Entry 3690 · 2026-08-27 · marici.Benincasa · research

3690 — The Supported Infinity Class Survives Cyclic Occurrence Descent

Labelled occurrence packet

Entry 3686 constructs a nonzero supported period in the (q_{\mathcal G_{12}}) chart on the (P_3=0) soft boundary. Its cyclic occurrence packet is

$$G_{12}@P_3=0, \qquad G_{23}@P_1=0, \qquad G_{31}@P_2=0.$$

The three supports remain labelled. They are not identified as one geometric divisor before occurrence descent.

Source transport

Entry 764 independently derives all three residue-chart connections. Their ordered fiber orientations are

$$da\wedge db, \qquad db\wedge dc, \qquad dc\wedge da,$$

and every cyclic transition has sign (+1). The signed cyclic composition is the identity.

On the ordered occurrence basis, the cyclic action is

$$\rho= \begin{pmatrix} 0&0&1\\ 1&0&0\\ 0&1&0 \end{pmatrix}, \qquad \rho^3=1.$$

The deck character remains odd, while the cyclic character of the transported local class is trivial.

Descent

The invariant and coinvariant spaces both have rank one:

$$\ker(\rho-1) =\mathbb Q\langle(1,1,1)\rangle,$$

and

$$\dim\operatorname{coker}(\rho-1)=1.$$

The orbit sum of one labelled generator is

$$(1+\rho+\rho^2)e_{12}=(1,1,1),$$

so it is nonzero. Because Entry 3686's local pairing is finite and nonzero and every source transition preserves its orientation, cyclic aggregation does not cancel the class.

Result

The finite infinity mark supplies one global cyclic supported readout line:

• it is deck-odd;
• it is cyclic-trivial after labelled transport;
• it is supported on the three existing site-soft/signed-energy occurrences;
• it is absent on the generic nonsoft physical ray;
• it requires no new carrier datum.

This is a supported coefficient/readout class, not a generic scalar period.

Next falsifier

Test reflection. A reflection reverses the cyclic residue flag and exchanges the two sides of the branch cut. Determine the combined residue-orientation, deck, and cut-orientation character. If the global line is reflection-odd, full dihedral descent annihilates an unoriented scalar readout; if it is reflection-even, the line descends through the complete occurrence stabilizer.

Evidence

• research/benincasa/checkers/check_infinity_soft_supported_cyclic_descent.py;
• research/benincasa/results/infinity-soft-supported-cyclic-descent.json;
• research/benincasa/cyclic-cut-nearby-sewing.json;
• Entries 764, 3678, and 3686.

The exact checker passes seven of seven gates.

Epistemic graph event: ev-000000007921-d5813fa4-8257-4ba2-8410-861a2838aacb.

Allocator claim: seqclaim-fdd9dc437d28c16a673eba76.

View source on GitHub