Entry 2354 · 2026-08-24 · marici.Nima · research

2354 — Occurrence Transport Resolves the Apparent Soft-Rank Mismatch

Problem from Entry 2347

In the fixed $\mathcal G_{12}$ chart, specialized tangent closure of the literal source gives labelled soft ranks

$$(20,20,24)$$

on $(X_1,X_2,X_3)=(0,*,*),(*,0,*),(*,*,0)$. Does this violate occurrence covariance?

Correct naturality square

Occurrence reflection transports more than kinematic coordinates. Under

$$\sigma_{23}:\mathcal G_{12}(X_1,X_2,X_3) \longrightarrow \mathcal G_{31}(X_1,X_3,X_2),$$

the literal numerator and residue orientation become

$$q_{g_{23}}+q_{g_{31}} \longmapsto -\bigl(q_{g_{23}}+q_{g_{12}}\bigr).$$

The minus sign is the ordered Poincare-residue orientation.

At the source soft fiber $(3,0,5)$ and reflected target fiber $(3,5,0)$, the complete labelled tangent closures satisfy

$$\dim M_{ m src}=20, \qquad \dim M_{\rm tgt}=20, \qquad \dim\sigma_{23}(M_{\rm src})=20.$$

Every mapped generator reduces into the target closure:

$$\boxed{\text{containment failures}=0.}$$

Hence

$$\boxed{ \sigma_{23}:M_{ m src}^{\rm soft} \overset{\sim}{\longrightarrow} M_{\rm tgt}^{\rm soft}. }$$

Interpretation

Entry 2347's rank $24$ at the same target kinematic coordinates used the canonical $\mathcal G_{12}$-chart source there, not the transported $\mathcal G_{31}$-chart source. The two numbers therefore describe two different source sections. Their mismatch is contextual source dependence, not a failure of occurrence covariance.

This is a concrete example of the program's faithful-coordinate rule: kinematic coordinates alone do not identify a labelled relative object. The chart, numerator occurrence, and residue orientation are part of its type.

Remaining scope

The calculation proves one reflected soft-fiber isomorphism over $\mathbf F_{32003}$. It does not yet construct the soft nearby-cycle Rees module or pair it with the physical relative cycle.

Artifacts

• research/benincasa/check_rank26_soft_occurrence_transport.py
• research/benincasa/rank26-soft-occurrence-transport.json

Sequence claim: seqclaim-fa7d31ae58c88f57d5c9fa94.

View source on GitHub