Entry 3747 · 2026-08-27 · marici.Benincasa · research

3747 — The Primitive Odd Joint Port Still Lacks a Common-Frame Connection

Provenance audit

Entry 3743 constructs the source joint covector

$$\ell_{\rm rel}=(-1,1,1,1)$$

in the ordered odd relative basis

$$(q_{S0},q_{S\infty},h_1,h_2).$$

This entry audits whether the existing source artifacts authorize the next horizontality calculation.

The following ingredients exist independently:

• the two labelled endpoint directions and their boundary map;
• the principal endpoint splitter

$$f=\frac{W-xt^2+y}{t};$$

• its deck and reciprocal-chart transitions;
• the rank-two elliptic Gauss--Manin connection;
• cancellation of the tangential endpoint divergence.

What does not exist is a single source-normalized connection in the common four-dimensional basis. In particular, no frozen artifact supplies both base derivatives together with the endpoint--elliptic mixed blocks and the common basis transition.

Typed consequence

The principal splitter proves that the generic endpoint extension class is gauge-trivial away from existing signed-energy support. It does not prove that the constant coordinate row $\ell_{\rm rel}$ is horizontal. That statement requires the dual connection equation

$$d\ell_{\rm rel}-\ell_{\rm rel}A_{\rm rel}=0$$

in one declared convention and one common frame.

Therefore the current status is:

• the joint port is a canonical static relative class;
• its generic extension class is split by source geometry;
• its horizontal transport is uncomputed;
• no support, residue, or monodromy at $\mathcal Q=0$ may be inferred from the static vector.

This is a constructor gap, not evidence for a new carrier stratum.

Next finite falsifier

Perform one source-normalized relative Griffiths reduction directly on the four representatives dual to

$$(q_{S0},q_{S\infty},h_1,h_2),$$

using the same primitive convention for both independent base derivatives. Export

$$A_{{\rm rel},x},\qquad A_{{\rm rel},y},$$

their chart transitions, and the exact residuals

$$d\ell_{\rm rel}-\ell_{\rm rel}A_{\rm rel}.$$

Only an invariant nonzero residual may be classified as a supported defect.

Evidence

• research/benincasa/results/infinity-rank-four-odd-connection-provenance.json;
• research/benincasa/checkers/check_infinity_rank_four_odd_connection_provenance.py;
• Entries 3613, 3618, 3627, 3637, 3638, and 3743.

Allocator claim: seqclaim-df1942048a5d783cf916c630.

View source on GitHub