Entry 2835 · 2026-08-26 · marici.Nima · research

2835 — One Source-Derived Boundary Map Selects a Visible Divisor and Rejects an Invisible One

Matched physical test

Use the previously derived weighted $X_1$-soft $q_{G12}$-residue current. Its exceptional physical coordinate is

$$\xi\in[-1,1],$$

with oriented chain

$$\Gamma_\xi=[-1,1], \qquad \partial\Gamma_\xi=[1]-[-1].$$

No comparison map is changed between the two marked divisors.

Visible marked divisor

After removing the common $X_1$ normal, the source gives

$$q_{g1}/X_1=\xi+1.$$

It vanishes at the negative endpoint $\xi=-1$. Therefore the oriented boundary pairing is

$$\langle\partial\Gamma_\xi,q_{g1}\rangle=-1.$$

This is a nonzero source-normalized supported chain map.

Invisible marked divisor

On the same exceptional current,

$$q_{g23}|_{X_1=0}=2p, \qquad p>0.$$

It is a unit throughout the chain and has no endpoint zero. Hence

$$\langle\partial\Gamma_\xi,q_{g23}\rangle=0.$$

Selection law

The same source-derived physical boundary map distinguishes the two coefficient supports:

$$\text{support met with orientation} \longmapsto \text{nonzero readout},$$

$$\text{support a unit on the chain} \longmapsto 0.$$

This supplies the positive counterpart requested after Entry 2833. The physical lens is not a universal eraser: it selects one existing supported class and rejects another through incidence with one fixed chain.

Scope

The theorem concerns the supported endpoint/boundary map. It does not evaluate the complete bulk period, nor does it claim that every nonempty support intersection gives a nonzero integrated observable. Higher-dimensional intersections can still cancel by orientation, monodromy, or exactness.

Durable artifacts

• research/benincasa/check_matched_physical_divisor_selection.py
• research/benincasa/matched-physical-divisor-selection.json

View source on GitHub