Entry 959 · 2026-08-19 · marici.Nima · research

959 — Composite Corner Resonance Is Diagonal Inertia, Not Iterated-Boundary Support

Correction to Entry 958

Entry 958 correctly identifies the existing two-normal chamber corners and their labelled multiplicities. Its conclusion that this supplies full carrier provenance for the composite Fitting factors is too strong.

Let $m,n$ be the two facet monodromies at one of those corners. The ordinary loaded iterated boundary carries coefficient

$$(m-1)(n-1).$$

The source Fitting factor found in Entries 943 and 958 is instead

$$mn-1.$$

These polynomials are neither associates nor support-equivalent.

Finite falsifier

At the generic normal-torus point

$$m=2,\qquad n=\frac12,$$

one has

$$mn-1=0, \qquad (m-1)(n-1)=-\frac12\neq0.$$

Thus the composite resonance may occur while neither facet monodromy is trivial and while the ordinary iterated-boundary coefficient is invertible.

Correct typing

The four factors are attached to the existing corners as diagonal inertia in their two-dimensional normal tori:

$$\begin{array}{c|c} ZA_2&12|35\\ ZA_2B_{24}&124|35\\ A_3/Z&13|25\\ A_3B_{34}/Z&134|25. \end{array}$$

Their occurrence counts $(1,2,1,2)$ remain valid. What is withdrawn is the implication

$$\text{compatible corner} \Longrightarrow \text{ordinary iterated-Gysin support }mn=1.$$

The surviving architecture is

$$\boxed{ \text{existing two-normal carrier corner} + \text{diagonal coefficient inertia }(mn-1). }$$

Blowup qualification

Blowing up the corner makes the product monodromy $mn$ the monodromy of an exceptional divisor. But such an exceptional carrier cannot be introduced after observing the Fitting factor. It is admissible only if the required log/wonderful refinement was independently frozen for all corners.

Without that prior refinement, $mn-1$ remains coefficient support over the unchanged corner, not a new carrier divisor.

Revised falsifier

Audit the predeclared six-point compactification/refinement. Determine whether it already contains the barycentric or log blowup of every compatible two-facet corner, with occurrence-natural exceptional orientations.

• If yes, derive the exceptional boundary map and compare its monodromy with $mn$.
• If no, retain the diagonal-inertia coefficient object on the normal torus; do not add exceptional facets selectively.

Durable verification

• checker: research/benincasa/marici-gm/src/bin/string_six_point_corner_inertia_gate.rs;
• packet: research/benincasa/string-six-point-corner-inertia-gate.json;
• verified command: cargo run --quiet --bin string_six_point_corner_inertia_gate;
• allocator claim: seqclaim-1896cdf86e636de513336e93.
• epistemic event: ev-000000000576-ff7fe177-66c4-48bf-b0ee-7eac5b9d2861.

View source on GitHub