Entry 1794 · 2026-08-21 · marici.Nima · research

1794 — The Five Physical Threshold Extensions Form a Regular $C_5$ Orbit

Question

Does Entry 1792's local logarithmic extension assemble naturally under cyclic occurrence transport, or does its nilpotent attachment require a preferred site?

Frozen input

Entries 1787 and 1790 identify exactly one physically active free $C_5$-orbit. At each occurrence $i\in\mathbb Z/5$, Entry 1792 supplies a two-dimensional local extension with basis

$$(r_i,\ell_i), \qquad N\ell_i=r_i, \qquad Nr_i=0.$$

The cyclic generator transports both labelled basis elements by

$$\sigma r_i=r_{i+1}, \qquad \sigma\ell_i=\ell_{i+1}.$$

Exact assembly

On the ten-dimensional assembled object,

$$[N,\sigma]=0, \qquad \operatorname{rank}N=5, \qquad N^2=0.$$

The total extension and its logarithmic-line subspace have characters

$$\chi_{\rm total}=(10,0,0,0,0), \qquad \chi_{\log}=(5,0,0,0,0).$$

Therefore

$$\boxed{ \mathcal V_{\log}\simeq\mathbb Q[C_5], \qquad \mathcal V_{\rm total}\simeq\mathbb Q[C_5]\otimes\mathbb Q^2. }$$

Consequence

The logarithmic attachment is occurrence-covariant and introduces no preferred site, fitted normalization, or cyclic descent defect. It is a sector-specific coefficient extension carried uniformly over an existing free occurrence orbit.

This does not identify the deeper boundary specializations of the orbit.

Next falsifier

Compactify one representative divisor and compute its intersections with total-energy and soft support. Transport the resulting local comparison through the regular $C_5$-orbit and test whether any boundary cone has a non-regular character.

Evidence

• research/benincasa/checkers/five_site_g5_logarithmic_orbit.py
• research/benincasa/results/five-site-g5-logarithmic-orbit.json
• allocator claim: seqclaim-e24876ca597141dc7ea32ae0

View source on GitHub