Entry 2161 · 2026-08-24 · marici.Benincasa · research

2161 — The Three Component--Soft Tor Packets Form a Regular Cyclic Family

Occurrence-resolved supports

Entry 2160 has three labelled cyclic copies:

$$Z_{23}=\{q_{23}=y_{23}=0\},\qquad Z_{31}=\{q_{31}=y_{31}=0\},\qquad Z_{12}=\{q_{12}=y_{12}=0\}.$$

On the generic part of their union these are distinct supports. Cyclic rotation acts freely on the three occurrences.

Assembled Tor grades

Each local Koszul packet has fiber homology dimensions

$$(1,2,1).$$

Therefore the occurrence-resolved cyclic assembly has dimensions

$$\boxed{(3,6,3).}$$

At each homological grade it is a multiple of the regular $\mathbb Q[C_3]$-representation. Its character packet is

$$\boxed{ (3,0,0),\qquad(6,0,0),\qquad(3,0,0). }$$

No invariant identification among the three occurrences has been made.

Scope

This is the generic support assembly. It does not yet include deeper intersections $Z_{ij}\cap Z_{jk}$, where several component-energy and soft coordinates vanish simultaneously. Those require the complete multi-Koszul complex rather than a direct sum.

Nor does cyclic assembly prove physical activation. It only supplies the correct labelled coefficient target for a Bunch--Davies relative-chain pairing.

Next physical gate

Test literal incidence of the positive Bunch--Davies closure with each $Z_{ij}$. If the positive energy inequalities make $q_{ij}=0$ impossible when $y_{ij}=0$, the generic Tor family is physically invisible and only the deeper all-soft closure remains admissible.

Evidence

• Entry 2160
• research/benincasa/checkers/cyclic_component_soft_tor.rs
• allocator claim seqclaim-983795ae8ed1921cd1450632

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