core/docs/analysis/fa1-holonomy-gate-preregistration.md

Pre-registration: does a repaired semantic ground carry meaning across languages?

FA-1 experiment · registered 2026-07-28 · criterion committed BEFORE any discrimination measurement is taken. Follows the ADR-0252 §5 precedent: the verdict is whatever the criterion says, a well-controlled NO-GO is full credit, and the criterion is not touched after the numbers exist.

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1. Why this experiment is not a fourth re-run of a settled question

Three geometric-operator experiments have returned negative (field-reasoner wedge 2026-06-04; relational-operator ablation 2026-07-19; ADR-0252 §5 structure-mapping 2026-07-28), and the cross-language holonomy resonance itself returned negative on 2026-06-14 — under the engine's own metric it anti-correlated. The reopening rule this repo set for itself is that a geometric hypothesis may not be re-proposed blind.

It is not being re-proposed blind. Two preconditions of the June measurement were false, and both are now measured facts rather than suspicions (docs/analysis/logos-substrate-collapse-2026-07-28.md):

1. The ground was flattened. In the mounted trilingual configuration the June experiment used, 48 surfaces share 11 coordinates and 37 distinct coordinates are gone. Aligned cross-language tokens are bit-identical, so "is the aligned pair closer than the misaligned one" was not a question about meaning — it was a question about which tokens had been overwritten with which.
2. The holonomy never closed. holonomy_encode returns the forward walk only; the reverse walk was deleted at fca6216e. ADR-0015's gate is closure. An open path product has no reason to be invariant across representations, so the June negative is what the implementation predicts, not evidence about the design.

A negative result measured with a broken instrument on a corrupted sample constrains the instrument and the sample, not the hypothesis. This is the first measurement of the designed gate. If it too returns negative, the hypothesis is genuinely damaged — and that is the outcome this registration exists to make binding.

2. The two repairs under test (both are mechanism, not tuning)

Neither repair invents anything; both call primitives the repo already ships.

R1 — blend on the group instead of overwriting.

def _blend_feature_versors(source, target, strength):
    if strength <= 0.0:
        return source
    return geometric_product(rotor_power(word_transition_rotor(source, target), strength), source)

algebra/rotor.py has shipped rotor_power (exact closed form for simple rotors, invariant bivector decomposition otherwise) and word_transition_rotor since the algebra layer's first commit. Verified: unit residual stays ~1e-7 across t ∈ [0,1] — three orders of magnitude inside VocabManifold's 1e-5 tolerance — with t=0 returning the source exactly and t=1 the target exactly. The declared strengths are used as written (0.10, 0.40, 0.40); they are not free parameters in this experiment and will not be tuned.

R2 — close the loop, and close it around the pair. The June measurement compared two open path-products with an external distance. Restoring H = F · reverse(F) for a single clause would be worse — that is a scalar by construction and carries no information at all. The object ADR-0015 actually describes is the loop formed by two representations of the same content: transport out along clause A, return along clause B.

F(X) = v₁ · v₂ · … · vₙ            ordered geometric product of X's word versors
H(A,B) = unitize( F(A) · reverse(F(B)) )
d(A,B) = ‖H(A,B) − 1‖              deviation from the identity multivector

If A and B carry the same content, F(A) ≈ F(B) and the loop closes: d → 0. If they do not, the loop has curvature. This needs no metric calibration and no threshold on a similarity score — the null hypothesis is the identity, which is why the June failure mode (Euclidean norm passing where the owned similarity metric inverted) cannot recur here.

Two deliberate choices, stated before the run:

• The per-token _position_rotor is excluded. It was introduced so that "path order survives even for scalar/vector fixtures" — degenerate test inputs — and it conjugates each token by its absolute index, so clauses of different lengths are transported through different schedules. Across languages, differing length is the norm, so the rotor injects a length artefact into every cross-language comparison. This is exactly RQ2 of the June finding ("is the position rotor drowning the semantic signal in path-order geometry?"), answered by removing it rather than by measuring around it.
• Order sensitivity is not lost by removing it. The geometric product is non-commutative, so F(w₁w₂) ≠ F(w₂w₁) intrinsically. G3 below tests this as a requirement rather than assuming it — if word-order sensitivity turns out to depend on the positional hack, the claim was never geometric and G3 fails, which is a result worth having.

R3 — resolve alignment edges by pack membership, not by an id-prefix table, so the 63 currently-dropped edges participate. This is a load-time correction with no free parameters: an edge whose target id belongs to no loaded pack becomes an error instead of a continue.

All three are applied in a scratch harness against a copy of the compiler. ../core's committed compiler is not modified by this experiment — the repaired contract is admitted to the keel (K1 algebra/, K3 logos/), and the experiment exists to tell the keel whether the repaired design earns its place there.

3. The corpus, fixed now

• Aligned triples — every alignment edge that resolves after R3, grouped into he/grc/en clause triples. Expected order 20–40 usable triples from the 83 authored edges; the exact set is whatever R3 resolves, chosen by the resolver and not by hand.
• Meaning-breaking negatives, three kinds, generated mechanically so no negative is cherry-picked (the specific failure of the June measurement, which used one hand-chosen substitution):
  1. Lexical substitution — replace one content token with a token from a different primary semantic domain, every valid substitution enumerated, not sampled.
  2. Word-order permutation — ADR-0015's own stated test ("word-order changes should change holonomy"). Every non-identity permutation of clauses with ≤ 4 tokens.
  3. Cross-triple pairing — the English clause of triple i against the Hebrew/Greek clause of triple j ≠ i. This is the strongest negative class: same corpus, same lengths, same construction, different meaning.

Amendment A1 (recorded before the run, no numbers seen). R3 resolves more of the corpus than this registration assumed: 24 aligned concepts, of which 6 carry all three languages and 18 carry two. Clause sets are therefore all C(24,3) = 2,024 combinations rather than the "20–40 triples" estimated above — a larger corpus than registered, in the direction that makes the test harder to pass, not easier.

That makes negative class 3 complete-enumeration quadratic (≈4 M pairs). It is bounded by a rule stated here, before any measurement: for each aligned pair, the cross negatives are the first 5 clause sets following it in the deterministic sorted enumeration that share no concept with it. Position in a sorted enumeration of concept keys is unrelated to meaning, so the bound is unbiased; it is deterministic, so the experiment is reproducible; and the count of generated negatives is reported, so nothing is dropped in silence. Classes 1 and 2 remain complete — every valid substitution, every non-identity permutation.

The G2 threshold is not relaxed to compensate. A bound on how many negatives are drawn does not change how well the aligned pairs must separate from them.

4. The criterion — committed, and deliberately unforgiving

Let d(A,B) be the loop-closure deviation of the cross-language loop (transport along clause A, return along clause B): d = ‖H − identity‖ after R2. Single declared metric; no alternative is consulted after the fact.

GO requires all four:

#	Condition	Threshold
G1	Separation — aligned pairs close tighter than negatives	median(d_aligned) < median(d_negative) with AUC ≥ 0.80 over all aligned vs all negatives
G2	Holds on the hardest class — cross-triple negatives alone	AUC ≥ 0.75 on class 3
G3	Word-order sensitivity — the ADR's own requirement	≥ 90% of non-identity permutations score d above their own unpermuted clause
G4	No collapse re-entry — the repair must not buy separation by flattening	mounted coordinates_lost = 0 under R1

NO-GO if any of G1–G4 fails. Any of these outcomes is a full-credit result:

• GO → cross-language holonomy closure becomes the keel's L3 validation gate (ADR-0015 as designed), and the K3 contract carries it with these numbers as provenance.
• NO-GO with G4 held → the geometry does not carry meaning across representations even on a clean, closed ground. The pillar is then formally re-scoped: the depth packs stay as lexical and morphological resources, the "holonomy resonance is the validation gate" claim is struck from ADR-0005/0015 by amendment, and every document repeating it is corrected. This is the outcome that would retire the largest piece of unearned design in the system, and it is worth as much as a GO.
• NO-GO with G4 failed → the repair itself is wrong; report and stop. No third attempt at the same encoding without a new mechanism.

5. Anti-gaming rules, binding

1. No threshold moves after numbers exist. If a threshold is wrong, that is a finding to record, not an edit to make; the experiment re-registers under a new date and says why.
2. No metric shopping. d as defined in §4 is the only quantity consulted. The June failure mode — Euclidean norm "passing" where the owned similarity metric inverted — is forbidden by construction: one metric, declared here.
3. No negative curation. All three negative classes are generated mechanically and all generated negatives count. Dropping any requires a stated rule applied to all.
4. The controls run first and are reported regardless of outcome: aligned-vs-aligned (the floor), and identity-vs-identity (d ≈ 0, proving the instrument can report closure).
5. The result is published whichever way it lands — as an analysis doc with the raw numbers, next to this registration, in the commit that produces them.

6. What the answer changes

The keel's L3 design branches here, which is why FA-1 precedes K3:

• GO → logos/ carries a real validation gate: a clause is admitted as understood when its cross-language loop closes. Perception (K4) gains a meaning criterion that is not template match — which is precisely the constraint the 1.28% read rate measures.
• NO-GO → logos/ is admitted as lexicon + morphology only, the gate claim is retired, and K4's meaning criterion must come from somewhere else. That is a smaller keel, honestly scoped, and the Growth Law's "coverage is data, not failure" covers it.

Either way the keel gets a ruled foundation instead of an assumed one, which is the entire purpose of running FA-1 before building on L2.

Related: docs/analysis/logos-substrate-collapse-2026-07-28.md (the defects this repairs) · docs/analysis/holonomy-resonance-proof-not-robust-2026-06-14.md (the prior negative and its open questions RQ1–RQ3) · docs/plans/2026-07-28-foundations-audit.md §FA-1 · docs/research/sme-experiment-verdict-797ebad5.md (the pre-registration precedent).