A registered result in its source context
Original ledger classification: Identity [I] (exact finite theorem; mod-p certificates valid over Q) + Physical [P] (residue typing)
Recorded statement: 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;…
Statement, assumptions and sources
Paper context: Architecture, E8 and the electromagnetic fixed point
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CAR.QTRANS.01
Original ledger classification: Identity [I] (exact finite theorem; mod-p certificates valid over Q) + Physical [P] (residue typing)
Original claim text
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
Original classification detail
Theorem: transport degree exactly 2 (minimal complete grade); QBL residue reduced to two interface statements
Dependencies as recorded
CAR.PAIR.01; CAR.PAIR.02; CAR.LADDER.01; ARCH.QUAD.01 (QBL); CAR.RANK
Open the original ledger source, row 195Location recorded in the ledger
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- Architecture, E8 and the electromagnetic fixed point
Navigation through a shared verification script
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- How to read this documenttfpt 1 architecture e8
- Honest statusinput 4 origin theory
- Honest statusorigin theory
- The hard reduction: the live residual as typed interfacesTFPT — Introduction and reading guide
- How to read this documenttfpt 1 architecture e8
- Honest statusOrigin Theory
- Front matter / supportTFPT — Introduction and reading guide; Verification reference catalog
- Honest statusinput 4 origin theory
Registered verification modules
- v111_quadratic_transport.pyRegistered verification module · registry
Read the description recorded in the module registry
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 (integer Jordan–Wigner model; spanning claims via mod-p full-rank certificates, valid over ℚ) — PARITY: all 10 linear words are sheet-odd, all 45 quadratic words sheet-even (code-preserving transport has even Clifford degree, the same ℤ₂ as v109/v110); MINIMALITY: sheet-even words of degree ≤ 1 are the scalars alone; GENERATION: the 45 quadratics (= dim so(10) = the Λ² term of the certified tower 1+45+210) generate the whole code from the vacuum at word length ≤ 2; COMPLETENESS (Burnside realised): products of length ≤ 2 span the FULL End(S⁺) = 256 — every code operation is a word in pair transport, all higher even-degree elements redundant ⇒ THE TRANSPORT DEGREE IS EXACTLY 2 (degree ≤ 1 generates nothing, degree 2 generates everything — a theorem, not a hypothesis); g=3 control: degree selected, not rank; QBL residue reduced to two interface statements: (a) seam Calderón involution sheet-odd, (b') certified state inventory = the ≤2-slot tower
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