[Matarener]

Requested by Mark

Before: #5421 (Ali Romman) owns nine helper relations on the reverse PR589 BIT word and leaves open whether a new relation space could give a further BIT gain. Target 6 of #5428 proposes systematic relation-space selection for this.

After: on that word the question is closed exactly. Modulo #5421's nine relations, every owned-helper relation subspace V, of any dimension and in any combination, removes paid rank mass at most 7.5 · dim V. Each dimension costs one rank-8 target, so every subspace loses at least 8^t − 7.5 = 0.4424 raw moment per local call at C = 0.00347207. The bound holds for every C < 0.031. This is a negative result: no new κ and no new BIT saving.

How. Model: a paid job (MOVE of rank r > 0, or COPY rank 7) becomes free iff the GF(2) row of its moved value lies in V. Certificate: by the matroid union theorem, if m copies of the job-row multiset E' (each row repeated rank times) split into p linearly independent sets, then m·w(V) ≤ p·dim V for every V. Edmonds augmenting paths make the split exact. Frame and pivot legality are relaxed, so the bound also covers legal V.

• Calibration on the source word: E' splits into 8 sets, and the only tight subspaces are exactly BIT saving 0.00344412 from nine owned helper relations #5421's nine (COPY H7 + MOVE H1).
• Modulo those nine: no tight row, and 2E' splits into 15 independent sets.
• Live controls: source 2E' into 15 sets fails; an extra rank-1 job on a COPY row breaks the 8-split. test_verify.py rejects a drifted input, a corrupted record rank, a dependent certificate part and a tampered RESULT.json.

Part 2 (complex, binding side). complex.py replays Cao Yifan's #4610 backward word exactly over Q. This is the local word of the selected #5383 → #5392 → #5398 → #5413 chain; #5413's extra 144 paid and 144 target rank-8 jobs cancel. #5383's eight owned relations free all eight centres and exactly eight rank-1 zero-site climbs. Modulo them, the 155 remaining pure-cold climb rows are linearly independent with rank mass ≤ 3, so any further relation subspace frees at most 3·dim V of paid mass against 9^t·dim V = 8.94·dim V of lost targets. That is a loss of at least 5.94 raw moment per extra dimension. The test does not cover relation sets that omit #5383's eight; the centre-exchange cap of research/owned-relation-exhaustion limits that family. Three more mutations are rejected (a dropped relation, an injected dependent row, a corrupted climb rank).

python3.12 -B scripts/research_package.py --package research/bit-relation-subspaces

PASS locally on CPython 3.12 (Windows), about 35 s for both parts, standard library only; check_research_commit.py passes. Scope: the fixed PR589 operation order, helper inventory and job set; a changed chronology or BIT word is not covered. The second commit is the unchanged docs/ci-verification.md repair from #5420, needed while main's CI section is stale.

Task card bit-helper-contract, scope changed (see TASK.json). Credit: DreamingOfClouds (#589), eumemic (#555), Ali Romman (#5421, #5383), zxv (#5428).

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