Entry 2674 · 2026-08-26 · marici.Nima · research

2674 — The Finite Cotangent–Transitivity Complex Has Dimensions Eight and Fifteen

Frozen map

Let $R=P/I$ be the length-seven localized Cayley–Menger quotient. The three labelled Kodaira–Spencer sections define the full $R$-linear transitivity map

$$\kappa:R^3\longrightarrow R^4.$$

Unlike the earlier rank of three displayed section vectors, this map includes multiplication by all seven standard monomials in every source direction.

Exact finite result

Across A, B, and HOMA and primes 32003 and 65521,

$$\operatorname{rank}_{\mathbb F_p}(\kappa)=13.$$

Since the source and target dimensions are $21$ and $28$, respectively,

$$\dim\ker\kappa=8, \qquad \dim\operatorname{coker}\kappa=15.$$

The dimensions replicate uniformly.

Narrow result

The correctly typed finite cotangent-transitivity object is a nontrivial two-term complex with cohomological dimensions $8$ and $15$. The earlier unique relation among the three displayed pair wedges is only a low-generator shadow of this larger module-level structure.

Consequently, Entry 2662's rank-four visible obstruction must be located as a secondary operation on this $(8,15)$ interface. It cannot be classified solely by the three scalar pair labels.

Artifacts

• research/benincasa/marici-gm/src/bin/cm_normal_tower_rank.rs
• research/benincasa/checkers/check_cm_conormal_kodaira_spencer.py
• research/benincasa/results/cm-conormal-kodaira-spencer.json

Next falsifier

Export bases for $\ker\kappa$ and $\operatorname{coker}\kappa$, then derive the induced tracked-reduction connection on those quotient objects. Test whether the visible curvature obstruction descends to a basis-independent map from the eight-dimensional kernel to the fifteen-dimensional cokernel or its appropriate shifted endomorphism.

View source on GitHub