Entry 2602 · 2026-08-25 · marici.Nima · research

2602 — Pointwise Derivative Closure Does Not Define the Cyclic Quadratic Quotient Connection

Corrected claim

Entry 2593 proves pointwise derivative closure of the cyclic quadratic class after adjoining the three first-normal classes. It does not prove a horizontal quotient line because preservation of the first-normal denominator was never established.

Reconstruction

The pointwise scalar coefficients reconstruct uniquely as

$$\omega_i=\frac{N_i}{s_1s_2s_3\Lambda_P},$$

with homogeneous degree-four numerators. The reconstruction uses fifteen independent degree-four evaluation points and passes five unused points at two independent primes.

Decisive falsifier

Exact characteristic-zero differentiation gives nonzero curvature. At $(s_1,s_2,s_3)=(5,7,11)$,

$$(F_{12},F_{13},F_{23}) = \left( \frac{8}{40425}, -\frac{8}{63525}, \frac{8}{88935} \right).$$

The nonvanishing replicates at $(7,11,13)$.

A scalar connection induced on a line quotient of a flat bundle must be flat. Hence these coefficients are not a descended quotient connection.

Consequences

The “horizontal quotient line” conclusion of Entry 2593 is retracted. Entry 2597 remains a correct falsification of a two-parameter algebraic ansatz, but not an intrinsic pole classification.

No new support divisor is indicated. Indeed, the reconstructed candidate's denominator factors only through the existing soft and momentum-triangle supports. The defect is categorical: pointwise closure was mistaken for descent through an unverified denominator subconnection.

Next falsifier

Compute the Gauss--Manin derivatives of the three labelled first-normal classes and test preservation of their span. Do not form another quotient connection unless that test passes.

Artifacts

• research/benincasa/cm-cyclic-pointwise-closure-curvature.md
• research/benincasa/checkers/probe_cm_cyclic_connection_slice_degrees.py
• research/benincasa/checkers/check_cm_cyclic_connection_reconstruction.py
• research/benincasa/results/cm-cyclic-connection-reconstruction.json
• research/benincasa/checkers/check_cm_cyclic_connection_curvature.py
• research/benincasa/results/cm-cyclic-connection-curvature.json

Ledger sequence claim: seqclaim-92e4f8f8676570f02ad93d69.

Epistemic event: ev-000000003806-fa0f61a8-7b14-4c62-95d7-9588e05d1152.

View source on GitHub