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A registered result in its source context

Original ledger classification: Conditional [C] (exact selector under the named axiom set A1-A4; axiom provenance from the compiler open)

Recorded statement: THE CONDITIONAL 4D DIMENSION SELECTOR [C] (registered 2026-08-27 from the external bird's-eye review, the master-route wave; machine-checked in v975, 16/16 sympy-exact). STATEMENT: under the named TFPT-compatible physics axiom set A1 (d >…

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Paper context: Research contracts

The exact identifier, original classification and full claim are available below.

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DIMENSION.SELECTOR.4D.01

Original ledger classification: Conditional [C] (exact selector under the named axiom set A1-A4; axiom provenance from the compiler open)

Original claim text

THE CONDITIONAL 4D DIMENSION SELECTOR [C] (registered 2026-08-27 from the external bird's-eye review, the master-route wave; machine-checked in v975, 16/16 sympy-exact). STATEMENT: under the named TFPT-compatible physics axiom set A1 (d > 2: propagating local gauge fields, d-2 >= 1 transverse polarizations), A2 (dimensionless Yang-Mills coupling), A3 (real self-dual/anti-self-dual 2-form sectors: the Euclidean Hodge star is an involutive endomorphism of 2-forms), A4 (chiral Weyl representations: even d), the spacetime dimension d = 4 is UNIQUE and MINIMAL on the exact scan window d = 2..12, and the selector is OVERDETERMINED: A2 alone = {4} ([g_YM] = (4-d)/2 forced symbolically from dimensionless-action power counting; unique zero d = 4) and A3 alone = {4} (* : Omega^2 -> Omega^{d-2} is a self-map iff d = 4; the explicit 6x6 star on Lambda^2(R^4) has *^2 = I with eigenvalues +-1 at multiplicities 3/3 -- the real SD/ASD split su(2)+ x su(2)-), while A1 & A4 alone give {4, 6, 8, 10, 12} -- chirality does NOT select 4 by itself (honest ablation ledger). Weyl chirality certified by exact Clifford algebras d = 2..7 (even d: gamma_* anticommutes with every gamma_mu, gamma_*^2 = I, tr = 0; odd d: the full product is CENTRAL and scalar -- no grading). Signature typed honestly: Lorentzian *^2 = -1 on 2-forms in d = 4 -- the real split is a EUCLIDEAN/OS-side statement. MUTANTS caught: the wrong power counting [g] = (6-d)/2 selects {6}; the 'A4 alone selects 4' overclaim is REFUSED. FIREWALL (binding): mu4 and g_car enter NOWHERE -- 'mu4 => 4D' stays forbidden per DIMENSION.UPLIFT.FIREWALL.01; this is a CONDITIONAL selector, not a derivation: AXIOM PROVENANCE IS THE OPEN HALF (kill criterion: if A1-A4 cannot themselves be forced from the compiler primitives {c3, g_car}, the selector is a consistency statement, not a prediction); no 4D construction contract is advanced by this row.

Original classification detail

Conditional [C]: d = 4 unique + minimal + overdetermined under {d > 2, [g_YM] = 0, real SD/ASD 2-form split, Weyl chirality} on d = 2..12; A2 and A3 each pin {4} alone, A1 & A4 alone = {4, 6, 8, 10, 12}; mu4 enters nowhere; axiom provenance from {c3, g_car} is the open half

Dependencies as recorded

DIMENSION.UPLIFT.FIREWALL.01; SEAM.BULK4D.RECON.01; QFT4D.OS.RECON.01; CHIRAL4D.NOMIRROR.01

Open the original ledger source, row 755

Location recorded in the ledger

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Registered verification modules

  • v975_dimension_selector_4d.pyRegistered verification module · core
    Read the description recorded in the module registry

    DIMENSION.SELECTOR.4D.01 [C, NEU] (Master-Routen-Welle 2026-08-27): **der konditionale 4D-Dimensionsselektor** — 16/16 sympy-exakt. Unter dem benannten TFPT-kompatiblen Axiomensatz A1 (d > 2: propagierende lokale Eichfelder), A2 (dimensionslose Yang-Mills-Kopplung), A3 (reelle selbstduale/anti-selbstduale 2-Form-Sektoren: der euklidische Hodge-Stern als involutiver Endomorphismus auf 2-Formen), A4 (chirale Weyl-Darstellungen: gerades d) ist d = 4 auf dem exakten Scanfenster d = 2..12 EINDEUTIG und MINIMAL — und der Selektor ist ÜBERDETERMINIERT: A2 allein = {4} ([g_YM] = (4−d)/2 symbolisch erzwungen, einzige Nullstelle 4) und A3 allein = {4} (expliziter 6×6-Stern auf Λ²(R⁴), *² = I, Eigenwerte ±1 mit Multiplizitäten 3/3), während A1 & A4 allein {4, 6, 8, 10, 12} geben — Chiralität selektiert 4 NICHT allein (ehrliche Ablations-Leiter). Weyl-Chiralität zertifiziert durch exakte Clifford-Algebren d = 2..7 (gerade d: γ* antikommutiert, γ*² = I, spurfrei; ungerade d: das Produkt ist ZENTRAL und skalar). Signatur ehrlich typisiert: lorentzisch ist *² = −1 auf 2-Formen — der reelle Split ist eine EUKLIDISCHE/OS-seitige Aussage. Mutanten gefangen ([g] = (6−d)/2 selektiert {6}; der 'A4 allein'-Overclaim verweigert). FIREWALL: μ₄ und g_car gehen NIRGENDS ein — 'μ₄ ⇒ 4D' bleibt verboten (DIMENSION.UPLIFT.FIREWALL.01); die Axiom-Provenienz aus {c₃, g_car} ist die OFFENE Hälfte (Kill-Kriterium der Ledger-Zeile); kein 4D-Konstruktionskontrakt wird bewegt.

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