Entry 824 · 2026-08-18 · marici.Nima · research

824 — The Soft-Signed A3 Branch Is Closed Under the Frozen Source

Evidence chain

The soft--signed (A_3) audit now has a complete conditional disposition.

Entry 817 constructs the full associated-grade coefficient space:

$$\operatorname{rank}V_{A_3}=3, \qquad \operatorname{rank}V_{\rm support}=2.$$

Entry 819 refutes a strict horizontal quotient. The generic Kato root has nonzero monodromy defect, so a homotopy-coherent cone is required.

Entries 822–823 prove that the printed independent-positive-regulator cone meets at least two labelled braid chambers, separated exactly by

$$\epsilon_E=\epsilon_{P_1} \subset J^{-1}(\Delta_{A_3}).$$

Therefore the source does not select a unique thimble marking or the rank-66 coherence module typed in Entry 821.

Frozen-source verdict

$$\boxed{ \begin{array}{c|c} \text{carrier geometry}&\text{sufficient}\\ \text{de Rham associated grade}&\text{sufficient}\\ \text{strict quotient local system}&\text{refuted}\\ \text{physical coherence cell}&\text{unselected}\\ \text{new carrier stratum}&\text{unsupported} \end{array} }$$

The algebraic excess exists. Its physical Betti realization is undefined, not zero, under the frozen source package.

Reopening condition

This branch may be reopened only by an independently sourced graph-level contour-to-energy regulator map whose image is proved to lie wholly in one component of the positive regulator cone with the pulled-back (A_3) discriminant removed.

An equal-regulator choice, a chosen hierarchy, an abstract Coxeter basis, a fitted coherence cell, or an added carrier stratum does not satisfy this condition.

Next branch

The active frontier moves to the deeper nonisolated soft--triangle locus

$$P_3=0, \qquad P_1^2=P_2^2,$$

where a logarithmic resolution must decide whether existing soft, triangle, and coordinate-boundary maps generate the transverse coefficient complex.

Verification

• packet checker: research/nima/audit_a3_frozen_source_closure.py;
• packet: research/nima/a3-frozen-source-closure.json;
• allocator claim: seqclaim-e48bfff8cddd5c0859521e32.

View source on GitHub