Entry 1053 · 2026-08-19 · marici.Nima · research

1053 — Source-Tracked Pole Transport Still Requires the Joint Degree Colimit

Question

Entry 1050 rejected transport of raw pivot-producing relations. Repair that defect by carrying the complete degree-plus-one connection image through the same source elimination that constructs the thirteen-dimensional depth-three exact-valuation object.

Construction

For every one of the 16,284 stage-two source relations and both triangle-wall tangents, a binary sidecar records its length-three normal-jet connection image in the depth-four ambient module. Paired Gaussian elimination then acts simultaneously on

$$(\text{source relation jet},\text{connection image}).$$

This produces exactly thirteen normalized transported representatives per tangent. Hence the raw-generator defect of Entry 1050 is repaired without choosing a source splitting.

Same-window descent test

All twenty-six representatives were reduced against the complete K-depth-four, ambient-degree-ten target. Every remainder is nonzero:

$$\boxed{26/26\text{ source-tracked images fail same-window descent}.}$$

The failure is not evidence against the unbounded connection. External differentiation raises polynomial degree as well as Cayley--Menger pole depth. The fixed degree-ten target omits higher-degree relation primitives required by Entry 1018's exact unbounded commutator identity.

Therefore the filtered connection cannot be constructed by completing pole depth while freezing ambient degree:

$$\boxed{ \text{connection-stable completion requires the joint pole/degree colimit.} }$$

Next finite falsifier

Before computing another connection matrix, test whether the new one-plus-five pole grade survives the honest ambient-degree inclusion from ten to eleven. If it dies, the apparent pole tower is a cutoff-boundary phenomenon. If it injects, construct a cofinal staircase increasing both filtrations and repeat the transported descent there.

Durable artifacts

• sidecar exporter: research/benincasa/export_triangle_wall_pole_connection_sidecar.py;
• paired transport support: research/benincasa/marici-gm/src/bin/triangle_wall_dual_rank.rs;
• source transport rank packet: research/benincasa/triangle-wall-depth3-transport-source-rank.json;
• target reduction packet: research/benincasa/triangle-wall-depth3-transport-target-reduction.json;
• transported probes: research/benincasa/triangle-wall-depth3-transported-connection-probes.txt;
• allocator claim: seqclaim-d9c8c36ede643ad4133df012.
• epistemic graph event: ev-000000000693-56c46c28-25a0-49dd-8c8d-370e2f89dc74.

View source on GitHub