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Collective Emergent Alignment: Measuring and Amplifying Interaction-Induced Reasoning Alignment in Multi-Agent LLMs

Boxuan Wang, Zhuoyun Li, Sarvapali D. Ramchurn, Xiaowei Huang, Yi Dong

arXiv:2610.34836v1cs.AIcs.MA

TL;DR

The paper asks whether multi-agent interaction adds reference-grounded reasoning alignment beyond matched self-refinement. It uses REMAP and studies information transfer and fact-level communication, finding broadly positive gains and improved results with compact exchange, alongside trade-offs from selective communication.

  • Problem

    It remains unclear whether multi-agent interaction adds reference-aligned reasoning beyond matched independent self-refinement, despite existing evaluations of reasoning traces and multi-agent task outcomes.

    Source: §1 · p. 1

  • Method

    REMAP measures alignment changes across agent trajectories and separates peer-information gains from local-content retention, then the study evaluates fact-level communication.

    Source: §1 · p. 2, §3.5 · p. 4, §5 · p. 8

  • Results

    Interaction yields broadly positive gains on non-owned content, and Compact-All improves alignment and pooled answer quality with fewer peer tokens than Full-MAS.

    Source: §4.4.1 · p. 7, §5 · p. 8

  • Takeaways & Limitations

    Collective emergent alignment can be quantified and linked to information-transfer patterns to guide multi-agent communication within the evaluated setting.

    Source: §5 · p. 8

    Composition and directional findings are exploratory because reused traces contain context mismatches and Mistral mixtures also change serving backend.

    Source: §4.3.3 · p. 6

Abstract

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Multi-agent large language model (LLM) systems can exhibit emergent behaviors through interaction, yet whether a similar phenomenon exists for reasoning alignment remains largely unexplored. We study whether agent interaction produces additional reference-grounded reasoning alignment beyond matched individual self-refinement, and introduce REMAP (Reference-Entailment-Matrix for Agentic Process), a framework that quantifies this effect through Semantic Coverage and interaction-specific alignment gains. Across diverse model families and two multi-hop reasoning benchmarks, we observe broadly positive interaction gains, particularly on reasoning content that depends on integrating evidence distributed across agents. These gains are consistently associated with independently measured peer-information recovery, while further analysis reveals composition-dependent heterogeneity effects and asymmetric information transfer across agent capability levels. Motivated by these findings, we further introduce a fact-level multi-agent communication framework that replaces full reasoning-trace exchange with compact, gap-aware, and selectively routed information. Our experiments show that compact fact exchange improves reasoning alignment and task performance while reducing communication overhead, whereas more selective communication exposes a trade-off between acquiring distributed information, retaining local content, and communication efficiency. Overall, our results show that collective emergent alignment can be quantified, linked to information-transfer patterns, and used to guide more effective multi-agent communication.

1 Introduction

The introduction asks whether interaction adds reference-grounded reasoning alignment beyond matched self-refinement, and presents REMAP to measure that gain and examine its relationship to information transfer and communication design.

1 Introduction

  • The open measurement gap is whether interaction adds reference-aligned reasoning beyond what the same agents gain through independent self-refinement.The paper calls this additional reference-grounded reasoning-alignment gain collective emergent alignment.Source: §1 · p. 1
  • REMAP compares reference units with agent reasoning units using bidirectional NLI, best-match Semantic Coverage, and matched initial-to-final coverage changes.Its ownership-aware variant isolates reference units initially supported by peers, and measurements are validated against answer quality and independent gold-item recovery.Source: §1 · p. 1
  • REMAP analyses associate collective gains with recovered peer information, composition-dependent gains, and exploratory directional differences.These observations motivate fact-level communication organized around the information available to each receiver.Source: §1 · pp. 1–2
  • The study asks how to quantify interaction gains, characterize associated information-transfer patterns, and use the findings to guide fact-level communication.The examined patterns include peer-information recovery, heterogeneous versus homogeneous composition, and owner–receiver directionality.Source: §1 · pp. 1–2
  • The paper contributes REMAP, empirical characterization across seven model families and two multi-hop benchmarks, and an evaluated fact-level communication framework.The framework connects peer-information acquisition, task performance, and communication efficiency.Source: §1 · p. 2

2 Related Work

Prior work evaluates reasoning quality and multi-agent coordination through varied metrics, while REMAP combines matched refinement and evidence ownership to measure interaction-associated alignment gains.

2 Related Work

  • Existing reasoning and multi-agent evaluation methods cover complementary process, alignment, coordination, and failure-analysis capabilities.Examples include SAS, ROSCOE, ReCEval, REVEAL, and NLI-hypergraph audits for reasoning, and MultiAgentBench, Who&When, MAST, and CARA for multi-agent systems.Source: §2 · p. 2
  • REMAP combines reference-based, multi-agent, matched-self-refinement, ownership, quality, and emergent-alignment capabilities to quantify interaction gains and distinguish peer acquisition from local retention.Its ownership-aware decomposition also informs multi-agent communication design.Source: §2 · p. 2
  • Table 1 compares methods by supported capabilities, including reference-based evaluation, multi-agent evaluation, matched self-refinement, ownership, quality, and emergent alignment.Its caption expands SAS, NLI-HG, MAB, W&W, and the reference-based ROSCOE variants.Source: Table 1 · p. 2, §2 · p. 2

3 Methodology

REMAP compares agents’ reference-grounded reasoning across matched self-refinement and multi-agent system (MAS) trajectories. It measures overall and ownership-aware coverage, then uses those findings to structure fact-level communication.

3.1 Preliminaries

  • Each agent’s response is scored against a fixed reference shared across agents, states, and conditions, using emitted reasoning steps and the conclusion.MuSiQue references use resolved subquestions and gold subanswers; corrected 2Wiki references use rendered evidence triples.Source: §3.1 · p. 2

3.2 Semantic Coverage

  • For each agent and state, REMAP compares every reference unit with every generated unit and retains each reference row’s best match.The matrix cell uses NLI entailment probabilities; a generated unit may match multiple reference rows.Source: §3.2 · pp. 2–3
  • The arithmetic mean of agent scores is the system score, preserving attribution of reference content to individual responses.Equal agent weighting yields a score in [0, 1]; overall coverage includes the conclusion, while ownership scores use intermediate rows.Source: §3.2 · p. 3, §3.4 · p. 4

3.3 Interaction-Specific Alignment Gain

  • REMAP compares matched initial-to-final coverage changes under self-refinement and MAS; positive EΔ means MAS gains more coverage, or loses less.Updates are synchronous and use matched questions, models, evidence allocations, update counts, and answer aggregation.Source: §3.3 · p. 3

3.4 Evidence Ownership

  • Ownership-aware coverage separates initially owned from non-owned evidence, so gains on peer-supported content can be read alongside local retention.Ownership is fixed by initial source allocation; the conclusion remains separate from ownership scores because it can depend on several sources.Source: §3.4 · pp. 3–4

3.5 Fact-Level Communication

  • Fact-level communication starts from fixed source cards and self-identified gaps, then compares broadcast, gap-aware selection, and confidence-guided routing policies.Compact-All shares both peer cards; GAP-Transfer selects by semantic match and screens with NLI; Jev-GAP uses action and confidence decisions with optional fallback.Source: §3.5 · p. 4, Figure 3 · p. 4

4 Experiments and Results

Experiments evaluate seven model families on held-out three-hop MuSiQue and corrected 2Wiki questions, comparing multi-agent interaction with matched self-refinement. Results cover alignment gains, peer-information recovery, team composition, directionality, and fact-level communication.

4.2.1 Cross-model alignment gains.

  • Interaction gains are positive throughout MuSiQue and for most models on 2Wiki, with positive non-owned gains in every reported setting.Gains are generally larger on corrected 2Wiki; Gemini still gains peer-supported content there despite a slightly negative overall contrast.Source: §4.2.1 · p. 5

4.2.2 Evidence gaps and answer saturation.

  • +100 percentage points in ΔF1 occurs for Terra and DeepSeek on all 174 question–seed units under the complementary-evidence 2Wiki protocol.The audit attributes the contrast to self-refinement abstention and correct MAS answers; the controlled split tests evidence integration, not general benchmark-wide performance.Source: §4.2.2 · pp. 5–6

4.3.1 Validity and peer recovery.

  • For Gemini and Qwen, correlations between E_nonΔ and gold recovery exceed corresponding correlations with ΔF1 on both tasks.Values are 0.525 and 0.664 on MuSiQue, and 0.612 and 0.606 on 2Wiki; positive associations persist under a strict 2Wiki subject-and-object check.Source: §4.3.1 · p. 6

4.3.2 Heterogeneous team gains.

  • Heterogeneous-team gains depend on model combination and comparison endpoint, although the weak-tier W1W1W2 mixture improves overall alignment and matched task gain over both endpoints on MuSiQue.Strong-tier mixing improves non-owned gain over one endpoint on both tasks but remains below the other.Source: §4.3.2 · p. 6, Table 4 · p. 7

4.3.3 Directional information recovery.

  • Adjusted recovery of strong-owned facts by weak receivers exceeds the reverse on both tasks, while medium-to-weak contrasts vary across tasks.The directional findings are exploratory because source traces include context mismatches and Mistral mixtures change serving backend; a context-consistent sensitivity test is pending.Source: §4.3.3 · p. 6, Table 5 · p. 7

4.4.1 Compact-exchange gains.

  • Compact-All and Jev-GAP-Fallback yield higher non-owned gains than evaluated topology baselines on both tasks, and Compact-All also improves overall alignment.The comparison uses fact cards from shared initial outputs; Table 6 reports matched Qwen/Gemini means over three seeds and two communication rounds.Source: §4.4.1 · p. 7, Table 6 · p. 8

4.4.2 Selection and local retention.

  • Jev-GAP uses the fewest peer tokens and retains more local content than Compact-All on 2Wiki, but acquires less peer-supported content; cost and performance leaders differ across methods.Compact-All has the highest F1 on MuSiQue and pooled, PEAR leads on 2Wiki, and AgentDropout has the lowest observed fees and latency; protecting local content can restrict peer acquisition.Source: §4.4.2 · p. 7, §4.4.3 · pp. 7–8

4.4.1 Compact-exchange gains.

  • In the evaluated distributed-evidence setting, Compact-All improves pooled F1 and source-information recovery over Full-MAS while delivering substantially fewer peer tokens on both datasets.MuSiQue F1 rises from 37.08 to 54.49 and delivered peer tokens fall from 1,725.7 to 407.4; 2Wiki F1 rises from 27.51 to 32.74 and tokens fall from 1,421.9 to 279.6.Source: §4.4.1 · p. 7, Table 6 · p. 8

5 Conclusion

The conclusion reports broadly positive interaction gains on non-owned reasoning content and introduces fact-level communication to manage acquisition, retention, and communication costs. The appendices specify how REMAP computes and decomposes coverage, its scoring properties, and its computational requirements.

5 Conclusion

  • Across model families, interaction yields broadly positive gains on non-owned content, and compact fact exchange improves alignment and pooled answer quality with fewer peer tokens.Selective communication exposes trade-offs among information acquisition, local retention, and communication efficiency.Source: §5 · p. 8

A.1 Notation Reference

  • REMAP scores each agent equally, with each agent’s non-owned reference units averaged equally within that agent.This preserves per-agent coverage rather than scoring the union of the team’s outputs.Source: §A.1 · p. 11, §A.2 · p. 11

A.2 Reference–Output Matching: A Worked Example

  • Row-wise best matches require neither step-order constraints nor a global one-to-one assignment, and REMAP averages agent scores rather than pooling team outputs.A pooled maximum can count peer facts even when no individual agent expresses them.Source: §A.2 · p. 11

A.3 Ranges and Invariances

  • A fixed question-specific offset cancels from the contrasts, but sampling variation and changes in reference representation require separate empirical controls.Under bounded local-score perturbations, the appendix derives deterministic sensitivity bounds; it does not assume a known NLI-error bound.Source: §A.3 · p. 12

A.4 Ownership Decomposition

  • A positive non-owned contrast can be offset by the combined owned and conclusion components, so these contributions need separate row-level measurements.The decomposition uses frozen ownership sets and weights.Source: §A.4 · p. 12

A.5 Computation and Caching

  • With caching, the uncached upper bound is 4N(T + 1)KJ directional evaluations per question; ownership changes only row aggregation and reuses the same scores.For the three-agent, three-state, four-unit example, this is at most 576 evaluations per question.Source: §A.5 · p. 12

B Data, Protocol, and Execution Details

The appendices detail deterministic reference construction for MuSiQue and corrected 2Wiki, matched self-refinement and MAS protocols, and the execution and uncertainty procedures. The corrected 2Wiki audit reports both reference-mapping checks and a held-out subset used for primary results.

B.1 MuSiQue Reference Construction

  • MuSiQue references resolve decomposition steps with earlier gold subanswers and append the gold conclusion, using 100 held-out questions selected with a frozen manifest.The held-out set excludes 30 pilot IDs; later model-family experiments reuse the same question IDs and evidence allocations.Source: §B.1 · p. 12

B.2 Corrected 2Wiki Construction and Audit

  • The corrected 2Wiki protocol renders official evidence triples as factual text, and primary results use the frozen 58-question subset outside the 30-question development/validation set.An audit found seven incorrect or insufficient mappings among 60 inspected assignments; all 88 exact-gold answer-evaluation invariants passed.Source: §B.2 · pp. 12–13

B.3 Condition Semantics

  • Self-refinement uses local evidence and the agent’s prior response, while MAS additionally receives peers’ previous responses under a synchronous update barrier.Each update consumes messages from the immediately preceding state, and the main three-unit runs require exactly three reasoning steps.Source: §B.3 · p. 13

B.4 Provider and Repetition Registry

  • Provider settings and fallback behavior are recorded, while provider support determines whether request-level seeds are effective.Output caps, reasoning settings, retries, and successful-record selection are described for the reported runs.Source: §B.4 · p. 13

B.5 Answer Aggregation and Uncertainty

  • Final answers use the same deterministic plurality rule in both conditions, and bootstrap intervals resample matched question-level outcomes across the realized runs.Seed means and standard deviations describe run variation separately from uncertainty across sampled questions.Source: §B.5 · p. 13

C.1 Absolute Scores and Task Response

The results compare semantic coverage and task outcomes across models and report seed-level variation and corrected 2Wiki answer saturation. The gold-recovery validation uses a separate lexical diagnostic, with stated limits on what value matching can establish.

C.1 Absolute Scores and Task Response

  • Gemini has final coverage 0.3303 and EΔ = 0.0217, while Terra has final coverage 0.2758 and EΔ = 0.0422, so the leaders differ by measure.Table 9 covers seven model families on both primary datasets, pairing coverage with F1 and alignment gain with matched task gain.Source: §C.1 · p. 13, Table 9 · p. 14, Table 10 · p. 15

C.2 Seed-Level Variation

  • Overall and non-owned contrasts have positive means in every displayed MuSiQue seed run, but task gains vary across seeds and models.Haiku has negative ΔF1 in two seeds and positive ΔF1 in one; Terra’s task gain is negative in all three, while Mistral’s is positive in all three.Source: §C.2 · p. 13, Table 11 · p. 15

C.3 Answer Saturation on Corrected 2Wiki

  • On corrected 2Wiki, Terra and DeepSeek have MAS F1 = 1 and self-refinement F1 = 0 in all 174 held-out question–seed units per model.Their constant profiles yield 100% MAS F1 and +100 percentage points for ΔF1; the audit attributes the floor–ceiling contrast to controlled evidence integration and peer-information recovery.Source: §C.3 · pp. 13–14

D.1 Deterministic Gold-Item Recovery

  • The independent lexical diagnostic measures gold-item recovery from emitted reasoning, but value mentions can miss paraphrases or match the wrong subject, relation, or polarity.A stricter diagnostic requires subject and object co-mention in the same structured unit.Source: §D.1 · p. 14

D.2 Task-Gain Criteria and Alternative Scorers

The appendices specify alternative task-gain criteria, auxiliary evidence-allocation protocols, the fact-level communication runtime, and matched-control caveats. They also describe how paired effects and communication costs are accounted for.

D.2 Task-Gain Criteria and Alternative Scorers

  • Alternative coverage scorers retain the best generated-unit match per reference row and the same time and condition contrasts; point-estimate rankings do not establish significance without joint resampling.The alternatives include token F1, ROUGE-L, and cached MiniLM cosine scores.Source: §D.2 · p. 15

D.3 Answer Transitions and Initial-State Diagnostics

  • Answer transitions classify matched final answers as correct or wrong, while initial coverage and ownership decomposition distinguish available headroom from recovery of non-owned content.Visible-length correlations with EΔnon are descriptive associations for the evaluated model–benchmark combinations.Source: §D.3 · p. 15

E Depth and Evidence-Allocation Protocol

  • Depth comparisons change question content and evidence allocation together, whereas agent-count comparisons hold questions and four supporting paragraphs fixed but alter evidence fragmentation and call budget.Within each configuration, self-refinement and MAS use matched questions, allocations, and response schedules.Source: E Depth and Evidence-Allocation Protocol · pp. 15–16

F.1 Architecture State and Runtime Inputs

  • GAP selects peer facts by matching receiver gaps to a fixed directory of initial facts, then gates candidates against receiver memory before integration.Candidates are deduplicated and capped at two; acquired claims are not recursively forwarded as new source facts.Source: §F.1 · p. 16

F.2 Condition Definitions and Matched Controls

  • Soft-versus-transfer comparisons include local-evidence presentation and later state changes, while hard-versus-transfer comparisons also include memory and control differences.The hard treatment additionally differs in preservation wording.Source: §F.2 · p. 16, Table 15 · p. 17

F.3 Common-Subset Execution

  • The retention comparison uses Qwen and Gemini on the primary sets under a shared-start protocol, and GAP-SOFT adds $2.6198 in generation cost.Architecture results are evaluated separately within their matched shared-start protocol.Source: §F.3 · p. 17

F.4 Accounting and Paired Comparisons

  • Communication-token totals count delivered peer payloads, while total tokens include full input and output usage; paired effects resample question clusters.Model selection, embedding work, and NLI-gate work are accounted for separately from API token and dollar totals.Source: §F.4 · p. 17

G.1 Common-Subset Architecture Outcomes

The common-subset follow-up compares communication architectures and their matched controls, then examines how routing decisions and scoring choices shape the reported contrasts. The results distinguish task outcomes from alignment, retention, and communication effects.

G.1 Common-Subset Architecture Outcomes

  • On MuSiQue, GAP-SOFT raises F1 from 35.99% to 43.45% versus GAP-Transfer, while owned change rises from −0.0490 to −0.0014.The follow-up reports architecture means on the common Qwen/Gemini subset; matched contrasts depend on the corresponding control assignment.Source: §G.1 · p. 17

G.2 Paired Retention Effects

  • For GAP-SOFT versus GAP-Transfer, the pooled non-owned effect is −0.0405 [−0.0514, −0.0296] and the pooled owned effect is 0.1016 [0.0836, 0.1200].On held-out 2Wiki, raw F1 differs by −3.65 points while the matched-change difference is +1.53 points because the controls differ.Source: §G.2 · p. 17

G.3 Routing Agreement and Later Divergence

  • First-update routing comparisons agree exactly, while second-update decisions differ in 29.89%–56.90% of the reported receiver cells.The soft and hard treatments differ in local-evidence presentation and retention instructions; the hard treatment also changes gate memory and its matched control.Source: §G.3 · pp. 17–18

H.1 Shared-Start Extension

  • The shared-start extension reuses initial records, runs two synchronous updates, and keeps references and gold labels out of generation-time state.The controller evaluates peers’ original local fact cards rather than retrieving the gold reference.Source: §H.1 · p. 18

H.2 Typed Outputs and Confidence Semantics

  • JEV-GAP sends up to two SEND candidates; fallback uses selective delivery only when a gap has a SEND candidate with confidence at least 0.70.The fallback otherwise supplies compact peer fact cards; the evaluated change replaces heuristic relevance/NLI routing with typed decision control.Source: §H.2 · p. 18

H.3 Scoring, Pairing, and Accounting

  • A frozen scorer evaluates reasoning states, while paired inference uses question resampling and combined estimates weight the two benchmarks by question counts.The report lacks a fresh contemporaneous baseline timing run and full controller-traffic cost allocation per method.Source: §H.3 · p. 19

H.4 Policy Comparisons

  • Controller variants are compared with GAP-Transfer and Full-MAS, with direct paired contrasts between selective and fallback delivery.Compact-All and Random-K are additional controls; these comparisons use the same initial cards and reasoning-update schedule.Source: §H.4 · p. 19

I.1 Architecture Outcomes

The architecture outcomes report pooled alignment, recovery, and answer metrics, followed by communication cost and paired policy contrasts. The accompanying baselines vary from compact fact-card controls to topology-level routing adaptations.

I.1 Architecture Outcomes

  • JEV-GAP-FALLBACK has pooled EΔ = 0.09318, E_nonΔ = 0.16420, ΔTgold = 0.32103, and F1 = 0.41653.Mean delivered peer payload is 329.175 tokens per question and run.Source: §I.1 · p. 19

I.2 Communication, Cost, and Latency

  • The fallback payload is 23.17% of Full-MAS on MuSiQue and 14.58% on 2Wiki, with a weighted combined ratio of 20.39%.Its reported workflow latencies are 17.30 and 13.97 seconds, respectively.Source: §I.2 · pp. 19–20

I.3 All Paired Contrasts

  • Against GAP-Transfer, pooled JEV-GAP F1 increases by 0.05511 [0.02492, 0.08629]; fallback raises non-owned gain by 0.03964 [0.03100, 0.04833].Fallback’s pooled F1 increment is 0.01935 [−0.00724, 0.04634].Source: §I.3 · p. 20

J Communication-Family Baselines: Protocol and Budgets

  • The shared-start baseline reports reuse frozen initial records, reference-free generation, and offline scoring after execution.Its baseline reports keep topology-level routing and fact-level communication as separate families.Source: J Communication-Family Baselines:… · p. 20

J.1 Compact and Random Controls

  • Compact-All broadcasts both initial peer fact cards at each update, while Random-K samples the same pool to match the fallback’s message count.Random-K controls selection content conditional on the target’s message-count schedule, not when messages are requested.Source: §J.1 · p. 20

J.2 Topology-Level Adaptations

  • AgentPrune and AgentDropout prune topology but retain Full-MAS packets; PEAR [6] routes at degree one with neutral first-step confidence.Each external method uses one development-selected configuration, with the reported budget mismatches retained.Source: §J.2 · p. 20

J.3 Executed Budget Profiles

The executed-budget profiles compare realized peer-token use and recorded runtime resources across communication methods. The pooled statistics summarize the fixed Qwen/Gemini population across the two benchmarks.

J.3 Executed Budget Profiles

  • AgentDropout uses 68.26% of fallback’s MuSiQue payload and 109.48% on 2Wiki; PEAR uses 107.04% and 203.38%, respectively.These profiles compare realized operating points; topology-optimization amortization is unspecified.Source: §J.3 · pp. 20–21

J.4 Statistics and Comparison Scope

  • Compact-All leads pooled acquisition and F1 means, while Jev-GAP uses the smallest peer payload in the fixed Qwen/Gemini population.Combined estimates weight the 100 MuSiQue and 58 2Wiki questions by their counts.Source: §J.4 · p. 21

K Complete Communication-Family Results

The communication-family results compare content acquisition, answer quality, and payload across compact, selective, and topology-based policies. A separate composition follow-up reports same-tier mixture contrasts and notes important trace and model-serving qualifications.

K.1 Random-K, Compact-All, and AgentPrune Contrasts

  • Against Random-K, fallback’s pooled non-owned difference is −0.00189 [−0.00930, 0.00554], while its owned contrast is 0.02264 [0.01218, 0.03323].Against Compact-All, fallback’s pooled overall gain, non-owned gain, gold recovery, and F1 differences are all negative, while its owned difference is 0.09749 [0.07512, 0.12122].Source: §K.1 · p. 22, Table 25 · p. 22

K.2 AgentDropout and PEAR Contrasts

  • Fallback’s MuSiQue F1 exceeds AgentDropout by 0.17111 and PEAR by 0.17179, but on 2Wiki it trails PEAR by 0.17010.In both tasks, fallback and Compact-All have positive non-owned and gold-recovery differences over AgentDropout and PEAR.Source: §K.2 · p. 22, Table 33 · p. 26, Table 34 · p. 27

L.1 Design and Tier Notation

  • The composition follow-up tests six same-tier mixtures and two W–M–S mixtures, assigning capability tiers from frozen MuSiQue self-refinement F1.It uses three seeds, three agents, two rounds, and rotates model-to-evidence positions across questions.Source: §L.1 · p. 28

L.2 Source-Trace Audit

  • Comparisons involving Mistral combine composition changes with a serving-backend change; inherited traces also have context mismatches on 69 MuSiQue and 29 2Wiki questions.A paired sensitivity analysis on the context-consistent subset is pending, and the composition and directional estimates retain exploratory status.Source: §L.2 · p. 28

L.3 Complete Same-Tier Comparisons

  • The same-tier tables retain paired contrasts against both homogeneous endpoints, with each row comparing one mixture to a particular component control.The two rows for a mixture show how its gain changes with the selected endpoint.Source: §L.3 · p. 28

L.4 Directional Recovery and Reciprocal Contrasts

This appendix documents directional recovery conventions, experimental scope and provenance, and normalized prompt and communication protocols.

L.4 Directional Recovery and Reciprocal Contrasts

  • Directional recovery distinguishes raw recovery among initially absent non-owned facts from self-refinement-adjusted gold gain, which uses a separate normalization.Reciprocal contrasts compare reversed ownership and receiver roles after subtracting self-refinement differences; the source report and main text present the contrasts with opposite signs.Source: §L.4 · p. 28, Table 40 · p. 31, Table 41 · p. 31

M Manuscript Artifacts and Research Scope

  • The experiments evaluate expressed reasoning in factual question answering on public benchmarks, with reference alignment based on annotated intermediate information and final answers.Interpretation depends on reference quality, evidence allocation, and the specified matching procedure.Source: M Manuscript Artifacts and Research… · p. 32

N Prompt Templates

  • Prompt templates normalize recorded protocol interfaces, but verbatim API requests are absent and remain necessary for byte-exact replication.References, gold labels, answer aliases, and evaluation scores are excluded from generation and routing inputs.Source: N Prompt Templates · p. 32

N.1 Matched Reasoning Trajectories

  • Matched trajectories use the same response structure, while MAS updates additionally receive prior-round peer responses alongside the agent’s own previous response.The corrected 2Wiki protocol also exposes peer-reported local facts for integration.Source: §N.1 · pp. 32–33

N.2 Fact-Level Communication

  • Fact-level communication emits a supported local fact and information gaps, then integrates delivered peer fact cards into updated reasoning.Fact-card generation and initial reasoning share one model call; variants differ in delivered cards and retention memory.Source: §N.2 · p. 33

N.3 Typed Jev Queries and Delivery Policy

  • Jev evaluates candidate facts for relevance, novelty, and conflict, then chooses to SEND, SKIP, or QUARANTINE them.A programmatic fallback broadens sharing when no SEND candidate meets the recorded 0.70 action-confidence threshold.Source: §N.3 · pp. 33–34

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