An Intrinsic Six-Sector Reynolds Cancellation Theorem for Local Regge Zero Germs

This article isolates an exact local cancellation mechanism in Lorentzian Regge calculus.

The finite source convention is stated explicitly: squared-edge variables, a six-mode spatial perturba-

tion map at τ = 7/10 with anchor T0 = 7/5, fixed Lorentzian angle branches, and an interior-hinge

flat-linearized Regge response. For a hinge with six incident four-simplex sectors, let ασ be the

sector-angle derivative covector on the mode space (XX,YY,ZZ,XY,XZ,YZ). If the sectors form

a complete simply-transitive S3 orbit and the source is exactly equivariant, then

6

σ=1

ασ = 6ΠS3 ασ0.

Thus cancellation in this branch is equivalent to absence of a trivial-isotype component; sectorwise

stationarity remains a distinct mechanism. In the natural spatial permutation representation,

the Reynolds projector has rank two and the test reduces to vanishing diagonal and off-diagonal

coordinate sums. The theorem is realized by a rooted-Kuhn Boolean rank-1/rank-3 family and by a

completed warped non-Boolean S3 star. A source-only census covers 115 authenticated occurrences,

representing 74 distinct triangle tuples: 43 are exact zeros, split into 31 orbit cancellations and 12

stationary cases. Prospectively frozen deterministic tests cover one recurrent Boolean occurrence,

18 catalog-transfer occurrences, and one non-Boolean occurrence, with maximum float64 decision

residual 3.63×10−15. A separate 90-digit reconstruction gives 2.51×10−91. The result is conditional

and finite-scope, not a global classification, arbitrary-mesh invariance, continuum limit, or nonzero-

amplitude law.