0a: static Fisher–Rao on Δ₃ proven constant-curvature 1/4, ∇R≡0 (symbolic).
0b: rossbyDriftFromChirality drift-flip metric has signature (2,1), drift
direction time-like at 3 exact rational points.
0c: drift-flipped metric is PROPER — not locally symmetric (108 nonzero
∇R components at centroid, exact), not semisymmetric, not Deszcz-
pseudosymmetric (inconsistent L ratios at two points).
0d: obstruction is carried by the drift direction.
Refutes the semi-symmetry hypothesis for the drift-FLIP geometrization at
m=4; Randers/torsion geometrizations and the m=8 Sidon-block case remain
open (Δ₇ run pending).
Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
Expands the NR bracket from a pure Cartan-connection lemma to a unified
proposal covering six formerly separate layers:
Core: [mu,mu]_NR = 0 (Layer 2c, new code)
YB: Yang-Baxter integrability via Sidon-disjoint blocks
TL: Temperley-Lieb quotient factorization
Analytic: Eigensolid convergence as the analytic dual
PIST: Same Sidon support separation drives classification gates
VCN: Zero-gap encoding = vanishing NR terms as structural signal
Each connection shows independent work — the specific argument, the
Layer-1 invariant that powers it, and what fails if the mechanism
breaks.
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.
