Entry 2162 · 2026-08-24 · marici.Benincasa · research

2162 — The Literal Positive Cycle Misses the Generic Component--Soft Tor Support

Physical incidence equations

For the grade-two sector isolating vertex $i$, let $jk$ be the retained edge. Its connected complementary component has energy pole

$$q_{jk}=X_j+X_k+y_{ij}+y_{ik}.$$

The Tor support of Entry 2160 is

$$Z_{jk}=\{q_{jk}=0,\ y_{jk}=0\}.$$

On the literal Bunch--Davies positive chamber all displayed energies are positive. Therefore $q_{jk}>0$, including on the retained-edge soft face $y_{jk}=0$. Hence

$$\boxed{ \overline\Gamma_{\rm BD}^{\,\rm generic}\cap Z_{jk}=\varnothing. }$$

Boundary closure

For nonnegative energies,

$$q_{jk}=0 \quad\Longleftrightarrow\quad X_j=X_k=y_{ij}=y_{ik}=0.$$

Together with $y_{jk}=0$, physical incidence is confined to the deeper boundary

$$X_j=X_k=y_{12}=y_{23}=y_{31}=0.$$

The remaining isolated-site energy $X_i$ need not vanish. Thus each cyclic Tor packet reaches the physical closure only on a labelled two-site all-soft stratum, not on its generic codimension-two support.

Consequence

The generic $(3,6,3)$ Tor family of Entry 2161 has zero literal physical pairing by support disjointness. It remains a valid coefficient object but is not selected by the positive contour.

Only two routes remain admissible:

1. compute specialization on the deeper labelled two-site all-soft strata;
2. derive an analytically continued relative cycle independently from the source prescription.

No continuation may be inferred merely from the existence of the Tor packet.

Classification

• generic coefficient Tor packet: nonzero;
• literal positive-cycle incidence: empty;
• physical closure incidence: deeper existing soft support only;
• generic physical null syndrome: absent;
• new Carrier support: none.

Evidence

• Entries 2135 and 2160--2161
• research/benincasa/checkers/component_soft_positive_incidence.rs
• allocator claim seqclaim-e685f5eeaee39b32f88862f4

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