A History-Tagged Wheel: E/T = ⊥ — Unified Mega Paper v1–v12.1

This is a unified, corrected proof-sketch in 13 chapters (v1–v12.1) for a history-tagged wheel R_H^{ret}. Two histories E = [[e^{iπ}+1]] and T = [[1-1]] have the same value val = 0 but different histories. Their difference is measured by a soft charge Q_soft with Q_E = 1, Q_T = 0, and by an obstruction class [c] with c(E,T) = 1. The paper collects 11 invariants: E/T = ⊥, Q_soft, universality, [c], K_0, Ext^2, tilting, classifying topos with Ω = {0, ⊥, 1}, U-rank = ω, S-matrix soft correction, and an O(n log n) algorithm on regular histories. This version is a corrected sketch with Lean value-checks for the E,T pair, not a fully formalized monograph. Full proofs of H^2, D^b, topos, and QFT formalization are listed as open gaps in the Epilogue. history-tagged wheel, soft theorem, K-theory, Hochschild homology, classifying topos