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arxiv: 2606.20695 · v1 · pith:P3QC2TTYnew · submitted 2026-06-15 · 💻 cs.MA · cs.AI

How Much Coordination Gain Is Real? A Paired Noise-Floor Protocol for Multi-Agent LLM Benchmarks

Alibek T Kaliyev , Artem Maryanskyy This is my paper

Pith reviewed 2026-06-27 02:45 UTC · model grok-4.3

classification 💻 cs.MA cs.AI
keywords multi-agent coordinationLLM benchmarksnoise floorpaired trialsreplication protocoltau^2-benchconfiguration equivalence
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The pith

Paired inert protocols on the same model produce gaps up to 18pp that exceed most published multi-agent coordination effects.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper measures disagreement between two configuration-equivalent but inert protocols on identical model and benchmark inputs, short of full identity replay. On Claude Haiku 4.5 with tau^2-bench retail, the no_coord versus intercept contrast yields signed paired gaps of +10pp and 0pp across two n=100 seeds, with a pooled upper Wilson CI near 15pp and no significant trial-0 contrasts after correction. Seven of ten recent multi-agent coordination architectures report headline effects below this observed local envelope. The work defines a minimum reporting protocol centered on coordination-active pass^k with sample-size targets. It also reports that pull and intercept readers show no improvement in trial-1 recovery under this setup.

Core claim

On Claude Haiku 4.5 against tau^2-bench retail, the clean configuration-equivalent contrast between no_coord and intercept, both inert at trial 0, produces signed paired gaps of +10pp and 0pp across two n=100 seeds; pooled across both, +5pp with Wilson CI [-2,+12], not significant. The envelope of observed paired gaps spans [-3,+18]pp across two seeds, with pooled upper Wilson CI ~15pp. Seven of ten recent multi-agent coordination architectures report headline effects below this local floor, and one more sits inside the envelope.

What carries the argument

The configuration-equivalent contrast between two inert protocols (no_coord and intercept) under code inspection plus SHA-256 byte audit of API inputs, which sets the paired noise floor for coordination claims.

If this is right

  • Headline effects below the observed 15pp upper bound cannot be distinguished from paired noise in this input-matched setting.
  • Any coordination claim must report coordination-active pass^k restricted to trials where the mechanism is logically active.
  • Sample-size targets and runtime hooks become required to place reported deltas outside the local envelope.
  • The same-model paired replication protocol is needed to test survival of original headline effects.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If the noise envelope varies by model size or benchmark domain, the minimum credible effect size would need to be remeasured for each new setting.
  • Extending the protocol to active coordination mechanisms might raise the observed floor when those mechanisms introduce additional input variation.
  • The lack of improvement from candidate readers on trial-1 recovery points to sources of variation beyond the configuration match itself.

Load-bearing premise

That the clean configuration-equivalent contrast between no_coord and intercept on Claude Haiku 4.5 against tau^2-bench retail accurately represents the noise floor that would apply to active coordination mechanisms under the same input-matching protocol.

What would settle it

Running the identical paired inert contrast on a different model or benchmark and consistently observing gaps above 18pp would show that the local floor measured here does not generalize.

Figures

Figures reproduced from arXiv: 2606.20695 by Alibek T Kaliyev, Artem Maryanskyy.

Figure 1
Figure 1. Figure 1: Reader-side architecture contrast. The two designs share the event store, writer policy, and MCP transport; they differ [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Headline visual (seed-1 of two 𝑛=100 seeds; §6.3.2 reports the second seed and pooled tests). The coordination-active head-to-head shows no detectable effect at the available power; the trial-0 paired gap is the noise-floor estimate. (a) Coordination￾active head-to-head. Success rate by protocol at trial 0 (empty store, coordination inert) and trial 1 (store filled). no_coord and intercept are configuratio… view at source ↗
Figure 3
Figure 3. Figure 3: Trial-0 paired-sign-test signed gaps across seed, model, domain, and contrast. The noise floor is a measurement output [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
read the original abstract

Multi-agent LLM coordination papers report small benchmark deltas as evidence that one architecture beats another. A prior question: how much paired trial-0 disagreement do two protocols produce on the same model and benchmark when their API inputs are configuration-equivalent (matched by code inspection plus a SHA-256 byte audit), short of full identity-replay? On Claude Haiku 4.5 against tau^2-bench retail, the clean configuration-equivalent contrast (no_coord vs. intercept, both inert at trial 0) gives signed paired gaps of +10pp and 0pp across two n=100 seeds; pooled across both, +5pp with Wilson CI [-2,+12], not significant. The largest single-seed contrast (+18pp pull-vs-intercept, p_corr=0.012) did not reproduce at the second seed (-3pp, p_corr=1.0); no trial-0 contrast is significant after Bonferroni at either seed or pooled. The envelope of observed paired gaps spans [-3,+18]pp across two seeds, with pooled upper Wilson CI ~15pp. Seven of ten recent multi-agent coordination architectures report headline effects below this local floor, and one more sits inside the envelope; whether they survive a same-model paired replication is, by construction, untested in their original settings. We define coordination-active pass^k, pass^k restricted to trials where the coordination mechanism is logically active, as the minimum reporting protocol, with sample-size targets and runtime hooks in the body. Measurements run on ET-MCP, a task-scoped negative-knowledge store conformant with MCP 2026-07-28, used as a substrate to isolate reader-side choices, not as a contribution. On Haiku 4.5 the candidate readers (pull, intercept) do not improve trial-1 recovery; we give a preliminary diagnosis of failure modes with refinements on existing production hook surfaces.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. The paper claims that a paired noise-floor protocol using two configuration-equivalent inert protocols (no_coord vs. intercept) at trial 0 on Claude Haiku 4.5 and tau^2-bench retail yields observed signed gaps with envelope [-3,+18]pp and pooled upper Wilson CI ~15pp; no contrast is significant after Bonferroni correction. It reports that seven of ten recent multi-agent coordination papers have headline effects below this local floor (with one inside the envelope) and defines a minimum reporting protocol using coordination-active pass^k.

Significance. If the local inert gap measurement is reproducible and the protocol is adopted more broadly, the work would be significant for establishing empirical baselines against which small coordination deltas can be evaluated, encouraging same-model paired replications. Strengths include the use of SHA-256 byte audit for input equivalence, Wilson intervals, Bonferroni correction, and explicit distinction of coordination-active subsets.

major comments (2)
  1. [Abstract] Abstract: the reported statistical results (n=100 seeds per contrast, specific gaps of +10pp/0pp, pooled +5pp with Wilson CI [-2,+12], non-reproduction of the +18pp contrast, and Bonferroni-adjusted non-significance) cannot be verified because the manuscript supplies no full methods, data tables, or code; this directly affects the soundness of the noise-floor envelope.
  2. [Abstract] Abstract: the central claim that seven of ten papers fall below the local floor treats the inert no_coord/intercept gap on Haiku 4.5 + tau^2-bench retail as representative of the relevant variability for active coordination mechanisms; the manuscript provides neither cross-model/cross-benchmark replications nor an argument that prompt complexity or decision branching under active mechanisms would not inflate variance beyond the inert baseline.
minor comments (1)
  1. The definition of coordination-active pass^k and the role of the ET-MCP substrate as a negative-knowledge store would benefit from an expanded methods subsection with concrete examples of how reader-side choices are isolated.

Simulated Author's Rebuttal

2 responses · 1 unresolved

We thank the referee for the constructive comments on our manuscript. We address each major comment below and indicate the revisions we will incorporate.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the reported statistical results (n=100 seeds per contrast, specific gaps of +10pp/0pp, pooled +5pp with Wilson CI [-2,+12], non-reproduction of the +18pp contrast, and Bonferroni-adjusted non-significance) cannot be verified because the manuscript supplies no full methods, data tables, or code; this directly affects the soundness of the noise-floor envelope.

    Authors: We agree that the absence of full methods, data tables, and code in the current manuscript version prevents independent verification of the reported statistics. In the revised manuscript we will add a dedicated methods section describing the paired protocol, SHA-256 audit procedure, seed handling, and statistical corrections; we will also include the complete data tables for both n=100 seeds and provide a permanent link to the open code repository containing the exact scripts used. revision: yes

  2. Referee: [Abstract] Abstract: the central claim that seven of ten papers fall below the local floor treats the inert no_coord/intercept gap on Haiku 4.5 + tau^2-bench retail as representative of the relevant variability for active coordination mechanisms; the manuscript provides neither cross-model/cross-benchmark replications nor an argument that prompt complexity or decision branching under active mechanisms would not inflate variance beyond the inert baseline.

    Authors: The manuscript presents the measured gap explicitly as a local noise floor for this specific model-benchmark pair and inert protocols, not as a universal representative. The core argument is that any coordination claim should be evaluated against a same-model paired baseline on the authors' own setup. We will add a clarifying paragraph in the discussion that (a) acknowledges active mechanisms may increase variance due to prompt complexity and branching, (b) positions the inert envelope as a conservative minimum reporting threshold rather than an upper bound, and (c) reiterates the recommendation for same-model paired replications. Cross-model and cross-benchmark replications are outside the scope of the present work. revision: partial

standing simulated objections not resolved
  • The manuscript does not contain cross-model or cross-benchmark replications of the inert gap measurement.

Circularity Check

0 steps flagged

No circularity; empirical measurements compared to external reports

full rationale

The manuscript reports direct experimental measurements of paired gaps between configuration-equivalent inert protocols (no_coord vs. intercept) on a fixed model and benchmark, then compares the resulting envelope to headline deltas from ten other papers. No equations, fitted parameters, self-definitional relations, or load-bearing self-citations appear in the derivation chain; the noise-floor envelope is an observed quantity, not one that reduces to the inputs it is used to bound. The generalization concern raised in the skeptic note is an external-validity question, not a circularity reduction.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The paper relies on standard statistical assumptions for binomial proportions and multiple-testing correction. No free parameters are fitted to produce the noise floor; it is measured directly from the paired trials. No new entities are postulated.

axioms (2)
  • standard math Wilson score interval is the appropriate confidence interval for the observed paired success-rate gaps
    Invoked when reporting the pooled CI of [+5pp] with bounds [-2,+12]
  • standard math Bonferroni correction adequately controls family-wise error for the set of contrasts tested across seeds
    Applied to declare no trial-0 contrast significant after correction

pith-pipeline@v0.9.1-grok · 5892 in / 1422 out tokens · 68541 ms · 2026-06-27T02:45:09.268793+00:00 · methodology

discussion (0)

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Reference graph

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