A pre-registered five-hypothesis validation study of Synchronization Resistance (SR) — a per-prompt scalar, derived from the Kuramoto order parameter R(K) over a coupling sweep, that measures how hard it is to make a population of language models agree on a question.
Scorecard: 3 pass · 1 inconclusive · 1 fail. We publish the failure with the passes.
| Hypothesis | Result | Key metric |
|---|---|---|
| H1 — SR tracks human intuition | INCONCLUSIVE | ρ=0.30 (p=0.26), exactly on the pre-registered boundary |
| H2 — R(K) curves are classifiable | PASS | 18/20 at R²>0.90 |
| H3 — Two-point shortcut | PASS | MAE=0.04 vs full 11-point sweep |
| H4 — Replication stability | PASS | 0/4 status flips |
| H5 — Category discrimination | FAIL | JT p=0.06; predicted ordering violated (Creative > Controversial) |
The headline finding is the failure: human categorical labels (factual / creative / controversial / speculative) do not segment LLM disagreement. A category containing both SR=0.00 and SR=2.00 prompts cannot route anything. The instrument crosscuts human intuition — which is either its value or its problem. That's what we want argued about.
Data correction (2026-07-20): four of the 66 sweep series had replayed a non-responding model as a zero-phase oscillator, reporting six members where five responded. The four series have been corrected in place (originals preserved in git history). Every disposition above is unchanged — H3's error tightens slightly, nothing flips. Full write-up: ADDENDUM_SR-01.md; machine-readable record:
data/CORRECTION_SR-01.json.
Every number above is derived from files in this repository. No engine, no API key, no GPU:
pip install numpy scipy
python3 analysis/reproduce.pyIt prints the whole scorecard in a few seconds. REPRODUCE.md explains what's in the box — and states the boundary plainly: we publish the derivation (R(K) → SR → the five tests), not the measurement that produced R(K). Those values are here as inputs we're asking you to check, not outputs you can currently regenerate. The substrate that ran the sweep is unreleased pending counsel review.
- Paper (v0.2.4):
paper/in this repo · DOI 10.5281/zenodo.20495904 - All versions: concept DOI 10.5281/zenodo.19953731
- Pre-registration & results (before any data collection): OSF registration xqy5w (framework, 2026-03-17) · OSF project xv9j6 (Battery 3C hypotheses, deposited 2026-04-07, pre-data)
Six local models (mistral 7B, gemma3 12B, glm4-flash, jamba-reasoning, phi4, qwen2.5 32B) via Ollama at temperature zero, 22 prompts committed at pre-registration, an 11-point coupling sweep K ∈ {0.0 … 1.0}. R₀ = baseline agreement at K=0; α = dR/dK = coupling susceptibility; SR = (τ−R₀)/α, capped at SR_MAX=2.0, with τ=0.70 fixed pre-data. Full definitions in the paper §3, methods §4.
This was built by a solo operator + AI collaborators, outside academia, on pre-registration discipline instead of institutional review. That means it has not been peer reviewed — you are the peer review. If the math is misapplied, the stats are underpowered, the Kuramoto framing is decoration, or the claims outrun the evidence — open an issue or say it in Discussions. Direct is better than polite.
Everything you need to make any of those arguments is in this repo — the prompts, the raw measurements, and the derivation. Run it, break it, and tell us what you found.
- Code (reproduction scripts in
analysis/): Apache License 2.0 — seeLICENSE. - Paper text: CC BY-NC-ND 4.0.
Patent and trademark rights are not licensed under the CC license (CC BY-NC-ND 4.0 §2(b)(2)). The Apache-2.0 patent grant applies only to the code in this repository and does not extend to any other BAION methods, systems, or substrate; methods described may be subject to pending or issued patents held by BAION Systems LLC or Steven A. Mullins Jr.
Copyright 2026 BAION Systems LLC.
Mullins Jr., S. A. (2026). Synchronization Resistance: Measuring Multi-LLM Agreement Difficulty: A pre-registered five-hypothesis study (Battery 3C). Zenodo. https://doi.org/10.5281/zenodo.19953731