A registered result in its source context
Original ledger classification: Formal [F] (Lean kernel; the consequence chain from the named ShellSystem hypotheses -- every statement an exact integer identity)
Recorded statement: LEAN 4 FORMALISATION of the global shell theorem's consequence chain (2026-08-08 round 36; TfptCarrier/GaussianShells.lean) -- AUDIT: PASS, no sorry, no native_decide, no domain axioms (#print axioms = propext, Classical.choice, Quot.sound…
Statement, assumptions and sources
Paper context: Research contracts
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FORM.E8.SHELL.GLOBAL.01
Original ledger classification: Formal [F] (Lean kernel; the consequence chain from the named ShellSystem hypotheses -- every statement an exact integer identity)
Original claim text
LEAN 4 FORMALISATION of the global shell theorem's consequence chain (2026-08-08 round 36; TfptCarrier/GaussianShells.lean) -- AUDIT: PASS, no sorry, no native_decide, no domain axioms (#print axioms = propext, Classical.choice, Quot.sound on all 7 theorems; lake build green 3418 jobs). THE PATTERN (the house discipline): the ARITHMETIC CONSEQUENCE CHAIN is kernel-checked while the finite/structural inputs stay NAMED hypotheses with verification provenance typed on each field -- the hypothesis bundle ShellSystem carries (H1) equidistribution 15 Theta_v = Theta_L - Theta_0 (provenance: Sp(4,2) transitivity + shell invariance, machine-verified finite-range in v875), (H2) doubling Theta_0(2m) = Theta_L(m), Theta_0(odd) = 0 (exact from 2 = -i(1+i)^2), (H3) Theta_L = 240 sigma_3 for n >= 1 (classical, cited; finite-range verified); the 7 kernel-checked consequences: dvd_diff (the /15 division exact), decomposition, walsh_formula (15 Thetahat_u = 16 Theta_0 - Theta_L; the 16-coset Walsh combinatorics absorbed into the definition, typed), theta_v_odd, walsh_odd (Thetahat_u(2m+1) = -16 sigma_3(2m+1)), walsh_odd_ratio (15 Thetahat_u(2m+1) = -Theta_L(2m+1) -- the -1/15 statement as an integer identity, no division anywhere), walsh_even. sigma_3 is mathlib's ArithmeticFunction.sigma 3 -- nothing bespoke; no modular-forms machinery imported or claimed. Mirrored numerically in v875 part B.
Original classification detail
Formal [F]: the shell consequence chain is a Lean theorem family (7 theorems from the named hypothesis bundle), standard axioms only, no sorry, full build green.
Dependencies as recorded
E8.SHELL.GLOBAL.01; FORM.QGEO.01
Open the original ledger source, row 717Location recorded in the ledger
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- Architecture, E8 and the electromagnetic fixed point
- Research contracts
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- Research Contract 2 — [formula in source]tfpt research contracts
- Research Contract 2 — [formula in source]Research contracts
- Research Contract 2 — [formula in source]tfpt research contracts
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