A registered result in its source context
Original ledger classification: Honest promotion of a proved shell law [typed evidence line: 15/15 checks, zero fails, verdict SHELL-GLOBAL-THEOREM; frozen spec SHA a4b2f6d9...]
Recorded statement: THE GLOBAL GAUSSIAN SHELL THEOREM (2026-08-08 round 36, v875; discovery probe gaussian_shell_global_probe.py 15/15, verdict SHELL-GLOBAL-THEOREM) -- the census->theorem upgrade: the v857 value law 'Thetahat_u/Theta_L = -1/15 on odd shells'…
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Paper context: Research contracts
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E8.SHELL.GLOBAL.01
Original ledger classification: Honest promotion of a proved shell law [typed evidence line: 15/15 checks, zero fails, verdict SHELL-GLOBAL-THEOREM; frozen spec SHA a4b2f6d9...]
Original claim text
THE GLOBAL GAUSSIAN SHELL THEOREM (2026-08-08 round 36, v875; discovery probe gaussian_shell_global_probe.py 15/15, verdict SHELL-GLOBAL-THEOREM) -- the census->theorem upgrade: the v857 value law 'Thetahat_u/Theta_L = -1/15 on odd shells' holds for ALL shells, no census cap. THEOREM: on V = L/(1+i)L of the Gaussian E8, for EVERY n >= 1: Theta_v(n) = (Theta_L(n) - Theta_0(n))/15 for all v != 0 (the division exact), Thetahat_u(n) = 16(16 1_{2|n} sigma_3(n/2) - sigma_3(n)) for every nontrivial character u, and at every ODD n: Thetahat_u(n) = -16 sigma_3(n), Thetahat_u(n)/Theta_L(n) = -1/15 EXACTLY. INPUTS (each warded): (i) LEMMA 1 -- every g in G31 is a norm-preserving bijection of L transporting classes ((4M)^T(4M) = 16I; complex linearity (4M)J = J(4M)); the induced group is Sp(4,2) (order 720, generated by the 60 symplectic transvections), TRANSITIVE on the 15 nonzero classes, and IDENTICAL to the shell-module class action (coordination verified on generators); (ii) LEMMA 2 -- (I+J)^T(I+J) = 2I and (1-J)/2 inverts (1+i) on L: Theta_0(2m) = Theta_L(m), Theta_0(odd) = 0 (from 2 = -i(1+i)^2); (iii) LEMMA 3 -- Theta_L(n) = 240 sigma_3(n) (classical Eisenstein E4; verified to n = 24 directly and via the v857 packet glue identity to n = 16500). The n <= 16500 census is RETAINED as the exact ward (matched everywhere, odd AND even). CONTROLS: the non-transitive subgroup <T_1> (11 orbits) admits an explicit invariant NON-uniform census with Walsh multiset {-48 x4, -16 x7, +16 x4} -- transitivity is load-bearing; the even-shell formula differs correctly (7/135 at n = 2: the -1/15 law is the ODD-shell statement only). This REPLACES the finite-census argument behind the v857 value theorem (dated note there); the consequence chain is kernel-checked in FORM.E8.SHELL.GLOBAL.01. NO physics claim beyond the audit statement.
Original classification detail
SHELL-GLOBAL-THEOREM: Sp(4,2) transitivity + (1+i) doubling + Theta_L = 240 sigma_3 => Thetahat_u/Theta_L = -1/15 at ALL odd shells; census n <= 16500 retained as ward; non-transitive control breaks the law.
Dependencies as recorded
E8.SIMPLEX.FOURIER.01; E8.G31.CLOCK_ALPHABET.01; v857; v858; v868
Open the original ledger source, row 716Location recorded in the ledger
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- Architecture, E8 and the electromagnetic fixed point
- E8 audit and bootstrap
- Research contracts
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- Group-theoretic audits (optional)input 5 tfpt 3 e8 audit bootstrap
- Research Contract 2 — [formula in source]tfpt research contracts
- Front matter / supportE8 audit and bootstrap
- Group-theoretic audits (optional)input 5 tfpt 3 e8 audit bootstrap
- Research Contract 2 — [formula in source]Research contracts
- Research Contract 2 — [formula in source]tfpt research contracts
Navigation through a shared verification script
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- How to read this documenttfpt 1 architecture e8
- Front matter / supportArchitecture, E8 and the electromagnetic fixed point
- How to read this documenttfpt 1 architecture e8
- Front matter / supportTFPT — Introduction and reading guide; Verification reference catalog
- 2026-10-18: Project separation and retained physics historyResearch changelog; TFPT — Introduction and reading guide
Registered verification modules
- v875_shell_global_lean.pyRegistered verification module · core
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E8.SHELL.GLOBAL.01: **SHELL-GLOBAL-THEOREM (15/15, + Lean-Skelett)** — das Zensus→Theorem-Upgrade: Θ̂ᵤ/Θ_L = −1/15 auf ALLEN ungeraden Schalen (nicht mehr nur n ≤ 16500). Die drei Inputs, jeder gewardet: (i) die G31-Klassenwirkung = die 60 symplektischen Transvektionen erzeugen Sp(4,2) (Ordnung 720), TRANSITIV auf den 15 Nichtnull-Klassen und IDENTISCH mit der Schalenmodul-Wirkung; (ii) Normverdopplung durch (1+i): Θ₀(2m) = Θ_L(m), Θ₀(ungerade) = 0; (iii) Θ_L = 240σ₃ (klassisch, Eisenstein E₄). Kontrollen: eine nicht-transitive Untergruppe liefert einen invarianten NICHT-uniformen Zensus (das Gesetz bricht — Transitivität ist tragend); die Gerade-Schalen-Formel weicht korrekt ab (7/135 bei n = 2). Lean-Skelett: TfptCarrier/GaussianShells.lean prüft die KONSEQUENZKETTE im Kern (7 Theoreme aus dem benannten Hypothesenbündel ShellSystem; jede Aussage eine exakte Ganzzahl-Identität, keine Division), die drei Inputs bleiben BENANNTE Hypothesen mit typisierter Provenienz — die Haus-Disziplin: das globale Statement kann keine Lücke verstecken.
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