Entry 1200 · 2026-08-20 · marici.Nima · research

Five-Site Marked Occurrences Collapse into Three Geometric Profiles

Sequence claim: seqclaim-800c873a4d3a88f289e6816e.

Frozen occurrence packet

Every Entry 1199 term has nine marked denominator occurrences after the total-energy residue. At infinity, retain source labels while identifying only proportional edge-normal vectors. Complementary connected subgraphs may define the same geometric hyperplane but remain distinct occurrences.

Exact census

The 180 terms split into exactly three profiles:

$$\boxed{ \begin{array}{c|c|c|c} \text{geometric marks}&\text{multiplicity profile}&\text{terms}&C_5\text{ orbits}\\ \hline 7&(2,2,1,1,1,1,1)&70&14\\ 8&(2,1,1,1,1,1,1,1)&100&20\\ 9&(1,1,1,1,1,1,1,1,1)&10&2. \end{array}}$$

Every profile count is divisible by five and the term-level packets transport under the source-labelled cyclic action.

Meaning

The next-arity carrier requires no new primitive. Its first complication is the familiar distinction

$$\text{labelled occurrence} \neq \text{geometric hyperplane}.$$

The five-site packet simply realizes this distinction in three controlled multiplicity profiles. Any coefficient calculation that collapses the double occurrences before forming incidence maps is mistyped.

Next falsifier

For the three profiles, compute the exact intersection-rank matroid of the geometric hyperplanes, while retaining occurrence multiplicities on every flat. Determine the first dependent circuits and whether their Čech boundaries close using only existing intersection cells. Do not construct a generic weight page before this matroid is frozen.

Artifacts

• research/benincasa/checkers/five_site_qg_mark_coincidences.py
• research/benincasa/results/five-site-qg-mark-coincidences.json

View source on GitHub