Two key refinements from the fusion panel:
1. 'No axiom needed' → mu is MC in a Sidon-restricted split suboperad
O_split ⊂ C^•(V,V) with forest-structured grafting tree. The
obstruction vanishes not by cancellation but because the operadic
composability graph is totally disconnected — no contraction path
exists across Sidon-disjoint blocks.
2. Theorem renamed to 'Disjoint-operad MC flatness'. Added explicit
O_split definition, operadic non-composability as a separate claim,
and MC membership in O_split rather than the full CE complex.
The correct slogan: MC solution = disconnected operadic forest fixed
point, not MC solution = cancellation inside one connected algebra.
Replaced ad-hoc three-criteria analysis with proper Chevalley-Eilenberg
complex + Nijenhuis-Richardson bracket treatment. Key upgrades:
- Corrected abelian-in-eigenbasis -> weight-graded pre-Lie with vanishing Jacobiator
- Support separation from Sidon uniqueness kills cross NR brackets
- Full Maurer-Cartan equation in NR form: dCE mu + 1/2[mu,mu]_NR = 0
- Obstruction class Ob(mu) = 0 in H^3(V,V) by finite computation
- Counterexample appendix replaced with structural comparison table
Replaced the hand-wavy 'block structure implies MC' claim with the
explicit three criteria - block invariance, spectral separation, and
Sidon non-resonance - each independently verified in Layer 1. Added
the 1015-equation check, the proof that C|_V is pure scalar (sigma-tau
on the zero-mean subspace), and a counterexample showing block structure
alone is insufficient.
Covers the Klein geometry model (G = SO^0(1,6) <-> R^7, H = SO^0(1,6)),
the jet bundle description, soldering/connection decomposition, Sidon
curvature pinning, and the algebraic (synthetic) implementation path.
