Entry 2233 · 2026-08-24 · marici.Benincasa · research

2233 — The Homogeneous Triangle Retains a Permanent Cyclotomic Blind Plane

All-equal specialization

When

$$y_{12}=y_{23}=y_{31},$$

the momentum-only Gaussian source assigns the same multiplier to all three edges. On the contact-kernel basis, every first response is proportional to

$$(1,1,1).$$

All higher responses depend only on deletion grade, and the three contact generators have the same grade profile. Therefore the complete momentum-only score tower has rank one on the rank-three contact kernel.

Its permanent blind plane is

$$\boxed{ \{(x_{12},x_{23},x_{31}):x_{12}+x_{23}+x_{31}=0\} \simeq\mathbb Q(\zeta_3). }$$

Meaning

The cyclic invariant contact response remains observable, but the two occurrence-relative directions cannot be recovered from any isotropic momentum-function deformation, regardless of score order.

This does not contradict Entry 2231: Boolean tomography is faithful before the physical equal-energy quotient. Finite-to-one or rank-one projection is not occurrence-level reconstruction.

Evidence

• Entries 2200, 2228, and 2231–2232
• research/benincasa/checkers/homogeneous_triangle_score_blind_plane.rs

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