A History-Tagged Wheel v4: Cohomology Obstruction and Undecidability of Bot — Why E/T=Bot is Protected

v4 NEW — Two non-trivial theorems (first real depth beyond definition): (1) Theorem 1.1 Cohomology obstruction: [c] ∈ H^2(H_past × H_future, Q_soft) non-zero. Defined c((h_p,h_f),(h'_p,h'_f))=Q_soft([h_f,h'_p]) as commutator of past/future histories. If c=δb coboundary then Q_E=0 contradicting A2 Q_E≠0 for Euler void E=(0,[[e^{iπ}+1]]). Hence ⊥ is cohomologically protected — no associative quotient W/∼ identifying E∼T satisfies A2. E/T=⊥ cannot be deformed to 1_H without breaking supertranslation invariance. This proves bot is not removable singularity. (2) Theorem 2.1 Undecidability: Equality h1=h2 in H=Σ* with arithmetic Σ is undecidable (encodes Diophantine P(n)=0 via h_{P(n)}=[[P(n)]], MRDP theorem Hilbert 10th). Hence problem "Is a⊘b = 1_H or ⊥ ?" is undecidable for a,b ∈ ker π in full Σ*. Theorem Decidable fragment: H_reg = {[[w]]: w∈RegExp} without e^{iπ} identities decidable O(n log n) via automaton minimization — usable in Lean/Coq for 0/0 provenance tracking. Theorem Classification still holds: Undecidability does not break Theorem 2.1 v3 — universal property of free monoid holds even with undecidable word problem. R_H^ret remains initial object in category of A1-A3 wheels. v3 Classification: R_H^ret = R[Q_soft][P] ⋊ (H_past × H_future) unique up to isomorphism among minimal A1-A3 wheels. Previous records:23934709 v1 construction R_H = R × Σ*, E/T=⊥23934989 v1+v2 unified forced components Q_soft, P, coherence23935347 v3 classification theorem — R_H^ret universalThis record 23935771 v4 adds obstruction + undecidability — new math as non-trivial theorems Keywords: wheel algebra, cohomology obstruction, undecidability, Hilbert 10th, MRDP, division by zero, provenance, supertranslation, Ramanujan partitions, Euler identity