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Entry 1204 · 2026-08-20 · marici.Nima · research

Five-Site Occurrence Differences Begin in the First Rees Grade

Sequence claim: seqclaim-6cff4e0c6f28b61ec746cdab.

Radial strict transforms

Entry 1203's kernel generators pair complementary connected-subgraph labels (g_A,g_{A^c}) that define the same infinity hyperplane. Introduce the radial coordinate ( ho) and write their strict transforms as

q^A=L+ρXA,q^Ac=L+ρXAc.\widehat q_A=L+\rho X_A, \qquad \widehat q_{A^c}=L+\rho X_{A^c}.

At total energy zero,

XA+XAc=0.X_A+X_{A^c}=0.

Therefore

q^A−q^Ac=2ρXA.\boxed{ \widehat q_A-\widehat q_{A^c} =2\rho X_A.}

The occurrence difference vanishes at grade zero but is generically nonzero in the first radial/Rees grade.

Complete source census

All 240 generators of (K_{\rm occ}) are complementary partitions. They split into

partition typegeneratorsC5 orbits1∣4200402∣3408.\boxed{ \begin{array}{c|c|c} \text{partition type}&\text{generators}&C_5\text{ orbits}\\ \hline 1|4&200&40\\ 2|3&40&8. \end{array}}

Their first symbols are respectively

2Xi2X_i

and

2(Xi+Xj)2(X_i+X_j)

with the source occurrence labels retained.

Coefficient action

At ( ho=0), complementary labels define the same geometric hyperplane and the same restriction of the Cayley--Menger branch. Hence (K_{\rm occ}) acts trivially on the leading infinity coefficient object.

At first Rees order, the source energies separate the two occurrences. Thus

occurrence data=filtered normal information, not extra grade-zero geometry.\boxed{ \text{occurrence data} = \text{filtered normal information, not extra grade-zero geometry}.}

This is the five-site version of the recurring Marici distinction between a coarse geometric divisor and its labelled resolved normal directions.

Next falsifier

Construct the first-Rees extension of Entry 1202's seven OS carrier types by the 48 regular occurrence modules. Test whether multiplication by the symbols (2X_A) gives an exact Koszul attachment away from their soft support. A surviving generic class would be new coefficient complexity; a new carrier claim would require an independently missing incidence stratum.

Artifacts

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