Original ledger status
CAR.QTRANS.01
CAR.QTRANS.01
QUADRATIC-TRANSPORT THEOREM (the transport half of the QBL analytic core becomes a theorem): grade seam transport by Clifford degree in the 10 field operators on the 5-slot Fock space (S = Lambda^*(C^5), 32-dim, S+ = 16 code states; integer Jordan-Wigner model, spanning claims via full-rank certificates mod p = 1000003, valid over Q) - (1) PARITY [exact block-zero]: all 10 linear words are sheet-ODD (map S+ -> S-), all 45 quadratic words are sheet-EVEN: code-preserving transport has even Clifford degree (the same Z2 as CAR.PAIR.01/02). (2) MINIMALITY: sheet-even words of degree <= 1 are the scalars alone (dim 1 < 256 = dim End(S+)): degree 2 is the first nontrivial code-preserving grade. (3) GENERATION: the 45 quadratic words (= dim so(10) = the Lambda^2 term of the certified tower 1+45+210) generate the ENTIRE code from the vacuum at word length <= 2. (4) COMPLETENESS (Burnside realised explicitly): products of length <= 2 of quadratics span the FULL operator algebra End(S+) = 256 - every code operation whatsoever is a word in pair transport; all higher even-degree elements (e.g. the 210 quartics) are redundant. CONSEQUENCE: THE TRANSPORT DEGREE IS EXACTLY 2 - degree <= 1 generates nothing, degree 2 generates everything; a theorem, not a hypothesis. (5) LADDER GENERICITY (anti-overclaim): the g=3 world behaves identically (15 quadratics = dim so(6) -> End = 16) - the theorem selects the DEGREE, not the rank g; g-selection stays with Pascal closure + rank-8 (CAR.LADDER.01/CAR.RANK). (6) CHANNEL READING: certified cross-sheet tower 256 = 1 + 45 + 210 = norm + transport generators + pair sector. (7) RESIDUE UPDATE [P]: QBL's remaining content = two interface statements - (a) seam Calderon involution sheet-odd (CAR.PAIR.02a); (b') certified STATE inventory = the <= 2-slot tower (Pascal-closure side, CAR.LADDER.01); nothing about transport remains hypothetical
Recorded status: Identity [I] (exact finite theorem; mod-p certificates valid over Q) + Physical [P] (residue typing)
Dependencies, status detail and source
Canonical status: Theorem: transport degree exactly 2 (minimal complete grade); QBL residue reduced to two interface statements
Dependencies: CAR.PAIR.01; CAR.PAIR.02; CAR.LADDER.01; ARCH.QUAD.01 (QBL); CAR.RANK
Scripts: v111_quadratic_transport.py
Location: tfpt_1
Original CSV, line 195