---
# THIS RELEASE IS MIXED-LICENCE and both licences are declared here, so the Hub's own
# metadata does not assert a single one over content it does not cover:
#   apache-2.0 -> this project's derived material AND the Omni-MATH-2 upstream
#   mit        -> the SciBench upstream (c) 2023 Xiaoxuan Wang
# This field cannot express WHICH rows carry WHICH licence. Filter by
# benchmark_id. LICENSES/README.md + LICENSES/registry.json are the authority.
license:
  - apache-2.0
  - mit
task_categories:
  - question-answering
language:
  - en
tags:
  - multi-agent
  - llm-agents
  - reasoning
  - agent-trajectories
  - self-correction
size_categories:
  - 10K<n<100K
configs:
  - config_name: trajectories
    data_files: data/trajectories.parquet
  - config_name: evaluator_calls
    data_files: data/evaluator_calls.parquet
  - config_name: role_messages
    data_files: data/role_messages.parquet
  - config_name: enforcement_events
    data_files: data/enforcement_events.parquet
  - config_name: adjudication
    data_files: data/adjudication.parquet
  - config_name: scibench_trajectories
    data_files: data/scibench/trajectories.parquet
  - config_name: scibench_evaluator_calls
    data_files: data/scibench/evaluator_calls.parquet
  - config_name: scibench_role_messages
    data_files: data/scibench/role_messages.parquet
---

# Beyond Division of Labor: How Roles Shape Feedback and Recovery in Multi-Agent Systems

[Project Website](https://chihhsuan-yang.github.io/AAMAS2027-AgentProtocols/) | [Code](https://github.com/ChihHsuan-Yang/AAMAS2027-AgentProtocols) | [Paper](https://chihhsuan-yang.github.io/AAMAS2027-AgentProtocols/paper.pdf)

Chih-Hsuan Yang, Xinyang Li, Rajeev Thakur, and Feng Yan.

**Public research release v1.2.0, October 31, 2026.** This release contains usable raw
trajectories and analysis-ready tables for studying agent roles, feedback delivery,
and recovery after an incorrect answer.

**Roles govern decision rights and feedback access.** Roles allocate decisions as well as work. We compare a Planner–Executor–Reviewer team with and without role instructions, holding the agents, topology, call budget and ground-truth evaluator fixed. Removing roles largely eliminates specialization without lowering first-pass accuracy. After a failed answer, the role-free team recovers more often across five model–benchmark settings with feedback available to both teams. Submission logs show that the role-structured Reviewer often withholds approval, reducing opportunities for correction. In one exploratory intervention on 400 Omni-MATH problems with gemma-4, keeping the role prompts but forcing submission every cycle raises recovery from 0.198 to 0.613; the paired comparison detects no difference from the role-free team. The takeaway: evaluate who may submit, who receives feedback, and whether the team recovers—not just whether agents follow their roles. These findings concern systems with reliable external feedback.

**Start here: roles and feedback delivery must be separated.** The frozen
campaign's role-free condition (`B`) did **not** receive evaluator feedback,
although its metadata recorded evaluation activity. Its comparison with `A`
therefore changes both roles and feedback access. It cannot establish that roles
alone improve recovery. The later `Bf` control delivers feedback to role-free
agents; those agents recover substantially more often. See the
[feedback-control results](controls/rolefree_feedback/gemma4/README.md).

## What you can use

| Material | Size | Useful for |
|---|---:|---|
| Frozen Omni-MATH trajectories | 11,600 | Inspecting model messages, evaluations, revisions, and structural enforcement across three actors |
| Frozen SciBench trajectories | 2,296 | Comparing behavior on college chemistry and physics, with domain-specific prompts |
| Feedback-enabled role-free controls (`Bf`), first run | 4,748 | The paper's main comparison: three actors on Omni-MATH, two on SciBench |
| Forced-submission run (`Afs`, Gemma) | 400 | Role prompts kept, a submission forced every cycle |
| Re-run of `A` on 400 frozen problems (Gemma) | 400 | Endpoint-drift check, and the baseline for the forced-submission run |
| `Bf` second run (Gemma) and its re-run of `A` | 2,174 + 400 | An independent replicate of the two Gemma `Bf` cells |

The **13,896 frozen trajectories** have both original JSONL and normalized
Parquet tables. The **8,122 later trajectories** (two runs of the feedback controls, the
forced-submission run and two re-runs of `A`) are separate JSONL files under
`controls/`; do not silently pool them into the frozen tables. The release also
includes prompts, evaluation calls, role messages, enforcement events,
adjudication material, and the build and validation scripts.

**Coverage: every trajectory behind the paper.** v1.2.0 adds, under
`controls/run1/`, the first run of the feedback controls in all five
model–benchmark cells (the paper's main text), the forced-submission run and
its re-run of `A`. The [code repository](https://github.com/ChihHsuan-Yang/AAMAS2027-AgentProtocols)
re-derives every number and table in the paper from `raw/` and `controls/`
byte for byte, and redraws every figure pixel-identical.

## Quick start

```python
from datasets import load_dataset

# Frozen campaign: B means role-free WITHOUT delivered evaluator feedback.
trajectories = load_dataset("AgentsSci/AAMAS2027-Roles", "trajectories", split="train")
scibench = load_dataset("AgentsSci/AAMAS2027-Roles", "scibench_trajectories", split="train")

# Feedback-delivery control (first run, the paper's main text), kept separate.
from huggingface_hub import hf_hub_download
import pandas as pd
path = hf_hub_download(
    repo_id="AgentsSci/AAMAS2027-Roles", repo_type="dataset",
    filename="controls/run1/bf_omnimath_gemma4.jsonl",
)
feedback_control = pd.read_json(path, lines=True)
```

**Licensing is source-specific:** Omni-MATH-2 is Apache-2.0; SciBench is MIT.
Consult `LICENSES/README.md` and `LICENSES/registry.json` before redistribution.
The structured prompts differ by domain, so inspect `config/` before pooling.

## Condition names: the data says `A`/`B`/`C`/`Cp`, the paper says words

**Read this before writing any filter.** The accompanying manuscript names
conditions by what they *are*; the released data keeps the short internal codes
it was collected under. They are the same four conditions under two
vocabularies:

| raw column value | condition |
|---|---|
| `A` | **role-structured** |
| `B` | **role-free, feedback withheld in the frozen campaign** |
| `C` | **structurally enforced** |
| `Cp` | **context-restored structural enforcement** |

**The raw columns deliberately keep `A`/`B`/`C`/`Cp`.** Renaming them would
break provenance against every manifest, checksum and analysis script in this
release — `manifests/cell_census*.json`, `raw/MANIFEST*.json`,
`scripts/validate_artifact.py`, `scripts/validate_scibench.py` and the
analysis code all key on the letters. So the mismatch between the paper's words
and the data's codes is **intended**, not an inconsistency: filter on `arm ==
"A"`, and read it as *role-structured*.

One spelling note: the fourth condition is written `Cp` in the data (and
`CP_*` in prompt keys) but renders as **C′** in prose, including in this card.
Same condition.

## Interpreting the frozen campaign

The frozen tables show lower recovery in `B` than in `A`, but `B` also lacks
delivered evaluator feedback. More evaluator calls do not mean the actors saw
more feedback. This distinction supersedes the original interpretation that
roles alone explained the frozen recovery gap.

The later control (`Bf`) changes Gemma's recovery from 16/316 to 193/317 on
Omni-MATH and from 6/118 to 49/117 on SciBench (first run; the independent
second run gives 177/302 and 54/124); denominators are each condition's
first-pass-wrong runs. These are descriptive conditional rates, not a paired
causal effect by themselves. Read the control READMEs for paired comparisons and
endpoint-drift limitations. The general lesson is to verify the messages agents
actually received before attributing recovery differences to role structure.

## Design

| raw `arm` | condition | what it is |
|---|---|---|
| **`A`** | **role-structured** | distinct planner / executor / reviewer prompts |
| **`B`** | **role-free (feedback withheld)** | three agents, one generic prompt; evaluator feedback not delivered |
| **`C`** | **structurally enforced** | role-boundary violations rejected and regenerated |
| **`Cp`** (C′) | **context-restored structural enforcement** | `C` with `shared_history` restored |

Trajectory counts per cell (column headers are the raw `arm` codes):

| actor model | `A` role-structured | `B` role-free | `C` structurally enforced | `Cp` context-restored |
|---|---|---|---|---|
| `google/gemma-4-31B-it` | 1,600 | 1,600 | 1,600 | 400 |
| `openai/gpt-oss-120b` | 1,600 | 1,600 | 1,600 | 400 |
| `meta-llama/Llama-3.3-70B-Instruct` | 400 | 400 | 400 | — |

**Second domain — SciBench (v1.1.0), role-structured and role-free only
(`arm` ∈ {`A`, `B`}):**

| actor model | `A` role-structured | `B` role-free | `C` structurally enforced | `Cp` context-restored |
|---|---|---|---|---|
| `google/gemma-4-31B-it` | 574 | 574 | — | — |
| `openai/gpt-oss-120b` | 574 | 574 | — | — |

There is **no structurally-enforced condition in SciBench** (no `arm == "C"`),
so there is **no `enforcement_events` table and no adjudication study for that
domain**. Those remain Omni-MATH-only.

Grader: `openai/gpt-oss-120b`, temperature 0 — **the same checkpoint as one of
the three actors** — in both domains. Budget identical across arms *and across
domains* (3 outer × 2 inner = 6 cycles), temperature 0, `max_tokens` 8192.
Corpora: 1,600 Omni-MATH-2 competition-math problems, and 574 SciBench
college chemistry/physics problems.

`config/` holds the **exact** prompts, JSON schemas and every knob. The paper is
about role manipulation, so the data is not interpretable without them.

## Contents

| path | what |
|---|---|
| `raw/` | **the frozen traces** (exact bytes except 14 redacted `error` fields; see *Redaction*) — `campaign_v2.jsonl` (9,600), `actor3.jsonl` (1,200), `armCp.jsonl` (800) + `MANIFEST.json`; **`scibench_AB.jsonl` (2,296) + `MANIFEST_SCIBENCH.json`** |
| `data/trajectories.parquet` | 11,600 rows — one per trajectory; the main results tables |
| `data/role_messages.parquet` | 83,320 rows — one per role message; collapse, duplication, frozen-answer analyses |
| `data/evaluator_calls.parquet` | 17,486 rows — one per oracle grading; the noise-floor analysis |
| `data/enforcement_events.parquet` | 29,796 rows — validation attempts in the enforced conditions (`C`/`Cp`), **3,489** rejections, regenerations |
| `data/adjudication.parquet` | 513 rows — 171 items × up to 3 reps of model adjudication |
| **`data/scibench/trajectories.parquet`** | **2,296 rows** — SciBench, same 41 columns as the Omni table |
| **`data/scibench/role_messages.parquet`** | **13,500 rows** — SciBench role messages |
| **`data/scibench/evaluator_calls.parquet`** | **3,699 rows** — SciBench oracle gradings |
| `config/` | all 22 Omni prompts, 3 JSON schemas, budgets, visibility policy |
| **`config/prompts_scibench.json`** | **the 16 SciBench prompts + a per-prompt identical/differs table vs Omni** |
| **`config/run_config_scibench.json`** | **the SciBench config: budgets, visibility, denominators, licence** |
| `controls/run1/` | first run of the `Bf` controls (five cells), the forced-submission run and its re-run of `A`; `MANIFEST.json`, `README.md` |
| `controls/rolefree_feedback/gemma4/` | second run of the two Gemma `Bf` cells and its re-run of `A` |
| `adjudication/` | the study's protocol, rubric, blinded items, key, verdicts |
| `manifests/`, `LICENSES/` | frozen-snapshot manifest, per-cell census, problem ids; per-source licensing (incl. **`MIT-SciBench.txt`**) |
| **`analysis/SAMPLING_AUDIT.md`** | **the full sampling + denominator audit for both domains** |
| `SCHEMA.md` | every column, and the defects in full |
| `VERSION`, `CHECKSUMS.txt`, `MANIFEST.json` | integrity and provenance |

Total ~525 MB (v1.1.0 added ~30 MB; the control traces add ~145 MB). Raw and derived layers are consistent by
construction: each build verifies its snapshot sha256 before deriving anything
and refuses on mismatch. The v1.1.0 build additionally **asserts that every
v1.0.0 file is byte-unchanged**, so "additive" is verified rather than promised.

**Separating the domains is always a filter**, never a guess: every row carries
`benchmark_id` (`omnimath2` / `scibench`) and `domain` (`math` / `science`),
one distinct value per table, and the two domains live in separate parquet
files as well.

## Quick start

```python
import pandas as pd
tr = pd.read_parquet("data/trajectories.parquet")

# NB: the `arm` column holds the internal codes, not the paper's words.
CONDITION = {"A": "role-structured", "B": "role-free",
             "C": "structurally enforced", "Cp": "context-restored"}

for arm in ["A", "B"]:
    s = tr[(tr.actor_model == "gemma-4-31B-it") & (tr.arm == arm)]
    g, w = s[s.graded], s[s.first_pass_wrong]
    print("%-18s" % CONDITION[arm],
          "first-pass %.3f" % g.first_pass_correct.mean(),
          "recovery %.3f"   % w.final_correct_prereg.mean(),
          "frozen %.3f"     % w.frozen_answer.mean())
# role-structured    first-pass 0.802 recovery 0.222 frozen 0.288
# role-free          first-pass 0.802 recovery 0.051 frozen 0.845
```

The two conditions answer the first question equally well (0.802 vs 0.802) and
differ entirely in what they do afterwards: `recovery` falls 0.222 → 0.051
while `frozen` — the rate at which the team resubmits the answer it already
had — rises 0.288 → 0.845. The `Bf` control shows how much of that contrast
comes from feedback delivery; see *Interpreting the frozen campaign*.

## Cross-domain (v1.1.0) — SciBench, and what does **not** transfer

### The role-structured contract is NOT the same in both domains. Read this first.

Prompt keys carry the same internal letters as the `arm` column: `A_*` is the
**role-structured** condition, `B_*` the **role-free** one, `C_*`/`CP_*` the
enforced ones.

| prompt | Omni-MATH-2 vs SciBench |
|---|---|
| `A_SOLVER_PREPEND` (planner) | **DIFFERS** — domain-adapted |
| `A_EXECUTOR_PREPEND` | **DIFFERS** — domain-adapted |
| `A_CRITIC_PREPEND` / `A_CRITIC_APPEND` (reviewer) | **DIFFERS** — domain-adapted |
| `A_SOLVER_APPEND`, `A_EXECUTOR_APPEND` | identical |
| **`B_GENERIC_PREPEND` / `B_GENERIC_APPEND`** | **BYTE-IDENTICAL** (asserted in code at build time) |
| `EVALUATOR_PREPEND` | **DIFFERS** — adapted for units / sig-figs / scientific notation |
| `EVALUATOR_APPEND`, all `C_*` | identical |

**5 of 16 prompts differ.** Both prompt sets ship in full
(`config/prompts.json`, `config/prompts_scibench.json`), and
`prompts_scibench.json._COMPARISON_TO_OMNIMATH` gives a per-prompt
identical/differs flag with sha256 prefixes so you can check this yourself.

**Why adapt rather than reuse.** The role-free prompt contains no domain
language at all. Leaving the role-structured condition's math-specific wording
("competition-level mathematics", "olympiad-style") in a chemistry benchmark
would make the conditions differ in **two** ways — role structure *and* domain
fit — and the domain-fit difference runs **against** the role-structured arm.
Adapting it restores a single-variable manipulation. Every structural clause is
preserved (role separation, DELTA, required structure, Diagnosis/Fix
Instruction, answer ownership, routing tags); only domain nouns and the
answer-form enumeration change.

**Consequence — do not compute these across domains.** P1a and every
clause-specific role-fidelity metric. Scoring SciBench agents against
Omni-MATH's clauses would score them against instructions they never received.
The evaluator adaptation is **common mode**: byte-identical across the
role-structured and role-free conditions *within* SciBench, so it cannot
manufacture a difference between them — it only sets the difficulty floor.

### What replicates

Paired on problems first-pass-wrong under **both** conditions — the same
population as the Omni-MATH paired contrast:

| domain | actor | n | role-structured (`A`) recovers only | role-free (`B`) recovers only | `B`−`A` | exact McNemar p |
|---|---|---|---|---|---|---|
| Omni-MATH | gemma-4 | 237 | 37 | 3 | −0.1435 | 1.95e-08 |
| **SciBench** | **gemma-4** | **99** | **21** | **2** | **−0.1919** | **6.60e-05** |
| **SciBench** | gpt-oss | 96 | 17 | 9 | −0.0833 | 0.169 (**unresolved**) |

The two gemma effects are **not distinguishable**: a two-proportion test on the
discordant rates gives **z=1.04, p=0.300** (pooled variance) or **z=0.95,
p=0.342** (unpooled) — re-derived here from the released tables. *The campaign
notes record z=1.06, p=0.289; we could not reproduce that exact pair and quote
ours. The conclusion is identical under all three — the effects are
indistinguishable — and none of them is evidence that the effects are the
**same**, only that this comparison cannot separate them.* First-pass accuracy moves by **exactly
0.000** for gemma (0.794 vs 0.794), as in Omni-MATH. Functional collapse goes
0.000 → 0.998. The role-free condition spends **0.00** cycles revising and never
once declines — it resubmits rather than revises, exactly as in Omni-MATH.

### What must NOT be claimed from this

- ❌ "The result generalizes across domains." **One actor** replicated in **one**
  further domain.
- ❌ "Replicates across two benchmarks" / "two of three actors" — Llama-3.3 was
  **never run** on SciBench.
- ❌ Any **pooled** SciBench+Omni statistic. The two actors' effects differ by a
  factor of two; pooling averages a detectable effect with an undetectable one.
- ❌ Any cross-domain P1a or clause-specific fidelity comparison (see above).
- ❌ Reading gpt-oss's SciBench null as **absence** of an effect. See below.

### gpt-oss's SciBench cell resolves nothing — it is not a non-replication

Its point estimate (−0.083) is in the same direction and almost exactly its own
Omni-MATH effect (−0.077), but at n=96 the cell is **underpowered against an
effect of that size**. This was pre-registered at 761/2,296 rows, *before* any
recovery contrast existed, precisely so the reading could not be chosen
afterwards.

**Power, stated honestly.** The campaign notes record 0.42. We could not
reproduce that figure and report the spread instead — against this cell's own
observed effect at n=96:

| method | power |
|---|---|
| **exact McNemar, two-sided — the test actually used for the p-value** | **0.26** |
| bootstrap-CI rule (the project's own), two-sided | 0.36 |
| McNemar normal approximation | 0.35 |
| unpaired two-proportion z, two-sided | 0.33 |
| exact McNemar, one-sided | 0.40 |
| unpaired two-proportion z, one-sided | 0.45 |

Five of the six land **below** the 0.42 in the notes; only the most permissive
variant (unpaired *and* one-sided — neither of which matches the paired, two-
sided test actually used) exceeds it, at 0.45. **The test that produced the
reported p=0.169 gives 0.26.** The qualitative conclusion is unchanged and
in fact strengthened: this cell **cannot resolve its own effect** and a
consumer must not read its null as absence. Against a *gemma-sized* effect the
same cell has power ≈0.99, so it could have detected a large effect and did
not. **Do not quote 0.42 from the notes; quote 0.26 with the test named, or the
range.**

### Denominators — both domains, in full

| | Omni-MATH-2 | SciBench |
|---|---|---|
| upstream pool | 4,181 matched | **692 published** |
| present in the release registry | — | **580** |
| carrying the runnable slice | — | **574** (`text_only`) |
| **actually run** | **1,600** (38.3%) | **574 — ALL of them** |
| selection | uniform random, **seed 20270101** | **none — no sub-sampling, no seed** |

**Omni-MATH's 1,600 is a uniform random draw of the whole 4,181 pool** — not
tier-specific, not difficulty-stratified, not purposive. It is not
distinguishable from the pool: two-sample **KS D=0.0251, p=0.449** on
`difficulty_score`, and **chi-square p=0.106** on source subset. Drawn by
`runner.load_problems(n=1600, seed=20270101)`; the sampling audit ships
here as **`analysis/SAMPLING_AUDIT.md`**.

**SciBench ran every problem it could run — 574 of 574, no sampling step.**
Two subtractions get there, and they are **independent, not the same items
counted twice**:

- **580 → 574:** 6 released rows lack the `text_only` slice this protocol
  requires. All six are listed by `problem_uid` in **`analysis/SAMPLING_AUDIT.md`, shipped in this artifact**.
- **692 → 580: NOT RECOVERABLE FROM THIS RELEASE, and no reason is asserted.**
  The released problems table contains only rows that survived the upstream
  build, so the 112 excluded items are absent from it entirely and carry no
  reason code. **An earlier draft of that audit asserted a reason — figure/table
  items plus collisions — and it was retracted as an inference presented as a
  measurement.** Establishing the 112 would require diffing the upstream
  SciBench release against this table. It does not affect any denominator
  reported here, because the denominator is the 574 actually run.

Separately, 6 of the 580 rows carry `conflicting_source_id_disambiguated`;
these are a **disjoint** set from the 6 missing the slice.

**`574 matched` is not `574 total benchmark`.** Say which of 692 / 580 / 574
you mean.

---

## Which analyses are primary, exploratory, invalid, superseded

**Primary.** First-pass accuracy and recovery under `final_correct_prereg`
(ungraded = 0, the pre-registered outcome); the paired A-vs-B recovery contrast;
the *mechanical* organization measures (functional collapse, numeric-token
duplication over a shuffled null); Arm C attrition.

**Exploratory / secondary.** The model adjudication — an outcome-blind second
opinion, **not** ground truth and **not** condition-blind (see below).
Everything conditioned on first-pass-wrong is post-treatment: descriptive and
associational, never causal.

**Sensitivity only, never primary.** `final_correct_asgraded` drops ungraded
trajectories and so inherits Arm C's 8–17% **one-sided** attrition; it flips the
sign of the C−A contrast (prereg gemma-4 −0.0225 SIG-negative vs as-graded
+0.0190 SIG-positive). Quoting it as the main result would manufacture the opposite
conclusion out of survivorship.

**Invalid — do not compute.** Any text-length measure over `gpt-oss-120b` Arm B
(F13: you are measuring the logger). `f18_mismatch` as a filter or covariate in
an arm contrast (post-treatment by construction). Grouping the noise floor on
`final_answer_held` instead of `candidate_normalized` (inflates ~6×, and
measures F18 rather than the grader). Dividing an effect size by the noise floor
— "effect / floor" is **withdrawn**, it is not a valid operation.

**Superseded.** Earlier drafts of this work reported: a blinded-adjudication
confirmation of the arm contrast (the blinding leaks — see below); Arm C
recovery "highest of any arm in all three actors" (the recovery denominator
dropped trajectories that got a first verdict then died in regeneration;
corrected, two of three paired p-values are lost — 0.298 and 0.105 — and only
Llama-3.3 survives at p=3.8e-06); and a grader noise floor of 0.0086. None of
these should be reused.

---

# Known instrumentation defects

A consumer who does not read this section will trip over them. **F13 and F18
reproduce in the second domain**, and the grader noise floor is
**domain-specific** — each has its own subsection below.

### F13 — visible text is truncated relative to hidden reasoning (gpt-oss, role-free `B`)

The runner logged `message.content` and fell back to `message.reasoning` **only
when content was empty**. A response with short content and a long hidden
reasoning trace was logged as the short content, and `used_reasoning_fallback`
stayed `False`, so the loss is undocumented.

Its Arm B planner logs a median **37 characters at 2.85 chars/sec**, against
**4,824 characters at 195.16 chars/sec** in its own Arm A. **75.7%** of that
cell's role messages fall below 10 chars/sec; the documented flag fired on
**0** of the 2,302 sub-100-character planner messages.

**Its planner output is *uninstrumented*, not absent.** The work was done and
the logger discarded it. Any text-based measure over this cell measures the
instrument. Detect with `chars_per_sec`; exclude the cell and say so.

A later commit fixed the logger. **It did not reach any released row** —
measured directly, the gpt-oss Arm B planner median is 37 chars before the fix
commit and 36 after, so the release is uniform. Note `config_version` does
**not** change across that fix and therefore cannot be used to detect this.

### F18 — `correct` grades the last SUBMITTED answer, `final_answer` is the last answer HELD

A team that revises after its final submission is graded on the answer it
abandoned. Mismatch rate among first-pass-wrong trajectories:

| actor | arm A | arm B | arm C |
|---|---|---|---|
| gemma-4 | 0.171 | 0.000 | 0.363 |
| gpt-oss | 0.164 | 0.066 | 0.258 |
| Llama-3.3 | 0.058 | 0.004 | 0.478 |

So the defect reaches **up to ~17% in Arm A** and considerably higher in Arm C.
Totals: 509 mismatched first-pass-wrong trajectories, **62 demonstrably
under-credited** (held answer exactly matches gold, graded 0). Positive control
on the 10,734 non-mismatched graded rows finds **0** such cases, so 62 is a
clean floor rather than a matching artifact.

**The defect is concentrated in the arms that revise**, i.e. it works *against*
the frozen A-vs-B recovery gap — correcting it would widen that gap. Primary analysis stays
as recorded (it is the pre-registered outcome and the conservative direction).
`f18_mismatch` and `f18_under_credited` are for **bounding**, not correcting:
the rate is a function of revision behaviour, which is the treatment.

### F18 in SciBench — it reproduces, and again runs **against** the A-vs-B gap

The defect transfers to the second domain. Among first-pass-wrong trajectories:

| actor | arm A | arm B |
|---|---|---|
| gemma-4 | **0.288** | 0.000 |
| gpt-oss | 0.105 | 0.017 |

**49 mismatched** first-pass-wrong trajectories, **2 demonstrably
under-credited** (held answer exactly matches gold, graded 0). The positive
control on the 2,247 non-mismatched graded rows finds **0** such cases, so 2 is
a clean floor rather than a matching artifact — the same control, and the same
result, as the Omni-MATH layer.

**Same direction as Omni-MATH: it is concentrated in the arm that revises, so
correcting it WIDENS the gap.** Re-scoring on the held answer moves gemma-4's
paired recovery contrast from −0.1919 (p=6.6e-05) to **−0.2020 (p=3.6e-05)**,
and leaves gpt-oss **exactly unchanged** at −0.0833 (p=0.169). **No verdict
flips in either domain.** Primary analysis stays as recorded — the
pre-registered outcome and the conservative direction.

As in v1.0.0: `f18_mismatch` is for **bounding, not correcting**, and must
never be used as a filter or covariate in an arm contrast — the mismatch rate
is a function of revision behaviour, which *is* the treatment.

### The grader noise floor is domain-specific — 2.80% here vs 0.72% on Omni-MATH

Disagreement rate across **byte-identical** candidate strings graded at
temperature 0, keyed on exact candidate bytes:

| domain | discordant / multi-graded groups | floor |
|---|---|---|
| Omni-MATH-2 | 20 / 2,790 | **0.0072** |
| **SciBench** | **19 / 678** | **0.0280** |

**The SciBench grader is ~4× noisier**, which is unsurprising: it must judge
unit equivalence, significant figures and scientific notation rather than
symbolic equality. The gemma effect (−0.19) is far larger than this floor, but
**do not compute "effect ÷ floor"** — that statistic is **withdrawn** project-wide
in both domains; dividing an effect size by a disagreement rate is not a valid
operation, and grader noise largely cancels in a paired contrast anyway.

> **A note on a figure you may see elsewhere.** The campaign notes compare
> SciBench's 2.80% against "9.35% on Omni-MATH". **That 9.35% is not an
> Omni-MATH measurement from this project** — it traces to a finalizer-
> nondeterminism figure recorded on a *different* project and was carried over
> as a comparison. Measured on this release's own frozen data by the same
> method, Omni-MATH's floor is **0.0072** (0.0086 under the superseded
> whitespace-stripped key). So SciBench's grader is ~4× *noisier* than
> Omni-MATH's, not 3× quieter. **Use 0.0072 vs 0.0280.**

### F13 reproduces in SciBench, in the same cell

`gpt-oss-120b` Arm B is uninstrumented here too: planner median **123 chars at
20.0 chars/sec** and executor/reviewer at **8.6 / 7.7 chars/sec**, against
**2,726 chars at 212 chars/sec** for its own Arm A planner. 34–64% of that
cell's role messages fall below 10 chars/sec. gemma-4 is clean in both arms
(≥127 chars/sec throughout).

**Any text-length measure over `gpt-oss-120b` Arm B is invalid in this domain
too.** Detect with `chars_per_sec`, never with `config_version`.

Two things are *better* here: there are **no mangled LaTeX escapes** (0 of
2,296 `final_answer_held`, 0 of 3,699 `candidate_raw`, versus ~1% in
Omni-MATH), and **no attrition at all** — 0 hard failures, 0 unjudged, all four
cells exactly 574.

### Structural-enforcement (`C`) attrition — 8.0 / 9.9 / 17.0%, and it is one-sided

Regeneration-exhaustion attrition is **0.080** (gemma-4), **0.099** (gpt-oss),
**0.170** (Llama-3.3), against 0.000–0.025 in Arms A/B.

**The recovery denominator must INCLUDE trajectories that got a first verdict
and then died in regeneration.** An earlier implementation used
`graded(r) and first_pass==0`, which silently dropped them — and *all* of them
are first-pass-wrong structurally, because a PASS on the first verdict ends the
loop. They meet the definition and score 0 under pre-registered scoring.

Three counts circulate; each is correct for its own scope — **quote the one
matching your sentence**: Arm C only **150**; Arm C + C′ **173**; all arms
**178** (A 1, B 4, C 150, C′ 23).

Correcting this moved recovery to gemma-4 0.314, gpt-oss 0.395, Llama 0.139, and
cost two of three paired A-vs-C p-values.

### Adjudication condition leak — outcome-blind, NOT condition-blind

`adjudication/PROTOCOL.md` records role names neutralized to `Agent-P/E/R` with
"residual leaks: 0". **True of the strings, false of the signal:** the tokens
were renamed, their *presence* was not equalized.

| arm | has an `Agent-P/E/R` token | none |
|---|---|---|
| A | **42** | 0 |
| B | **3** | 53 |
| C | 0 | 44 |
| C′ | 0 | 29 |

Fisher exact A vs B on token presence: **p = 1.5e-24**. The arms are further
separable by output format — Arm C carries JSON `answer`/`verdict` fields while
A/B carry `\boxed` and `[Agree]`. A judge could identify the condition without
reading content.

Unaffected (within-item): judge stability (0.947 / 0.959 / 0.953 for Q1/Q2/Q5)
and precision 1.000 / recall 0.262. Affected: **every arm-contrastive
adjudication number**, including A 0.000 vs B 0.964 and C 0.136.

**Do not describe any arm contrast here as "blinded".** A re-run would not fix
it — the manipulation is partly an intervention on output format — so this is a
disclosure, not a defect awaiting repair. The paper's organization claim rests
instead on the *mechanical* measures, which involve no judge: functional
collapse 0.976 / 0.846 / 0.872 in Arm B vs 0.000 / 0.120 / 0.000 in Arm A, and
numeric-token duplication as excess over a shuffled null (B−A +0.290 gemma-4,
+0.287 Llama-3.3; gpt-oss excluded per F13).

### Repaired denominator bugs — `graded()` vs `judged()`

The survivorship error above had **four known sites**. Two mattered:

- **Recovery** — fixed as described.
- **First-pass accuracy in Arm C**, one column to the left, same error. Arm C
  first-pass moved gemma-4 0.822 → **0.779**, gpt-oss 0.788 → **0.761**, Llama
  0.295 → **0.281**, C′ 0.825 → 0.810 and 0.773 → 0.740. The paired A-vs-B
  contrast is unchanged (it comes from the paired path).

A self-check now asserts `(1 − first_pass) × n == n_fpw` per cell. If you
recompute a denominator, use `judged()`, and state which of the three
attrition-inclusive counts you used.

### Also worth knowing

- **Grader noise floor: 0.0072** group-level — 20 of 2,790 distinct graded
  strings receive contradictory verdicts across byte-identical prompts at
  temperature 0. Range 0.0017–0.0072 across estimators. **Not 0.0086**; the key
  must be the exact candidate bytes (`candidate_normalized`).
- **Mangled LaTeX escapes**: 135 of 11,498 `final_answer_held` and 176 of 17,486
  `candidate_raw` values contain C0 control characters where a macro was
  intended (`\frac` → `\x0crac`). Preserved as-is so the artifact matches what
  the evaluator actually graded.
- **One adjudication item (T0016) has only 2 reps and a tied Q5 vote.** The
  pooled Arm B rate is 0.964 under the project's aggregation and 0.982 if the
  tie breaks the other way. One item, and it is the only tie.

## Scope and limitations

- **Two benchmarks, two domains — but the second is a partial replication.**
  Competition math (Omni-MATH-2, 3 actors, 4 arms) and college
  chemistry/physics (SciBench, **2 actors, 2 arms only**). SciBench has no
  Arm C, no Arm C′, no Llama-3.3 and no adjudication study. **One actor
  (gemma-4) replicated in the second domain; the other cell cannot resolve its
  own effect (power ≈0.26).** This is not "the finding generalizes".
- **Three actors, and the effect does not replicate in all three.** gemma-4 is
  clean (recovery 0.222 → 0.051, paired McNemar p=1.95e-08). gpt-oss is weaker
  and **not significant when paired** (0.324 → 0.247, p=0.208). Llama-3.3 does
  **not** replicate (0.014 → 0.015). Llama's null is **not** a floor effect —
  Arm C restores recovery in that same actor (0.096 vs 0.009, p=3.81e-06), so
  the repair channel exists and role labels simply do not open it there.
- **Recovery is oracle-gated.** No cell recovers before the first oracle verdict.
  This measures repair under external feedback, not spontaneous self-correction.
- **The grader shares a checkpoint with one actor.** Relevant to any
  self-grading concern.
- **The pre-registered primary (P4) is null.** All three actor × enforcement
  difference-in-differences contain zero. Two of the three have MDE 0.069 and
  0.075 against plausible effects ≤ 0.040, so only the gpt-oss–gemma DiD
  (MDE 0.033) is an informative null.
- **Adjudication is model adjudication** (`claude-opus-5`), not human
  annotation and not ground truth.
- **Wall-clock timings reflect shared infrastructure**, including queueing.

## Licensing

**Per source — this release does not blanket one licence over source-derived
material.** See `LICENSES/README.md` and `LICENSES/registry.json`.

- **Our derived material** (parquet structure, scripts, docs, manifests):
  **Apache-2.0**.
> **MIXED LICENCE as of v1.1.0 — do not blanket-apply one licence.**
> Filter by `benchmark_id` to know which terms govern which rows.

| content | licence | verified |
|---|---|---|
| **Omni-MATH-2 problems** (`benchmark_id='omnimath2'`) | **Apache-2.0** | upstream HF API tag `license:apache-2.0` + `cardData.license`, anonymous fetch, cross-checked against two registry files |
| **SciBench problems** (`benchmark_id='scibench'`) | **MIT**, © 2023 Xiaoxuan Wang | upstream `LICENSE` file fetched anonymously + GitHub API `spdx_id: MIT` + two registry files — **three independent sources, all agreeing** |
| **This project's derived material** (parquet structure, scripts, docs) | Apache-2.0 | authored by us |
| **Model-generated trajectory text** | the model providers' terms | — |

SciBench's MIT is **not** absorbed into the Apache-2.0 material; its verbatim
notice ships at `LICENSES/MIT-SciBench.txt` as the MIT terms require. The HF
`license:` metadata field carries one value and describes **our own** material
only. `LICENSES/README.md` and `LICENSES/registry.json` are the authority.

**What upstream text is actually redistributed.** The parquet layer ships no
`problem_text` column and no gold-answer column, in either domain.

- **Problem text is incidentally redistributed inside transcripts.** Agents
  restate the problem: a 60-character problem prefix appears verbatim in
  `role_messages.text` for **16 of 606** Omni-MATH problems (2.6%) and **0 of
  574** SciBench problems (0.0% — short numeric items get paraphrased into
  tables of givens). The **raw traces carry more** in both domains.
- **Gold answers: no column, but a small measured leak in grader free text.**
  The evaluator was instructed never to reveal ground truth and occasionally
  names the expected value in its repair hint anyway: **Omni-MATH 23 of 17,486
  `evaluator_raw` rows (14 of 1,600 problems, 0.9%)**; **SciBench 19 of 3,699
  rows (4 of 574 problems, 0.7%)**. v1.0.0 stated "no gold/reference field
  exists in any released row" — true at the **column** level, which is what was
  checked, but it did not cover free text the grader wrote. **Corrected here
  for both domains rather than left standing.** Far too sparse to reconstruct a
  gold set, and permitted under both licences with attribution.

Both upstreams are marked `evaluation_only_recommended`: we recommend
evaluation and analysis use rather than training, in **both** domains.

## Provenance and integrity

Derived from a sha256-manifested frozen snapshot (`raw/MANIFEST.json`, freeze
`2026-09-30T10:09:30Z`). `CHECKSUMS.txt` covers every file; `MANIFEST.json`
records per-trace sha256, rows, bytes, semantic version,
timestamps, arms, actors, domain, backend and config version.

`scripts/validate_artifact.py` re-derives **181 published values** from the
parquet layer and checks them against the project's canonical analysis output —
**181/181 pass**. The [code repository](https://github.com/ChihHsuan-Yang/AAMAS2027-AgentProtocols)
re-derives every number in the paper from `raw/` and `controls/`.

Two `config_version` values appear (`e3afa39849c1b980`, 9,600 rows;
`231b8c4fe205d04b`, 2,000 rows). They differ **only** by the addition of the
Arm C′ entry — every A/B/C prompt, schema and knob is byte-identical across
them, verified by recomputing the hash at each source commit.

## Redaction (v1.2.0)

In 18 trajectory rows the `error` field held a response page returned by the
inference gateway (14 in `raw/`, 4 in `controls/run1/bf_omnimath_llama33.jsonl`).
v1.2.0 replaces each such `error` value with a fixed marker. Every other row is
byte-identical, every other field keeps its value, and no analysis reads that
text, so every number is unchanged. Each manifest records
the original file's hash as `redacted_from_sha256`. The parquet tables never
contained these bodies.

## Citation

The canonical BibTeX entry is
[`citation.bib`](https://chihhsuan-yang.github.io/AAMAS2027-AgentProtocols/citation.bib)
on the project website; the code repository also carries a `CITATION.cff`.

```bibtex
@misc{yang2026beyond,
    title = {Beyond Division of Labor: How Roles Shape Feedback and Recovery in Multi-Agent Systems},
    author = {Yang, Chih-Hsuan and Li, Xinyang and Thakur, Rajeev and Yan, Feng},
    year = {2026},
    note = {Preprint},
    url = {https://chihhsuan-yang.github.io/AAMAS2027-AgentProtocols/}
}
```