[DreamingOfClouds]

Claim. Research package research/p104-surplus-hub-form-note (complements #6868 and #6877). No new kappa and no word. Under an explicit hypothesis ledger it states:

• the surplus identity S = 760 = v(L-1) - Lc at the selected record, recomputed from the stored profile;
• the ratio lemma N >= 1 + dim ker(R+I) for words of isotropic rank-one units;
• the surplus bound S <= sum_p (L_p - 1) - sum_j c_j, in which the target size cancels (conditional on H1-H6);
• a hub rank law: rank Z(D) = v, the cocycle relation, divisibility, and at least v coordinates in every LOCAL mask, at every nonzero D (conditional on the coordinate-mask grammar);
• a form-capacity lemma: ku >= v for every kd in a stated one-pass stop family;
• label corrections: the identical-representative requirement at a scalar gate is a construction choice of the frame lemma, sufficient but not shown necessary, and symbolic exactness in D and ascend-only public paths are verifier behaviour.

Scope and caveats.

• H1 and H4 rest partly on hand arguments, marked CONDITIONAL.
• H5 (one hosted Q-odd unit per LOCAL) is a family assumption, not a theorem. With two, the same arithmetic allows 2632.
• H6 includes the query price and c >= 56. Whether a shear-typed supplier can be priced below a rank-one leaf is open.
• The hub-law replays are gauge-equivalent to a direct sum, so the proof, not the replays, carries that claim.
• The form-capacity solver cells are numerical generic-solution evidence (numpy pinned); the proof carries the theorem. Landings of down rows at a line after the register reached V exceed the bound, as a control shows, and are out of scope.
• Invoice-total arithmetic uses typed-in constants, not a recomputation from a word. No word from any pull request is replayed here.
• Nothing is claimed about the denominator or about kappa.

How to verify. python3.12 -I -B research/p104-surplus-hub-form-note/check.py (about 20 s; prints PASS_P104_SURPLUS_HUB_FORM_NOTE). Registered check: python3.12 -B scripts/research_package.py --package research/p104-surplus-hub-form-note prints PASS_REGISTERED_RESEARCH_PACKAGE. The interpreter needs numpy==2.4.2.

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