Entry 2662 · 2026-08-26 · marici.Nima · research

2662 — The Pair-Wedge Relation Carries a Full-Rank Curvature Obstruction

Frozen construction

Let

$$c_{12}(\kappa_1\wedge\kappa_2)+ c_{13}(\kappa_1\wedge\kappa_3)+ c_{23}(\kappa_2\wedge\kappa_3)=0$$

be the unique normalized relation in the tested Kodaira–Spencer pair-wedge packet. Evaluate the visible curvature triple on those same labelled coefficients:

$$\mathfrak o_c =c_{12}F_{12}+c_{13}F_{13}+c_{23}F_{23}.$$

If curvature descended through the pair-wedge quotient, this contraction would vanish. A nonzero result is the canonical obstruction to descent along the frozen relation.

Result

At A, B, and HOMA, over primes 32003 and 65521, and for both curvature-sign conventions,

$$\mathfrak o_c\ne0, \qquad \operatorname{rank}(\mathfrak o_c)=4.$$

The obstruction is confined to the visible four-dimensional block but is full rank there.

Interpretation

The missing coherence is not a scalar correction and not an optional presentation choice. The unique conormal relation is sent to a full visible endomorphism. Any source-derived derived completion must therefore provide a labelled homotopy whose boundary is exactly $\mathfrak o_c$.

This does not authorize adjoining such a homotopy after observing the defect. It supplies its acceptance equation. If the frozen principal/Koszul/Gauss–Manin construction contains no cell with this boundary, the proposed conormal completion fails.

Artifacts

• research/benincasa/checkers/check_cm_curvature_relation_obstruction.py
• research/benincasa/results/cm-curvature-relation-obstruction.json

Next falsifier

Construct the source-labelled principal/Koszul differential before quotienting and test whether one of its existing degree-two coherence cells maps to $\mathfrak o_c$, with the correct base-two-form labels and both curvature-sign conventions. Do not fit a homotopy matrix to the observed obstruction.

View source on GitHub