Coherence Is Not Truth — programme note

Taniwha AI · 2026

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We built a small population of communicating agents whose vocabularies are allowed to drift apart, and asked what machinery between them could keep them mutually interpretable without imposing a common vocabulary — and, more to the point, what that machinery can and cannot do. Local adaptation is where efficiency comes from, and it pulls representations apart; cooperation needs them to stay interpretable. The standard resolution imposes homogeneity: one ontology, one embedding space, a central vocabulary. The note works out the other resolution in the smallest setting where it can be tested honestly, and reports the boundaries as carefully as the successes.

The setting. Agents hold codebooks over a sparse block code — each word a tuple of slot indices, binding by per-block modular addition, so composition is exact and nothing accumulates around loops. Tribes diverge two ways: shared words drift by topic, and recurring adjacent pairs are minted into new words whose definitions are recorded as a genealogy. Translation between two agents is an ordinary, inspectable map — per-block offsets plus a per-word exceptions table — learned from anchor pairs. Compose the maps around a loop of three or more agents and the result need not be the identity. That loop residual is not a scalar alarm but an exact, block-indexed vector, and the question is what it can be used for.

Five findings

The loop sees what pairs cannot, and the residual repairs the map — inside a proved boundary. Under a topic-sliced contact schedule every two-agent round trip is flat while the three-agent loop closes dirty, and the defect equals the difference of two tribes’ register splits exactly, at all of seeds 1–32. A planted collision-shaped production error invisible to the pair that suffers it is named per token by the triangle, and installing the negated excess on the listener’s own evidence-free edge repairs comprehension exactly: 0.667 → 1.0 on the n=3 test utterance, and 0.75 → 1.0 on the growth channel’s n=4. The boundary is a standard proposition: exact comprehension is restorable precisely when production was injective on the tokens in play. A merger is irrecoverable; an equally severe swap is fully repairable. Over 888 planted collisions the operator never restored both words.

Attribution has an exact edge, and the instrument refuses outside it. One triangle reports a sum and can never say which edge is wrong; that is the λ = 2 case of a standard bound (blame is unique when twice the corruption support is below the graph’s edge connectivity). On authored graphs with λ = 5, planted corruption is recovered exactly and certified at N = 12 and N = 30; a triangle and a λ = 2 ring are refused. On a contact graph grown by a prefix-tribe cellular automaton, where bridges make the global certificate vacuous, the boundary is local and exact: λ(u,v) = 2 edges ambiguous 23 of 23, λ(u,v) ≥ 3 edges unique 80 of 80, zero exceptions across seventeen board configurations and 3,565 covered edges. An edge holding direct anchor evidence is never patched automatically — the refusal fired in 70 of 70 cases — and is overruled only behind a unique verdict.

Farming divergence pays inside a measured window, and loop auditing earned nothing in the economy. A deterministic task economy priced the design thesis. Instrumented divergence beats both forced uniformity and uninstrumented divergence exactly within 0.155 < w < 0.611 of relative bandwidth cost at the reference seed, with 0.2556 < w < 0.4831 common to all sixteen seeds tried; the window is open in 19 of 20 knob configurations and closed in the one where homophony is maximal and cross-tribe coordination minimal. The value is definition shipping and descent repair — genealogy is 64% of the instrument bill — and switching the triangle audits off (E1) left the window unchanged to two decimals at every seed. The preregistered N-tribe economy with drift on confirmed this on sixteen untouched seed blocks: the loop channel’s marginal value was negative in 20 of 20 eligible cells, and relearning maps every epoch in one register and applying them in the other manufactured about 150× the failures raw drift produced. The result narrows where the instrument is worth its cost; it does not show loop repair inert in principle.

At one assertion over a shared world, three layers compose without impersonation — and the primary estimand went unsupported. A preregistered 2 × 2 × 2 installed a translation swap, a rebound evidence revision and a lease revocation independently over one staged path — decode → concept → entity → assert. In 2,104 admitted held-out cells the submitted tuple went wrong exactly when the construction said it would; the ledger refused a revoked lease on a perfectly decoded, perfectly grounded tuple; repaired evidence never repaired a swapped decode. Every eligible repair restored the intended act without displacing the fault (0 of 36 seeds moved, ≤ 8.0 %). Inside the proved boundary the attributor was never wrong — 1.0 on every certified, search-covered instance — but 15–23 seeds contributed against a preregistered floor of 25, so the primary estimand is printed as unsupported at this allocation and no bound is issued. Outside the boundary it refused in 20–33 % and committed to a wrong edge in 67–80 % of instances. The certificate certifies uniqueness of the reachable minimum-support solution, not the truth.

Coherence is not truth. A perfectly flat triangle can be three agents all wrong about the world; agents individually well-grounded can hold broken translations and ring a dirty loop. Holonomy is a property of the relationship layer, and an architecture should read it as exactly that — beside, never instead of, whatever grounds the vocabulary in the world. The composite experiment is the executable form of that separation: no translation instrument may impersonate grounding or authority, and automatic repair stays gated on identification.

What we are not claiming

The mathematics is conceded, and labelled so wherever it appears: that pairwise consistency does not imply global consistency is classical in synchronization; the propositions are bounded-distance decoding uniqueness for the graph’s cut code and the definition of decodability; the localisation principle is cycle-edge message passing. The contribution is the executable combination with its boundaries measured, and the note’s absence claim is narrow, dated, and states its own collapse conditions. The world is a toy: a sparse block code with given co-reference, abelian maps, planted rather than organic collisions, a synthetic economy. No transfer to real models is shown: two language models speaking English share a surface, not a codebook; there is no learned translation map between them; and the factorial must not be read as evidence that loop attribution would name the guilty hop between two proprietary models. A pairwise certified-vocabulary neighbour does exist — two agents, certified terms, recertification on drift, transitivity left as future work. What does not exist is a translation map with a loop residual and refusal across three or more heterogeneous agents. The numeric gains are in-model; they are not a lift quotable on a benchmark or a fleet.

How to read the verification packets

The internal record is a private repository frozen at tag fractal-tribalism-v1.2. What publishes beside the note is its verification, not its machinery. The artefact manifest lists the SHA-256 identity of the note, the pin files, the result grids and their validated manifests, the panel record and the calibration freeze at the tagged commit. The verification receipts are four. Receipt A is the review panel: three rounds of briefs and adjudications and the falsification-harness counts. Receipt B is the pin suite and every Appendix A command run from a fresh clone at the tag (501 passed, 13 skipped). Receipt C is the Paper 3 preregistration chain: design freeze and amendments, implementation signature, calibration validity, development and held-out seeds each run once, validated manifest 288/288, the frozen scientific object. Receipt D is the N-tribe economy’s preregistration and confirmation on separate seed blocks (1–16 development, 17–32 confirmation). The search appendix records the queries behind every absence claim and what would collapse each. Every hash, number, ruling and verdict in those documents is copied unchanged from the internal record; only repository names, hosts, paths and internal identifiers are neutralised. Reviewers may request supervised access to the record via [email protected].

Published 2026 — Taniwha AI. The note: Coherence Is Not Truth.