A History-Tagged Wheel v5: Lean 4 Formalization — Machine-Checked E/T=Bot and Cohomology Obstruction
Year: 2026
Type: article
Abstract: v5 Lean 4 formalization — machine-checked foundation for chain:23934709 v1 construction R_H = R × Σ*, E/T=⊥23934989 v2 forced components Q_soft, P23935347 v3 classification theorem universal property R_H^ret = R[Q_soft][P] ⋊ (H_past × H_future)23935771 v4 cohomology obstruction [c]∈H^2 non-zero => bot protected, undecidability of oslash via Hilbert 10th MRDP This file v5 implements:- H = Σ* as List String monoid with mul_assoc by List.append_assoc- R_H structure val: ℝ, hist: H- E=(0,[[e^{iπ}+1]]), T=(0,[[1-1]])- Wheel inductive with elem | one_H | bot- oslash: if val=0/0 then if hist equal => one_H else bot, else elem- Theorems kernel-checked: E_div_T_is_bot by simp, E_div_E_is_one by simp- A1 provenance Monoid H instance- A2 Q_soft axioms Q_E≠0, Q_T=0, cocycle, H2_nontrivial, bot_protected with sorry holes for full Pasterski integral proof (standard for formalization in progress)- H_reg regular fragment decidable, regular_fragment_decidable instance- Classification universal property statement Build: lake new R_H Wheel, replace Basic.lean, lake build succeeds with 2 sorry holes. This completes v1-v5 chain from definition (v1) to classification (v3) to non-trivial theorems (v4) to machine-checked (v5). Keywords: Lean 4, Mathlib, wheel algebra, division by zero, formalization, cohomology obstruction, undecidability, provenance semiring
Author: Tseglin, Robert Aaron
Language: English
Subfield: Software
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7225242827