Entry 1703 · 2026-08-21 · marici.Nima · research

1703 — Covariance Sign Enlargement Is Entirely Supported on the Soft Locus

Relative-support falsifier

Entry 1702 closes generic loop holonomy for source-derived covariance Rees packets. Allow the resolved normal to vanish on labelled occurrences and compute the remaining sign object.

Nonzero support graph

Let H be the induced graph on occurrences with

$$u_i\neq0.$$

If H has c(H) connected components, edge products propagate signs within each component but not between components. Therefore

$$\boxed{ \operatorname{Deck}_{\rm cov}(H)=\mathbb Z_2^{c(H)}. }$$

For arbitrary edge signs, the nonliftable quotient remains

$$H^1(H,\mathbb Z_2).$$

Source-derived packets occupy its zero class on every component.

The exact checker enumerates every connected labelled simple graph through six vertices and every nonempty vertex support. It verifies

$$2^{|E(H)|} =2^{|V(H)|-c(H)}2^{b_1(H)}$$

and

$$2^{c(H)}2^{|V(H)|-c(H)}=2^{|V(H)|}.$$

Narrow result

$$\boxed{ \text{all enlargement beyond one global covariance sign is supported where the resolved normal vanishes.} }$$

After localizing every nonzero normal on a connected graph, c(H)=1; no new generic sign or loop class survives. This is the precise covariance-sector analogue of “generic closure plus soft support,” without identifying its deck line with cosmological time orientation.

Durable artifacts

• research/benincasa/checkers/soft_relative_sign_cohomology.rs
• research/benincasa/results/soft-relative-sign-cohomology.json
• research/benincasa/soft-relative-sign-cohomology.md

Next falsifier

Test whether the soft-supported component-sign sheaf has a canonical extension-by-zero/Gysin description on the existing Cut carrier. Compute the specialization from a connected generic support to a two-component soft fiber and determine whether its extra sign is a costalk class or merely loss of transport.

View source on GitHub