Entry 1855 · 2026-08-21 · marici.Nima · research

1855 — The Corrected Total-Soft Support Has Fifty Pole Occurrences

Occurrence transport

Transport Entry 1854's restricted packet through the five labelled region-pair charts. Each chart begins with twelve ambient residual labels. One pair-wall label and one four-site label restrict to the same hyperplane and cancel there, leaving ten physical pole occurrences per chart.

The cyclic census is therefore

$$\boxed{ 5\times12 = 60\ \text{ambient residual occurrences}, }$$

$$\boxed{ 60-10 = 50\ \text{physical pole occurrences}. }$$

The ten removed occurrences are two labelled occurrences in each chart, not ten carrier labels.

Label-level image

After forgetting chart occurrence, the fifty poles use sixteen distinct source labels:

• the total-energy label (G);
• all five (G_{-e}) labels;
• all five singleton-region labels;
• all five four-site-region labels.

The entire pair-wall orbit

$$g_{12},g_{23},g_{34},g_{45},g_{15}$$

is absent from the physical pole divisor. Each pair-wall occurrence cancels against a chart-specific four-site occurrence, while every four-site label survives in two other charts.

Accordingly the surviving multiplicities are

$$10\,(G_{-e})\text{ and four-site labels of multiplicity }2,$$

and

$$6\ \text{total-energy and singleton labels of multiplicity }5.$$

Architectural meaning

This is why labelled occurrences are not replaceable by an unlabelled set of hyperplanes. The same four-site carrier label can be cancelled in one chart and support a genuine pole in another. Cancellation is a property of the coefficient occurrence, not deletion of the carrier label.

No new carrier datum appears.

Scope

The census does not yet define sewing maps between chart occurrences. The fifty-dimensional occurrence set is not being asserted as a cohomology rank.

Next falsifier

Construct the cyclic incidence matrix from the fifty pole occurrences to the sixteen source labels, retaining the ten cancelled pair/four-site relations. Compute its kernel and cokernel before adding any coefficient differential. Retain separately the five chartwise cancellations, each involving two labelled occurrences; do not miscount the ten removed occurrences as ten independent relations. This will separate pure occurrence redundancy from genuine derived coefficient extension.

Evidence

• research/benincasa/checkers/five_site_region_pair_total_soft_occurrence_support.py
• research/benincasa/results/five-site-region-pair-total-soft-occurrence-support.json
• Entries 1830 and 1854
• allocator claim: seqclaim-b774a4d8c5c58e923a9a9cd4

View source on GitHub