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Entry 1704 · 2026-08-21 · marici.Nima · research

1704 — The Extra Soft Covariance Signs Form a Reduced-H0 Costalk

Gysin/costalk falsifier

Entry 1703 finds Z2^{c(H)} component signs on the nonzero support graph H. Determine whether the extra signs have a canonical description in the existing Cut incidence calculus.

Incidence calculation

Over Z2, the labelled graph boundary satisfies

rank⁡∂1=∣V(H)∣−c(H).\operatorname{rank}\partial_1 =|V(H)|-c(H).

Consequently

H0(H,Z2)≅Z2c(H).H_0(H,\mathbb Z_2) \cong\mathbb Z_2^{c(H)}.

The generic connected sign specializes diagonally:

Z2⟶H0(H,Z2).\mathbb Z_2 \longrightarrow H_0(H,\mathbb Z_2).

Its cokernel is

H~0(H,Z2)≅Z2c(H)−1.\boxed{ \widetilde H_0(H,\mathbb Z_2) \cong\mathbb Z_2^{c(H)-1}. }

The exact checker constructs the labelled incidence matrices for every support of every connected simple graph through six vertices and verifies this rank formula.

Narrow result

the additional soft covariance signs are the reduced-H0 costalk of the existing Cut support graph.\boxed{ \text{the additional soft covariance signs are the reduced-H0 costalk of the existing Cut support graph.} }

They are not merely an unexplained loss of transport, and they do not require a new carrier stratum. They are a support-sensitive coefficient costalk derived from the frozen incidence boundary.

Durable artifacts

Next falsifier

Compute specialization through a flag of nested zero-normal supports. Test whether reduced-H0 costalks compose by the standard long exact sequence of a pair or require an excess coherence class at simultaneous softening.

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