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RCWT: Measuring Task-Budget Displacement from Coordination Content in LLM Calls
Brenda Lelis, Rodrigo Cabral-Carvalho
Intelligence
Status: succeeded | Model: Gemma-4-26B-A4B | Prompt: intel-v1 | Confidence: 93%
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Summary
The paper introduces the Roundtable Context Window Test (RCWT), a protocol for measuring task-budget displacement in LLM calls. It demonstrates that under fixed context budgets, increasing coordination content (e.g., multi-agent state, summaries) displaces task-specific evidence, leading to sharp performance degradation when residual evidence falls below a critical threshold. An ablation study shows that when task evidence is kept intact and total prompt length increases, performance remains stable, suggesting the primary issue is displacement/truncation rather than semantic interference from coordination volume alone.
Entities (9)
Relation Signals (8)
RCWT → evaluates → GPT-4.1-mini
confidence 95% · In that setting, all tested calls return every scored field correctly across GPT-4.1-mini...
RCWT → evaluates → Claude Haiku 4.5
confidence 95% · In that setting, all tested calls return every scored field correctly across... Claude Haiku 4.5...
RCWT → evaluates → Gemini 2.0 Flash
confidence 95% · The tested model IDs are gemini-2.0-flash...
RCWT → measures → Task-Budget Displacement
confidence 95% · RCWT is a measurement primitive for context-allocation budgeting... measuring this task-budget displacement effect.
Intact-Task Ablation → tests → Semantic Interference
confidence 90% · This ablation narrows the claim: the main RCWT cliff is best read as task-budget displacement, not as proof that coordination volume alone causes semantic interference
RCWT → uses → GSM8K
confidence 85% · External benchmark packs: GSM8K... are grouped into 10-item packs
RCWT → uses → MMLU-Pro
confidence 85% · External benchmark packs: GSM8K, MMLU-Pro, and DROP... are grouped into 10-item packs
RCWT → uses → DROP
confidence 85% · External benchmark packs: GSM8K, MMLU-Pro, and DROP... are grouped into 10-item packs
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Abstract
Abstract:Multi-agent and memory-augmented LLM systems often place coordination content, shared state, prior discussion, tool outputs, summaries, and role instructions, inside the same finite prompt used for the current task. This creates a practical allocation problem: every token spent on coordination is unavailable to task instructions or evidence when a call is assembled under a fixed context budget. We introduce the Roundtable Context Window Test (RCWT), a controlled protocol for measuring this task-budget displacement effect. RCWT varies coordination content while controlling total budget, position order, task family, and scoring. In the main context-dependent recall task at $W=4096$, three commercial models remain near baseline through moderate overhead and then degrade sharply once residual reference evidence falls to a few hundred tokens. Window-scaling summaries are consistent with a task-specific residual-budget interpretation rather than a fixed percentage threshold, but we treat this as descriptive evidence rather than a universal law. To test whether the fixed-budget cliff persists when task evidence remains intact, we add an intact-task ablation: the full task/reference block is kept present while coordination tokens increase by expanding total prompt length. In that setting, all tested calls return every scored field correctly across GPT-4.1-mini, Claude Haiku 4.5, and Gemini 2.5 Flash up to a 95\% coordination ratio. This ablation narrows the claim: the main RCWT cliff is best read as task-budget displacement, not as proof that coordination volume alone causes semantic interference in the original open-ended task. RCWT is therefore a measurement primitive for context-allocation budgeting, not a complete theory of multi-agent benefit or session-level coordination.
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- Source: https://arxiv.org/abs/2607.12216v1
- Canonical: https://arxiv.org/abs/2607.12216v1
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RCWT: Measuring Task-Budget Displacement from Coordination Content in LLM Calls Brenda Lelis CloudWalk, Inc. São Paulo, Brazil brenda.lelis@cloudwalk.io &Rodrigo Cabral-Carvalho CloudWalk, Inc. São Paulo, Brazil rodrigo.motta@cloudwalk.io Corresponding author. Abstract Multi-agent and memory-augmented LLM systems often place coordination content, shared state, prior discussion, tool outputs, summaries, and role instructions, inside the same finite prompt used for the current task. This creates a practical allocation problem: every token spent on coordination is unavailable to task instructions or evidence when a call is assembled under a fixed context budget. We introduce the Roundtable Context Window Test (RCWT), a controlled protocol for measuring this task-budget displacement effect. RCWT varies coordination content while controlling total budget, position order, task family, and scoring. In the main context-dependent recall task at W=4096W=4096, three commercial models remain near baseline through moderate overhead and then degrade sharply once residual reference evidence falls to a few hundred tokens. Window-scaling summaries are consistent with a task-specific residual-budget interpretation rather than a fixed percentage threshold, but we treat this as descriptive evidence rather than a universal law. To test whether the fixed-budget cliff persists when task evidence remains intact, we add an intact-task ablation: the full task/reference block is kept present while coordination tokens increase by expanding total prompt length. In that setting, all tested calls return every scored field correctly across GPT-4.1-mini, Claude Haiku 4.5, and Gemini 2.5 Flash up to a 95% coordination ratio. This ablation narrows the claim: the main RCWT cliff is best read as task-budget displacement, not as proof that coordination volume alone causes semantic interference in the original open-ended task. RCWT is therefore a measurement primitive for context-allocation budgeting, not a complete theory of multi-agent benefit or session-level coordination. Keywords: Large language models; Multi-agent systems; Context windows; Benchmarking; Prompt allocation. 1 Introduction Modern LLM applications assemble many kinds of information into a single call: task instructions, retrieved documents, memory summaries, prior agent messages, tool observations, role prompts, and shared state [15, 16, 19, 9]. The application-level question is not only whether a model advertises a large context window, but how much of the current call is allocated to the task block that must be read and acted on. Prior long-context work shows that models do not use all positions uniformly and that longer inputs can degrade performance even when relevant information is available [13, 1, 10, 7]. This paper studies a narrow, operational version of that problem. For a single model call with context budget W, let c be coordination content and let W−cW-c be the remaining task block. We estimate RM(c,W,T)∈[0,1],R_M(c,W,T)∈[0,1], where M is the model and T is the task family. We use the term task-budget displacement for the main effect: under fixed W, increasing coordination content can physically reduce or truncate the task evidence needed by the current call. We introduce the Roundtable Context Window Test (RCWT). RCWT is a single-call benchmark protocol that varies coordination allocation while controlling prompt order and scoring. It intentionally excludes full multi-agent session dynamics such as turn scheduling, retrieval policy, memory writes, tool failures, and agent topology. Those factors matter, but mixing them into the same experiment would obscure the local allocation effect. The contributions are: 1. A controlled protocol. RCWT varies coordination allocation under fixed budget with position control, explicit token accounting, and task-level scoring. 2. A fixed-budget displacement result. On a technical-specification recall task, accuracy remains high at moderate overhead and drops sharply only when the residual task block becomes very small. 3. A truncation-disambiguating ablation. When the full task block remains intact and total prompt length grows to accommodate coordination, we detect no cliff-sized degradation across tested models and ratios. 4. Task dependence and boundary evidence. Self-contained tasks remain stable, while passage-heavy benchmark packs require larger residual task budgets and expose a model–task exception before truncation. 5. A scoped engineering implication. Coordination context should be budgeted against task-specific residual needs. RCWT does not measure the net benefit of coordination. 2 Related Work Long-context behavior. The Lost in the Middle result showed that LLMs can fail to use relevant information depending on position [13]. LongBench and RULER broaden long-context evaluation across retrieval, QA, summarization, synthetic tasks, and configurable sequence lengths [1, 10]. RCWT differs by holding a call budget fixed and varying allocation between coordination-like content and task evidence. Attention and systems bottlenecks. Long-context use is constrained by attention and KV-cache costs. LongLoRA, FlashAttention, Longformer, and BigBird address feasibility through training or attention mechanisms [4, 6, 2, 20]. RCWT asks a complementary application-level question: given a feasible context, how much of it is left for the task block? Context compression. Prompt compression systems such as LLMLingua and LLMLingua-2 reduce token count while trying to preserve task-relevant information [11, 14]. RCWT can evaluate whether compression moves a call away from a high-displacement regime. Multi-agent coordination. Multi-agent LLM systems introduce communication, role, orchestration, verification, and memory overhead [3, 12]. They may also produce benefits through decomposition, critique, and specialized roles. RCWT measures only the per-call token cost side of that ledger. It does not estimate net system value. 3 Method 3.1 Fixed-budget RCWT The main RCWT task is context-dependent recall over a technical software specification. The task asks for a structured technical analysis whose scored facts must be recovered from a reference block. The coordination block is synthetic but structured like multi-agent shared context: role/protocol text, agent messages, shared propositions, and tool schemas. Token accounting is deterministic in the artifact. Prompt construction uses the cl100k_base tokenizer to size blocks. Let u be the fixed task-instruction block, c the coordination block, and r the technical-reference block, so that c+u+r=Wc+u+r=W. In the released main runs, u=337u=337 construction tokens. The runner controls a target ratio q=c/(W−u)q=c/(W-u), then sets c=⌊q(W−u)⌋c= q(W-u) and r=W−u−cr=W-u-c. The full-budget coordination share used in the analysis is therefore p=c/Wp=c/W, and the residual task budget is W−c=u+rW-c=u+r. The raw proportion field stores q, not p. For each target allocation, the coordination template is repeated or prefix-truncated to c tokens. The reference template is likewise repeated or prefix-truncated to r tokens. Provider-reported token counts are saved with every trial, but the allocation itself is built from this common tokenizer so the sweep is reproducible across providers. The main experiment uses W=4096W=4096 and target ratios q∈0,25,50,75,90,92,94,96,98%.q∈\0,25,50,75,90,92,94,96,98\\%. These targets realize p∈0,22.9,45.9,68.8,82.6,84.4,86.3,88.1,89.9%p∈\0,22.9,45.9,68.8,82.6,84.4,86.3,88.1,89.9\\% after accounting for u. Each condition is run in two orders: coord_first and reason_first. The primary suite uses N=20N=20 trials per order, or 40 calls per model–target pair. The tested model IDs are gemini-2.0-flash, claude-haiku-4-5-20251001, and gpt-4.1-mini. The original open-ended responses are scored with a binary fact-checking judge over 10 items, with two known floor-effect items excluded from the effective score. The 8 effective items are: 1. three encryption options; 2. recommendation of per-document symmetric key; 3. PostgreSQL LISTEN/NOTIFY 8KB payload limit; 4. Redis Pub/Sub approximately 100K messages/sec; 5. Redis Streams approximately 5ms latency versus Pub/Sub approximately 1ms; 6. ProseMirror as the rich-text recommendation; 7. backend team needs 1 week CRDT ramp-up; 8. WebSocket/infrastructure migration takes about 2–3 weeks. The two excluded items are crdt_throughput and mls_rfc, which behaved as floor-effect parsing items in the original baseline. The artifact reports both raw and effective scores. 3.2 Candidate curves and residual-budget summary For the main task, we fit logistic, power-law, exponential, quadratic, and piecewise-linear descriptive curves. The logistic form is RM(c,W,T)=R01+exp(k(c/W−p0)).R_M(c,W,T)= R_01+ (k(c/W-p_0)). This is not a mechanistic proof. The cliff-region sampling makes a threshold-like family likely to fit well. We use the curve as compact interpolation, not as evidence of a universal law. We also summarize the transition with a task-specific residual budget parameter θ: p0(W)=1−θW.p_0(W)=1- θW. Here p0p_0 is expressed as the realized full-budget share c/Wc/W, so θ=W(1−p0)θ=W(1-p_0) is the fitted residual task budget u+ru+r; the corresponding reference-only reserve is θ−uθ-u. This relation is an empirical description over the tested window sizes. With only a small number of window sizes, θ should be read as a calibration estimate, not as a validated invariant. 3.3 Intact-task ablation We add an ablation that probes whether a cliff-sized degradation persists when task evidence is kept intact rather than truncated. The full task/reference block is kept intact in every condition. Coordination tokens are varied around it, and the total prompt length grows accordingly. Thus, the task is never physically shortened. The ablation uses deterministic JSON scoring rather than an LLM judge. It asks for eight exact fields matching the same reference facts used in the main task. In this ablation, the coordination ratio is c/(c+t)c/(c+t), where t is the intact task/reference block; this differs from the fixed-budget experiment, where the ratio is c/Wc/W. The measured task/reference block has t=698t=698 construction tokens. Tested ratios are 0,0.50,0.75,0.90,0.950,0.50,0.75,0.90,0.95, corresponding to 0, 698, 2,094, 6,282, and 13,262 coordination tokens and estimated prompt sizes of 702, 1,401, 2,797, 6,985, and 13,965 tokens. Both prompt orders are tested with N=5N=5 per order, so each model-ratio cell pools 1010 calls and 8080 binary field decisions. Models are GPT-4.1-mini, Claude Haiku 4.5, and Gemini 2.5 Flash. The Gemini model differs from the historical main table because Gemini 2.0 Flash was unavailable during later reruns. 3.4 Boundary tasks and packs We additionally retain two boundary probes: • Self-contained algorithmic task: the task block contains all information needed to answer execution-trace questions; coordination is irrelevant. • External benchmark packs: GSM8K, MMLU-Pro, and DROP [5, 17, 8] are grouped into 10-item packs so that task-block size can become binding under fixed W. Each model–share aggregate contains 100 calls: 10 items, two prompt orders, and five repeated trials. 4 Results 4.1 Fixed-budget main task The main fixed-budget result shows stable accuracy through moderate overhead, followed by sharp degradation when the task block becomes very small. Figure 1 shows the main fixed-budget result. All three models remain close to baseline at moderate coordination overhead, then drop once residual reference evidence is reduced to a few hundred tokens. Exact aggregate values and the distinction between target ratio q and realized share p=c/Wp=c/W are reported in Appendix Table A1. Figure 1: Fixed-budget RCWT at W=4096W=4096 across three providers. The horizontal axis reports the realized full-budget coordination share p=c/Wp=c/W. Error bars are 95% stratified call-level bootstrap intervals over the two prompt orders. Effective fact recall remains high through moderate coordination overhead, then falls sharply once residual reference evidence is reduced to a few hundred tokens. At target q=90%q=90\%, a realized coordination share of p=82.6%p=82.6\%, the reference block contains 376 tokens and the total residual task budget u+ru+r is 713 tokens. The drop from baseline is 34.1 percentage points for Gemini, 30.6 for Haiku, and 14.7 for GPT. This supports a fixed-budget warning: average prompt length and nominal context window are not sufficient safety signals; the residual task budget matters. 4.2 Window scaling A fixed-percentage account would place the transition at roughly the same realized p across window sizes. The observed summaries do not match that account. At target q=90%q=90\%, W=4096W=4096 realizes p=82.6%p=82.6\% and leaves 376 reference tokens; W=8192W=8192 realizes the larger share p=86.3%p=86.3\% yet leaves 786 reference tokens and shows less degradation. The W=8192W=8192 sweep uses 20 trials per order (40 calls per model–target pair); the W=16384W=16384 sweep uses 10 per order (20 calls per pair). Table 1: Window-scaling summary for the main task. θ is estimated from the W=4096W=4096 fit. This is descriptive calibration, not a validated invariant. Model θ Pred. p0p_0(8K) Obs. p0p_0(8K) Obs. p0p_0(16K) Gemini 2.0 Flash 665 91.9% 92.1% 95.9% Claude Haiku 4.5 650 92.1% 92.2% 96.0% GPT-4.1-mini 568 93.1% 93.1% 96.4% The relation is consistent with residual-budget displacement over these runs. It is not strong evidence that θ is stable outside this task, these models, or these window sizes. 4.3 Intact-task ablation The task/reference block is never truncated in this ablation. Coordination tokens are added around the intact task block, increasing total prompt length. Every model–ratio cell has 10/10 calls with all eight fields correct, equivalent to 80/80 correct field decisions. Treating complete-call success as the unit, 10/10 gives a Wilson 95% interval of approximately [0.722,1.000][0.722,1.000] [18]. Across the 15 heterogeneous cells, the descriptive totals are 150/150 complete calls and 1200/1200 correct fields; we do not use the pooled field count as an independent-sample confidence interval. The main fixed-budget cliff does not, by itself, show that coordination text harms reasoning while task evidence remains intact. In this task and scoring setup, we detect no cliff-sized semantic-interference effect even with large coordination blocks, as long as the reference remains present. The sample does not exclude smaller effects. Because the ablation also changes the task from open-ended structured analysis to exact-field extraction, it is easier than the main task; it should therefore be interpreted as evidence against a large interference effect in this extraction-style intact-evidence setting, not as a full semantic-interference test for the original task format. The main effect is best interpreted as displacement or truncation of task evidence under fixed budget. 4.4 Boundary tasks and external packs The self-contained algorithmic task remains stable across overhead levels for all three providers. This shows that extra text alone is not sufficient to cause degradation in the tested range. Most model–pack pairs remain close to baseline while the full task pack fits, then fall when task content is partially or fully truncated. One material exception is Claude Haiku 4.5 on the untruncated GSM8K pack: accuracy falls from 0.60 at p=0p=0 to 0.40 at p=0.25p=0.25 and 0.38 at p=0.50p=0.50. The pack probes therefore support task-budget sensitivity but do not identify truncation as the only possible source of degradation. Table 2: Task-dependent logistic midpoint summaries at W=4096W=4096. Pack probes are RCWT stress probes, not leaderboard estimates. Probe Logistic p0p_0 range Approx. reserve Truncation onset Task 1 spec recall 0.838–0.861 568–665 tok target q=90%q=90\% GSM8K-pack 0.853–0.893 438–602 tok 90% MMLU-Pro-pack 0.733–0.755 1003–1094 tok 50% partial DROP-pack 0.481–0.624 1539–2126 tok 50% 5 Discussion 5.1 Scope of the contribution The controlled allocation protocol is useful. RCWT isolates one factor that appears in real multi-agent systems: coordination content can consume the same prompt budget needed for task evidence. The main data support a practical engineering rule: measure the residual task budget needed by a task family and budget coordination around it. 5.2 Limits of interpretation A broader interpretation, that the paper proves general reasoning degradation from semantically irrelevant coordination, is not supported. The main task is recall-heavy; the cliff aligns with small residual reference blocks; the intact-task ablation stays at ceiling. The supported claim is narrower: RCWT measures fixed-budget task displacement, and semantic interference requires separate evidence. The ablation provides evidence against a cliff-sized semantic effect in this extraction-style setup; it should not be read as proof that semantic interference is zero in the original open-ended task format. 5.3 Cost versus benefit RCWT measures cost, not net value. Real coordination can improve quality through decomposition, verification, tool use, or memory. A coordination block can be overhead for one agent and the task input for another. The correct practical question is not whether coordination hurts, but whether this coordination content provides enough benefit to justify the task-budget it consumes. RCWT supplies only the cost-side measurement. 5.4 Coordination heterogeneity The central coordination block is synthetic and structured. Real coordination varies: dense tool outputs, verbose transcripts, retrieved documents, distilled state, uncertainty annotations, or contradictory agent claims may behave differently at the same token count. The current results should not be generalized across all coordination types without a design that varies content type independently of length. 6 Limitations The fixed-budget sweep was developed iteratively: cliff-region cells were added after early flat-region observations. The resulting curves are compact descriptive summaries, not pre-registered tests of a universal functional form. The main figure uses a stratified call-level bootstrap over the two prompt orders. Because calls reuse the same task and reference facts, these intervals quantify run-to-run variation conditional on this prompt; they do not represent uncertainty over a population of independently sampled tasks. The main result is strongest for one technical-specification recall task. The benchmark packs broaden coverage but do not constitute a pre-registered task-complexity ladder. In the main task, prefix truncation removes facts in a fixed order, so the fitted midpoint partly reflects reference layout and fact order rather than an intrinsic task constant. The coordination template also overlaps topically with some scored concepts, including CRDTs, MLS, Redis, WebSockets, and migration timing. Future runs should randomize fact order and vary coordination content independently of topical overlap. The main task uses an LLM judge for open-ended parsing. Cross-vendor rescoring did not remove the qualitative cliff, but judge-specific strictness remains a limitation. The intact-task ablation uses strict per-field deterministic JSON scoring to reduce this risk, but it also changes response format, task demand, and scoring method. Therefore, the ablation is best interpreted as a test for a large semantic-interference effect in an extraction-style intact-evidence setting, not as a token-identical rescore of the open-ended main task. A deterministic rescore or human audit of the main open-ended responses remains complementary validation. Provider tokenizers differ. The scripts use cl100k_base for construction plus provider-reported token counts where available. The distinction between the runner target q=c/(W−u)q=c/(W-u) and the reported full-budget share p=c/Wp=c/W is now explicit, but native token accounting should be preferred in future runs. Gemini 2.0 Flash was available during the original fixed-budget runs but was unavailable during later reruns. Historical aggregate files are retained; new reruns and the intact-task ablation use current model IDs. RCWT is a single-call protocol and does not model session-level multi-agent dynamics, retrieval policy, tool failure, memory summarization, or coordination benefit. 7 Conclusion RCWT is a controlled protocol for measuring task-budget displacement from coordination content in LLM calls. The main fixed-budget experiment shows a sharp high-overhead cliff on a context-dependent recall task, and window summaries are consistent with a task-specific residual-budget interpretation. The intact-task ablation shows that when the full task block remains present, we detect no large degradation from extra coordination content in an extraction-style setup, while small semantic effects and harder-task interference remain possible. This narrows the contribution: coordination context is not cost-free under fixed budgets, but the main evidence supports displacement of task evidence rather than a general semantic competition law. Practical systems should track residual task budget, not only nominal context size or total prompt length. Code and artifact availability The source code, prompt templates, and aggregate result files are available in the public repository: https://github.com/cloudwalk/rcwt-agent-coordination. Acknowledgements LLM tools were used for grammar correction and drafting assistance. The authors take responsibility for the experiments, analysis, and claims. References [1] Bai, Y., Lv, X., Zhang, J., Lyu, H., Tang, J., Huang, Z., Du, Z., Liu, X., Zeng, A., Hou, L., Dong, Y., Tang, J., Li, J.: LongBench: A Bilingual, Multitask Benchmark for Long Context Understanding. In: ACL (2024). [2] Beltagy, I., Peters, M.E., Cohan, A.: Longformer: The Long-Document Transformer. arXiv:2004.05150 (2020). 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Transactions of the Association for Computational Linguistics 11, 1316–1331 (2023). [16] Schick, T., Dwivedi-Yu, J., Dessi, R., Raileanu, R., Lomeli, M., Hambro, E., Zettlemoyer, L., Cancedda, N., Scialom, T.: Toolformer: Language Models Can Teach Themselves to Use Tools. In: NeurIPS (2023). [17] Wang, Y., Ma, X., Zhang, G., Ni, Y., Chandra, A., Guo, S., Ren, W., Arulraj, A., He, X., Jiang, Z., Li, T., Ku, M., Wang, K., Zhuang, A., Fan, R., Yue, X., Chen, W.: MMLU-Pro: A More Robust and Challenging Multi-Task Language Understanding Benchmark. In: NeurIPS Datasets and Benchmarks Track (2024). [18] Wilson, E.B.: Probable Inference, the Law of Succession, and Statistical Inference. Journal of the American Statistical Association 22(158), 209–212 (1927). [19] Wu, Q., Bansal, G., Zhang, J., Wu, Y., Li, B., Zhu, E., Jiang, L., Zhang, X., Zhang, S., Liu, J., Awadallah, A.H., White, R.W., Burger, D., Wang, C.: AutoGen: Enabling Next-Gen LLM Applications via Multi-Agent Conversations. In: First Conference on Language Modeling (2024). [20] Zaheer, M., Guruganesh, G., Dubey, A., Ainslie, J., Alberti, C., Ontanon, S., Pham, P., Ravula, A., Wang, Q., Yang, L., Ahmed, A.: Big Bird: Transformers for Longer Sequences. In: NeurIPS (2020). Appendix A. Prompt and task examples The experiments use controlled prompt fragments rather than production logs. Full prompt templates and aggregate files are kept in the open-source artifact repository. Main context-dependent task. The task/reference block is a technical software specification. The coordination block is synthetic role, protocol, shared-state, and agent-message text varied independently of that reference. Representative reference facts state that PostgreSQL LISTEN/NOTIFY has an 8KB payload limit, Redis Pub/Sub handles roughly 100K messages per second but has no persistence, and Redis Streams provides persistence with about 5ms latency versus about 1ms for Pub/Sub. The model is asked for a structured technical analysis, and binary scored items check whether these facts are recovered correctly. Self-contained algorithmic task. The task block gives a Python function that partitions items=[3, 10, 15, 7, 10, 22, 4] around threshold=10. Representative scored questions ask whether the sum is 71, whether indices 2 and 5 are above threshold, and whether the maximum above-threshold value is 22. The answers are fully determined by the code and input, so the coordination block is irrelevant. External benchmark packs. GSM8K, MMLU-Pro, and DROP examples are grouped into 10-item packs. Each model–share aggregate contains 100 calls across 10 items, two prompt orders, and five repeated trials. The pack probes are stress tests for task-budget sensitivity rather than leaderboard estimates. Table A1: Detailed main context-dependent RCWT task at W=4096W=4096, pooled over position order. The runner controls q=c/(W−u)q=c/(W-u); p=c/Wp=c/W is the realized full-budget coordination share, u=337u=337, and r is the residual reference block. Scores are effective binary accuracy over 40 calls per model–target pair. Target q Realized p Ref. r Gemini 2.0 Flash Haiku 4.5 GPT-4.1-mini 0% 0.0% 3759 1.000 0.972 1.000 25% 22.9% 2820 0.960 0.906 0.972 50% 45.9% 1880 0.944 0.894 0.988 75% 68.8% 940 0.894 0.875 0.981 90% 82.6% 376 0.659 0.666 0.853 92% 84.4% 301 0.400 0.441 0.609 94% 86.3% 226 0.016 0.113 0.413 96% 88.1% 151 0.009 0.103 0.284 98% 89.9% 76 0.006 0.038 0.331