is a location, vi∈ℝdv_i ^d a unit embedding, aia_i an observation day, and oio_i an upsert or delete (whose non-key fields may be absent). Sequence νi _i totally orders an identifier’s events. Query Q specifies center, radius r≥0r≥ 0, unit vector, inclusive cosine threshold τ∈[−1,1]τ∈[-1,1], time, maximum record age and watermark lag, and requested certificate ρreq∈[0,1] _ req∈[0,1] (Table I). TABLE I: Notation. Time is represented by integer replay day in the pilot. Symbol Meaning Symbol Meaning i stable object identifier νi _i totally ordered event sequence pi,ℓp_i, object and query locations vi,qv_i,q unit object and query vectors d embedding dimension r inclusive range radius τ inclusive cosine threshold tqt_q query day aia_i object observation day AmaxA_ maximum object age W committed source watermark Δmax _ maximum watermark lag B,DWB,D_W immutable base and current delta ℒWL_W live view at W C,bC,b spatial cell and semantic block LCpL_C^p spatial lower bound Ubs,UbaU_b^s,U_b^a semantic and age upper bounds U unexamined, possible blocks A A verified returned identifiers MremM_ rem residual physical-slot count ρreq _ req requested certified recall DtD_t drift statistic Exact verification uses great-circle distance, cosine similarity, and age; exponential freshness is only a monotone reparameterization: di d_i =dgeo(pi,ℓ), =d_ geo(p_i, ), si s_i =q⊤vi, =q v_i, (2) gi g_i =(tq−ai)+, =(t_q-a_i)_+, ϕi(tq) _i(t_q) =exp⁡(−λgi). = (-λ g_i). The implementation uses gi≤Amaxg_i≤ A_ , equivalent for λ>0λ>0 to ϕi≥exp⁡(−λAmax) _i≥ (-λ A_ ), but never multiplies similarity by decay. Record age and source currency obey distinct contracts: 0≤tq−W≤Δmax,gi≤Amax.0≤ t_q-W≤ _ , g_i≤ A_ . (3) The first concerns completeness of the captured source prefix; the second filters a stored observation day. Neither proves recent physical inspection. Pilot observation/event days are deterministic experimental attributes, not historical OSM edits, so freshness claims apply only to the replay. At watermark W, the range-complete answer is AW∗(Q)=i∈ℒW:di≤r,si≥τ,tq−ai≤Amax.A_W^*(Q)=\i _W:\ d_i≤ r,\ s_i≥τ,\ t_q-a_i≤ A_ \. (4) All predicates are inclusive; subsequent ranking cannot alter membership. I-B Index and Current-View Semantics FRESH-GEORANGE separates an immutable base from a mutable replacement delta. For the general event model, latest-write-wins semantics are eiW e_i^W =arg⁡maxe∈B∪D≤W:e.i=ie.ν, = e∈ B∪ D_≤ W:e.i=i \ e.ν, (5) ℒW _W =eiW:eiW.o=. =\e_i^W:e_i^W.o= upsert\. The pilot is narrower: apply_events replays the complete prefix to a private one-value-per-ID dictionary, whose final sequence-ordered value is an upsert or tombstone. It atomically publishes that dictionary and W under a re-entrant lock; queries hold the lock throughout. Dictionary membership hides an old base copy. Building privately leaves readers on the preceding complete state, while publishing W before the dictionary would invalidate the proof. Thus calls are serializable, but there is no retained MVCC, lock-free reading, or durable recovery: tq<Wt_q<W and tq−W>Δmaxt_q-W> _ are rejected. Past-prefix republication is an evaluation operation, not a historical query. Inputs must have complete, deterministic sequences. The pilot generator produces a unique, gap-free sequence; malformed or conflicting external sequences are outside the implemented contract. Figure 1 separates the current-view path from scripted drift feedback: the graph orders work; safe summaries and full delta scanning support correctness. Pinned day-30 base snapshot Complete replay prefix of events E≤WE_≤ W Range query (ℓ,r,q,τ)( ,r,q,τ); (tq,Amax,Δmax)(t_q,A_ , _ ) 10∘10 cells and semantic micro-blocks Exact-kkNN graph approximate proposer Private full-prefix delta reconstruction Watermark-lag check record-age check Immutable base view arrays + summaries exact-kkNN proposer Atomic locked publication of (DW,W)(D_W,W) One locked current query view: base index, (DW,W)(D_W,W), and validated Q Safe base pruning spatial + semantic + age Exact scan of every delta value Ordered exact base verification (graph first) Deduplicated verified IDs and physical residual count Scripted JSD monitor day 50: rebuild if JSD >0.05>0.05 Exact set Mrem=0M_ rem=0, certificate 11 Certified set A A and lower bound R¯ R Fig. 1: FRESH-GEORANGE pilot architecture. Solid arrows are implemented data or query paths. The dashed path is the scripted drift experiment: it performs a full rebuild at a fixed checkpoint, not continuous retraining, partial repartitioning, or the benefit-aware policy in Eq. (14). The day-30 base alone fits a deterministic 48-D word/character TF–IDF–SVD encoder. Normalized vectors are grouped by fixed 10∘10 cells and approximately 64-record semantic blocks; dense record arrays remain the verification authority. A brute-built exact-kkNN graph is traversed approximately only to propose base records—it is not HNSW or evidence of absence. Every current delta value is scanned, so unseen insertions remain discoverable. A replacement or tombstone hides its physical base slot; this auditable design trades delta latency for safety. For cell C, let cCpc_C^p be its center and let ρCp _C^p cover the complete cell region under the declared great-circle metric. The implementation uses a meridian-then-parallel path with the parallel length evaluated at the cell latitude closest to the equator. The triangle inequality yields LCp(ℓ) L_C^p( ) =max⁡0,dgeo(ℓ,cCp)−ρCp, = \0,d_ geo( ,c_C^p)- _C^p\, (6) UCp(ℓ) U_C^p( ) =dgeo(ℓ,cCp)+ρCp. =d_ geo( ,c_C^p)+ _C^p. Hence LCp>rL_C^p>r safely eliminates a cell, including near poles or the date line. For each base block b, store the arithmetic center cbc_b, radius ρb=maxi∈b⁡∥vi−cb∥2 _b= _i∈ b v_i-c_b _2, normalized center μb=cb/∥cb∥2 _b=c_b/ c_b _2 when the norm is nonzero (one member vector is used otherwise), and angular radius θb=maxi∈b⁡arccos⁡(μb⊤vi) _b= _i∈ b ( _b v_i). Cauchy–Schwarz and the spherical triangle inequality give two independent safe upper bounds: Ubball(q) U_b ball(q) =min⁡1,q⊤cb+ρb, = \1,q c_b+ _b\, (7) ηb(q) _b(q) =max⁡0,arccos⁡(clip⁡(q⊤μb,−1,1))−θb, = \0, (clip(q _b,-1,1))- _b\, Ubang(q) U_b ang(q) =cos⁡(ηb(q)), = ( _b(q)), Ubs(q) U_b^s(q) =min⁡Ubball(q),Ubang(q). = \U_b ball(q),U_b ang(q)\. Clip arccos arguments to [−1,1][-1,1]. Both components upper-bound every block dot product, so their minimum is safe. For abmax=maxi∈b⁡aia_b = _i∈ ba_i, age requires Uba=abmax,Uba≥tq−Amax.U_b^a=a_b , U_b^a≥ t_q-A_ . (8) A fixed outward margin protects bounds; verification uses float64. Pruning is only a disjunction of necessary-condition failures: prune⁡(b,Q)⇔ (b,Q) LC⁡(b)p(ℓ)>r∨Ubs(q)<τ L_C(b)^p( )>r\ \ U_b^s(q)<τ (9) ∨Uba<tq−Amax. \ U_b^a<t_q-A_ . No learned score prunes. Immutable base blocks and a full delta scan avoid dynamic radius expansion in this pilot. For any i∈bi∈ b, q⊤vi=q⊤cb+q⊤(vi−cb)≤q⊤cb+ρbq v_i=q c_b+q (v_i-c_b)≤ q c_b+ _b because ∥q∥2=1 q _2=1. Spherical triangle inequality gives angle at least ∠⁡(q,μb)−θb (q, _b)- _b; cosine decreases on [0,π][0,π]. Metric triangle inequality proves (6). Therefore loose summaries admit false positives but cannot prune true members, assuming normalized nonzero vectors and the outward margin. Sampled bound audits check implementation maxima but do not replace this proof. I-C Exact and Certified Execution Algorithm 1 describes exact mode as implemented. Graph traversal only changes the order of some checks; completion scans every unexamined slot in every non-pruned base block. Each candidate is checked for delta shadowing, hard age, exact dot product, and exact great-circle distance. Algorithm 1 Exact-Range(Q)(Q) 1: acquire the index lock and capture (B,DW,W)(B,D_W,W) 2: tq≥Wt_q≥ W and tq−W≤Δmaxt_q-W≤ _ 3: encode and normalize q; compute non-pruned base blocks S 4: A^←∅ A← ; E←∅E← 5: for each value in DWD_W do 6: if it is an upsert and Verify passes then 7: add its identifier to A A 8: end if 9: end for 10: for each graph-proposed base slot in S do 11: mark the slot in E and exactly verify it, including visibility 12: end for 13: for each base slot in ∖ES E do 14: mark and exactly verify the slot; add every passing identifier 15: end for 16: return sorted A A, certificate 11, and watermark W Certified mode scans all deltas, takes graph proposals, then visits surviving blocks by decreasing semantic upper bound. For examined base slots E and non-pruned blocks with unexamined slots U, define Mrem=∑b∈|j∈b:j∉E|.M_ rem= _b |\j∈ b:j∉ E\ |. (10) This physical count includes shadowed and predicate-failing records; such overcounting only weakens the bound. For exactly verified IDs A A, R¯ R =1,|A^|=0∧Mrem=0,|A^|/(|A^|+Mrem),otherwise, = cases1,&| A|=0\ \ M_ rem=0,\\ | A|/(| A|+M_ rem),&otherwise, cases (11) stop if Mrem=0∨R¯≥ρreq. if M_ rem=0\ \ R≥ _ req. Algorithm 2 Certified-Range(Q,ρreq,b,ef)(Q, _ req,b,e_f) 1: capture and validate the locked current view 2: prune base blocks safely; exactly scan every current delta value 3: request at most efe_f graph proposals; exactly verify allowed slots 4: compute MremM_ rem and R¯ R 5: while R¯<ρreq R< _ req and fewer than b+efb+e_f base slots are examined do 6: choose the remaining block with largest Ubs(q)U_b^s(q) 7: scan its unexamined slots until the block or cap ends 8: update A A, MremM_ rem, and R¯ R 9: end while 10: return sorted A A, R¯ R, MremM_ rem, and W The certificate assumes the locked snapshot, safe bounds, exact verification, and normalized vectors, but no graph recall. For missed answers ℳ=AW∗(Q)∖A^M=A_W^*(Q) A, all deltas were checked and Eq. (9) excludes pruned blocks; each miss therefore maps to an unexamined physical slot in (10): |ℳ| |M| ≤Mrem⟹ ≤ M_ rem (12) Recall⁡(A^) ( A) =|A^||A^|+|ℳ|≥R¯. = | A|| A|+|M|≥ R. Empty truth has recall one; the bound reaches one only when the residual is zero, as exact mode ensures. An unexamined shadowed slot conservatively remains in MremM_ rem; examining it removes the slot without adding an answer. Delta answers may enter the numerator because they were verified, and never enter the residual because all deltas were scanned. ID deduplication prevents double counting. Thus the certificate is a lower bound, not empirical-recall estimation; tightness reflects how quickly pruning/scanning removes slots. I-D Drift, Maintenance, and Cost Policy For a full deployment, fixed, smoothed histograms can track spatial occupancy, semantic-cluster occupancy, query location, radius, and threshold. With reference distribution Pj,0P_j,0, recent distribution Pj,tP_j,t, and Mj=(Pj,0+Pj,t)/2M_j=(P_j,0+P_j,t)/2, define Dt D_t =∑jαjJSD⁡(Pj,t,Pj,0), = _j _jJSD(P_j,t,P_j,0), ∑jαj _j _j =1, =1, (13) JSD⁡(Pj,t,Pj,0) (P_j,t,P_j,0) =12KL(Pj,t∥Mj) = 12KL(P_j,t\|M_j) +12KL(Pj,0∥Mj). + 12KL(P_j,0\|M_j). A defensible production decision would require persistent drift and amortized benefit: REBUILDt= _t= [min0≤h<kDt−h>γD] 1\! [ _0≤ h<kD_t-h> _D ] (14) ⋅[HΔL^p99>Crebuild]. ·1\! [H L_p99>C_ rebuild ]. Here H is forecast query count and ΔL^p99 L_p99 conservative per-query benefit in rebuild-cost units; compaction is separate. The pilot does not implement Eq. (14): it uses a smoothed 24-bin query-location histogram and one day-50 rebuild after a scripted shift if JSD >0.05>0.05. This checks mechanism, not online optimality or partial rebuilds. More generally, a configuration π could be selected with normalized costs and hard guarantees: minπ _π wLL^p99+wUC^update+wMM w_L L_p99+w_U C_ update+w_M M (15) +wS(tq−W)^+wBC^rebuild +w_S (t_q-W)+w_B C_ rebuild s.t. .t. R¯π≥ρreq,tq−W≤Δmax,Mπ≤Mmax. R_π≥ _ req, t_q-W≤ _ , M_π≤ M_ . Hats denote division by preregistered reference scales. Equation (15) uses MπM_π for memory footprint (not MremM_ rem) and is a design objective, not an optimizer implemented or tuned in this pilot. I-E Complexity, Limits, and Edge Cases For m surviving blocks, nscann_ scan examined base slots, delta size |DW||D_W|, and graph degree g, query work is O⁡(md+nscand+|DW|d)O(md+n_ scand+|D_W|d) plus at most efe_f vertices’ graph work; worst-case exact search is linear. Storage is O⁡((N+|DW|)d+Ng)O((N+|D_W|)d+Ng), including duplicated graph vectors. Brute-force neighbor construction can be O⁡(N2d)O(N^2d): no HNSW or sublinear guarantee is claimed. Full-prefix replay and embedding makes a pilot publication O⁡(|E≤W|d)O(|E_≤ W|d), not a production append-only O⁡(d)O(d); reported update throughput is implementation-specific. Boundary equality is resolved only by the exact inclusive predicates. A zero radius returns co-located matches; τ=−1τ=-1 disables semantic exclusion, while τ=1τ=1 is checked in float64. Great-circle distance and wrapped longitude handle date-line and polar queries. Multiple events for an identifier resolve by final sequence order; a tombstone hides all base state. An exact empty answer has certificate one, whereas an early empty answer with residual slots has certificate zero. Unknown-region delta objects remain safe because the delta is not spatially pruned. Missing trustworthy observation time should disable the object-age predicate rather than substitute last-edit time. The method assumes finite embeddings in one fixed model generation; the current prototype normalizes nonzero outputs, treats a zero vector as having zero cosine with every query, and does not implement dual-generation migration. These restrictions delimit the claims evaluated in Section IV. IV Experimental Evaluation This section reports a functional CPU pilot, not a publication-scale comparison. The narrow purpose is to check the query semantics, exact mode, certificate accounting, and update-overlay plumbing on an executable workload. It does not substitute for the proposed OSM-diff evaluation, and the IVF, graph, lexical, and LIST-router implementations are local reference proxies rather than the authors’ systems. Results are therefore interpreted within this pilot only. IV-A Experimental Setup Data and replay. We pinned a 2,500-row airport sample from the OpenFlights-format airport file [36]; every retained row declares OurAirports, whose official page releases the data to the Public Domain [37], as its source (SHA-256 0ad06d…44cd). Its names, cities, countries, facility fields, and coordinates are source attributes. We used the first 2,000 rows as the day-30 base and held out 500 real rows for insertions on days 31–60. A seeded generator added 160 metadata updates and 80 deletions, yielding 740 replay events and 2,420 live objects on day 60. Event types, event days, and observed_day are simulated, so this experiment tests a simulated age predicate and source-watermark behavior; it provides no evidence about historical airport changes or real record-freshness distributions. Table I records the snapshots. TABLE I: Pilot data snapshots. Object attributes are real; replay operations and times are simulated. Snapshot Objects Countries Events Pinned raw sample 2500 155 0 Base 2000 132 0 Live after replay 2420 154 740 Table IV records the resolved, executable settings rather than an intended configuration. All later plot data and prose macros are exported from the matching run. TABLE IV: Resolved pilot configuration. Values are exported from the YAML files and execution manifest. Setting Resolved value Raw/base/live objects 2,500 / 2,000 / 2,420 Simulated replay events 740 Primary seeds 101, 211, 307, 401, 503 Queries per seed / total 36 / 180 Radii (km) 150, 500, 1500, 4000 Cosine thresholds 0.15, 0.25, 0.35, 0.45 Maximum simulated ages (days) 14, 30, 60, 60 Encoder / dimensions TF–IDF+LSA / 48 Cell / block size 10.0 deg / 64 records Graph degree / proposal budget 12 / 64 Certificate target 0.95 CPU / logical CPUs AMD EPYC 9V74 80-Core Processor / 9 Python / scikit-learn 3.12.14 / 1.8.0 Representation and index settings. A deterministic word-and-character TF–IDF pipeline followed by 48-dimensional truncated SVD produced unit-normalized vectors. It was fit on the day-30 base only; insertion and update text was unseen during fitting. FRESH-GEORANGE used 10∘10 spatial cells, semantic blocks of at most 64 records, a degree-12 exact-kkNN reference graph used only for proposal order, and search budget 64. Certified queries requested a 0.95 lower bound; exact queries continued verification to completion. The query driver applied the complete event history through a watermark before querying. This replacement-batch API assumes one writer and a complete history; it is not a retained, concurrent micro-batch implementation. Queries, comparators, and ground truth. For each of five seeds (101, 211, 307, 401, and 503), we sampled 36 day-60 queries from the live corpus, for 180 distinct queries. A query center is a small perturbation of a sampled airport and its phrase is formed from that row’s derived facility kind, city, and country. Radii rotate over 150, 500, 1,500, and 4,000 km; cosine thresholds over 0.15, 0.25, 0.35, and 0.45; and maximum simulated ages over 14, 30, 60, and 60 days. These broad radii and source-derived phrases make this a predicate smoke test, not an independently judged emergency-resource workload. Brute-force, spatial-first, and semantic-first exact scans establish set-valued ground truth. We additionally tested a lexical spatial grid, IVF post-filter, an exact-kkNN graph post-filter, a LIST-style cluster router, and a spatial index rebuilt every 15 days, plus FGR-Cert95 and FGR-Exact. The local IVF, graph, lexical, and LIST-style implementations neither reproduce HNSW, LIST, nor an IR-tree nor justify external superiority claims. Ten methods over 180 queries produced 1800 method–query executions. Measurement and statistics. For truth T and output A, recall, precision, and Jaccard are |A∩T|/|T||A∩ T|/|T|, |A∩T|/|A||A∩ T|/|A|, and |A∩T|/|A∪T||A∩ T|/|A∪ T| (empty–empty is one). Higher set scores and throughput are better; lower latency, staleness, footprint, and rebuild cost are better. Method order was randomized within each measured query, but every query–method pair was timed only once. Latency is therefore exploratory single-query wall-clock time. The driver issued one query at a time on a CPU environment exposing 9 logical CPUs: AMD EPYC 9V74 80-Core Processor, Linux 6.18.35, Python 3.12.14, NumPy 2.3.5, pandas 2.2.3, scikit-learn 1.8.0, and SciPy 1.17.0. Peak process RSS was 283,452 KiB. Footprint is protocol-5 serialized object size, not resident memory. “Examined” is meaningful within a method but is not comparable across methods because the implementations count different operations. For inferential summaries, the five independently constructed seeds—not the 180 dependent query rows—are the paired units. We applied two-sided Wilcoxon signed-rank tests and Holm adjustment within each metric; intervals in Table VI bootstrap the five paired seed differences. The pooled query-row recall intervals in the main summary are not used for inference. With n=5n=5, the tests are coarse and underpowered and are included as an uncertainty check rather than evidence of equivalence or superiority. IV-B Primary Result: Correctness at a Latency Cost Table V gives the principal result. FGR-Exact attained 100.00% recall, precision, and Jaccard on all 180 primary queries. FGR-Cert95 attained 99.91% mean empirical recall and 100.00% precision while reporting a 99.41% mean lower bound. The mean empirical-minus-certified gap was only 0.50 p; the certificate-violation count was 0 of 180, the minimum certificate was 95.26%, and the below-target count was 0. Across five seeds, a separate audit made 6,080 sampled semantic-bound comparisons; the smallest slack was positive (3.56×10−123.56× 10^-12). Ten unit tests also covered exact/certificate behavior, normalization, terminal cells, non-divisor grids, poles, the dateline, singleton graphs, and watermark rules. These checks support the certificate on the declared path—normalized vectors, a committed snapshot, complete-history replay, and one ordered writer—but are not a general production proof. Repeated versions, moves, late or gapped events, concurrent writers, malformed embeddings, and semantic outlier streams remain outside the property suite. TABLE V: Executed day-60 pilot results across five seeds and 180 queries per method. Recall and precision are percentages. Footprint is standalone pickle size, not resident memory. Method Recall ↑ Precision ↑ Median ms ↓ p95 ms ↓ Examined Serialized MB Brute-force exact 100.00 100.00 1.39 2.03 2420.0 5.07 Spatial-first exact 100.00 100.00 1.24 1.99 265.4 5.18 Semantic-first exact 100.00 100.00 1.23 1.86 448.5 5.07 Lexical spatial 99.96 100.00 1.44 2.76 265.4 5.40 IVF-post 85.45 97.78 1.29 1.84 592.9 5.12 kNN-graph post-filter 32.56 55.56 2.31 3.19 96.0 5.18 LIST-router proxy 85.59 98.33 1.27 1.79 504.8 5.11 Periodic rebuild (15 d) 68.01 78.20 1.28 2.14 257.9 5.04 FGR-Cert95 (this work) 99.91 100.00 7.24 12.39 1047.4 5.39 FGR-Exact (this work) 100.00 100.00 7.27 12.53 1048.5 5.39 The efficiency result is negative. FGR-Cert95 required a 7.24-ms median and 12.39-ms p95, versus 1.24 ms and 1.99 ms for spatial-first exact—a 5.85× median slowdown (6.22× at p95). It was also essentially tied with FGR-Exact (7.27 ms), saving only 1.1 reported examinations on average. On this small corpus, certification and overlay bookkeeping dominate, and early termination provides no meaningful latency win. Serialized footprint was 5.39 MB versus 5.18 MB for spatial-first. The correct conclusion is feasibility of the narrow correctness contract, not a performance advantage. Figure 2 reaches the same conclusion across budgets. Increasing the FGR request from 0 to 0.95 raised empirical recall from 77.88% to 100.00% and its reported bound from 55.63% to 99.71%; median latency remained between 5.56 and 6.85 ms because the corpus is tiny and timing noise masks a monotone work trend. The IVF proxy reaches 100.00% only when all 32 clusters are probed, whereas the graph proxy reaches just 37.46% at its largest budget. The plotted proxy curves measure these local implementations only and provide no comparison to official ANN systems. 2244662020404060608080100100Median latency (ms)Recall (%)(a) Recall–latencyFGRIVF proxyGraph proxyLIST proxy000.50.51160608080100100Requested certificatePercent(b) Certificate tightnessEmpiricalCertified Fig. 2: Recall–latency and certificate frontier. This is a single-query CPU pilot over 2,500 airport rows with a simulated 740-event replay; IVF and graph lines are local proxies, not official implementations. Table VI reinforces the limits on comparative interpretation. The estimated FGR-Cert95 recall differences were +0.143+0.143 versus the LIST-router proxy, +0.145+0.145 versus IVF, and +0.673+0.673 versus the graph proxy, but every Holm-adjusted p-value was at least 0.5625. Its difference from FGR-Exact was −0.00092-0.00092. Five seed pairs cannot sustain a strong performance claim. TABLE VI: Paired recall differences: FGR-Cert95 minus comparator. CIs are bootstrap 95%; pHp_H is Holm-adjusted Wilcoxon. Comparator Mean diff. 95% CI pHp_H LIST-router proxy 0.143 [0.105, 0.194] 0.56 FGR-Exact -0.001 [-0.001, -0.000] 0.62 Periodic rebuild (15 d) 0.319 [0.280, 0.352] 0.56 Spatial-first exact -0.001 [-0.001, -0.000] 0.62 IVF-post 0.145 [0.117, 0.174] 0.56 kNN-graph post-filter 0.673 [0.631, 0.709] 0.56 IV-C Sensitivity, Freshness, and Replay Cost Radius and threshold sweeps in Fig. 3 reuse a fixed cohort within each panel. At radii through 1,000 km, both recall and certificate were 100.00% and 100.00%, respectively; at 5,000 km, latency rose to 8.45 ms, recall was 99.90%, and the bound was 99.00%. Tightening the cosine threshold from 0.05 to 0.60 reduced mean answer count from 148.3 to 29.6 and latency from 10.29 to 5.44 ms; recall rose from 99.83% to 100.00%, while the bound rose from 98.97% to 99.81%. This is consistent with fewer qualifying records, but only for this cohort and encoder. 10210^210310^37788Radius (km)Latency (ms)(a) Radius000.20.20.40.40.60.666881010Cosine thresholdLatency (ms)(b) Threshold Fig. 3: Radius and threshold sensitivity in the single-query, 2,500-row airport pilot with simulated updates. Points are aggregates over fixed 20-query cohorts; they are not population-level estimates. Figure 4(a) times full-history replacement, not sustained incremental ingestion. Replaying 50, 100, 250, 500, and 740 events took 55.4, 108.2, 285.0, 576.5, and 721.6 ms, respectively, for a median 903 and maximum 1025 replayed events/s. A full re-embedding and rebuild took 384.6–509.8 ms. The last evaluated batch where replay was cheaper contained 250 events, and the first where it was slower contained 500; the present delta representation therefore does not demonstrate update scalability. A credible dynamic benchmark still needs retained micro-batches, operation-stratified latency, compaction, and concurrent query interference. Panel (b) isolates watermark staleness on one 24-query cohort. FGR-Exact, given the complete history through each query day, retained at least 100.00% recall. Immediately before each scheduled rebuild, the periodic view’s recall fell from 98.95% at five days of lag to 95.52% at ten days and 81.40% at 15 days. After the next rebuild it recovered to 95.81%, then declined to 77.89% recall and 82.44% precision at day 60. This supports the elementary point that an old watermark changes the answer set; because event time and record age are simulated, it does not quantify real-world source freshness. 00101020203030404010210^2102.510^2.5Events/base (%)Batch time (ms)(a) Full-history replayDelta replayRebuild303040405050606080809090100100Replay daySet quality (%)(b) StalenessFGR recallPeriodic recallPeriodic precision Fig. 4: Full-history replay cost and 15-day rebuild staleness. Both panels use the 2,500-row CPU pilot and simulated event stream; replay is replacement batch application, not concurrent incremental throughput. IV-D Diagnostic Stress Tests and Ablations Figure 5(a) is deliberately a scripted trigger test. A forced query-region shift raises Jensen–Shannon divergence from 0.09 on day 40 to 0.55 on day 45; a hard-coded day-50 rebuild costs 298.3 ms. The measured p95 then changes from 7.43 ms (day 45) to 5.85 ms (day 50), while the mean certificate changes from 99.43% to 98.09%. Because the workload changes and there is no simultaneous no-rebuild counterfactual, this cannot be attributed causally to recovery or used to validate an adaptive policy. Panel (b) shows serialized FGR size increasing from 3.88 MB at 500 objects to 5.01 MB at 2,000, compared with 3.82 to 4.88 MB for spatial-first. Four small points describe the pilot footprint; they do not establish asymptotic scaling. 404050506060000.20.20.40.40.60.6Replay dayJSD(a) Scripted drift triggerJSDRebuild5005001,0001,0001,5001,5002,0002,000444.54.555ObjectsSerialized MB(b) Index sizeFGRkNN graphSpatial Fig. 5: Scripted drift instrumentation and serialized footprint in the 2,500-row CPU pilot with simulated replay. The trigger is hard-coded and the graph line is a local exact-kkNN proxy. Selectivity in Fig. 6(a) exposes the same overhead: FGR-Cert95 median latency rises from 5.93 ms for empty answers to 9.23 ms above 2% selectivity, while spatial-first remains between 1.15 and 1.39 ms. FGR recall is at least 100.00% through the 0.1–0.5% bin and 99.67% above 2%. We do not compare “examined” counts because their definitions differ by method. Panel (b) is a dictionary-normalization sanity check, not a multilingual retrieval evaluation. The fixed lexicon raises category recall from 56.82% to 61.36% for French, 56.53% to 61.36% for Spanish, 57.10% to 60.51% for German, and 55.97% to 60.51% for an English synonym; English remains 60.51%. Labels are circularly inferred from the word “international,” and tested translations appear in the lexicon, so no language-generalization claim follows. 002244224466Selectivity binLatency (ms)(a) SelectivityCertifiedSpatialFGR exact0022440.560.560.580.580.60.6Phrase IDCategory recall(b) Dictionary sanity checkRawLexicon Fig. 6: Selectivity and dictionary-normalization diagnostics on the single-query airport pilot with simulated replay. The lexical intervention is constructed and does not measure multilingual robustness. Finally, Table VII and Fig. 7 show that removing the graph proposer preserves recall (99.68% versus 99.68%) and the mean certificate (99.20% versus 99.20%) while changing latency from 8.17 to 6.93 ms; the no-graph variant is faster in this run. Removing semantic bounds or merging to one semantic block per spatial cell changes latency to 7.93 and 8.18 ms. These small, unreplicated ablations provide no positive component-level speed evidence and cannot establish behavior at scale. The decisive row is the deliberately unsafe stale-base variant: omitting the delta lowers recall from 99.68% to 59.38%. Its certificate is suppressed because advancing the watermark without applying the events violates the certificate premise. TABLE VII: Component ablation. The no-delta row is deliberately freshness-noncompliant, so no certificate is reported. Variant Recall (%) Cert. (%) Latency (ms) Full 99.68 99.20 8.17 No graph proposer 99.68 99.20 6.93 No semantic bounds 99.88 99.20 7.93 One semantic block per cell 99.68 99.20 8.18 Stale base, no delta (uncertified) 59.38 – 4.73 000.50.5111.51.5222.52.5333.53.544005050100100Variant IDPercentRecallCertificate Fig. 7: Guarantee ablation; variant IDs and latency are in Table VII. The stale-base variant is uncertified. IV-E Threats to Validity and Deployment Limits Local proxies, single timings, and Python code limit internal validity; source-derived queries, simulated freshness, and serialized size limit construct validity. One uneven 2,500-airport sample, five seeds, and one CPU limit external and statistical validity. Single-writer replay omits concurrency. No personal data are used, but the pilot is not safety-ready. Pinned artifacts aid reproduction. Archived OSM diffs [38], official baselines, independent queries, concurrent updates, and broader property tests remain required. Correctness passes, but efficiency fails: FGR-Cert95 is 5.85× slower than spatial-first exact. Publication claims are no-go. V Conclusion FRESH-GEORANGE addresses semantic-spatial range enumeration when applications need every qualifying object from a current snapshot rather than an approximate ranking. The design combines geographic cells, semantic microblocks, admissible spatial and cosine bounds, a graph used for proposal ordering, and a latest-write delta overlay. Exact mode accounts for every nonprunable record; certified mode converts verified answers and an unresolved-record count into a deterministic recall lower bound. In the CPU pilot, exact mode returned the complete reference set on all 180 queries, while the 95-percent mode reached 99.91% empirical mean recall with a 99.41% reported mean certificate and no certificate violation. 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