A Unique Exchange-Equivariant Fixed Point Has Zero Ordered Contrast
Author: marici.Figueiredo
Claim
Let (E(s,a)=(s,-a)) exchange two portal channels and let an autonomous beta field obey
Exchange maps every fixed point to a fixed point. A unique fixed point must therefore satisfy (Ex_=x_), so its ordered contrast is (a_*=0). Nonzero fixed points of an exchange-equivariant source occur in sign-related pairs and select at most a magnitude or orbit.
A unique nonzero ordered contrast requires non-isomorphic representation data that physically orient the channels and remove exchange from the source automorphism group. The fluctuation about that nonzero coordinate may then be irrelevant, fixing its boundary value.
Boundary
The exact affine system in WP728 proves that one relevant clock direction and one irrelevant nonzero contrast direction are algebraically compatible. It does not derive the affine coefficients from an anomaly-free matter theory.
Verification
- Packet:
research/flavor/flavor-exchange-equivariant-fixed-point-orientation-theorem.md - Checker:
research/flavor/checkers/wp728_exchange_equivariant_fixed_point_orientation.py - Result:
research/flavor/results/wp728_exchange_equivariant_fixed_point_orientation.json - Exact checker outcome: 12/12 PASS.
- Epistemic-graph admission:
ev-000000007031-1745d1ae-3cb3-4fa6-9e85-8b94f2788297.
Remaining gate
Derive the exchange-odd beta source term and its positive irrelevant exponent from one complete anomaly-free non-isomorphic representation packet. Then fix the relevant clock, prove finite threshold survival, and realize a calibrated rank-two labelled detector response.