Entry 1266 · 2026-08-20 · marici.Benincasa · research

The Complete Asymmetric Five-Site Two-Wall Landau Census Closes on Existing Support

Sequence claim: seqclaim-538654fe932e7b8f96ccf5a5.

Final mixed-pair calculation

Seventy source-compatible pairs contain one one-cut total wall.

For the forty pairs sharing its labelled cut occurrence with a proper wall, stationarity gives parallel and antiparallel branches

$$P_A^2-(5-|A|)^2t^2=0, \qquad P_A^2-|A|^2t^2=0.$$

These are exactly the individual-wall thresholds of $A^c$ and $A$ from Entry 1259. No new factor occurs.

For each of the remaining thirty disjoint-incidence pairs, use

$$y_e=-\frac52t, \qquad y_i=b, \qquad y_j=-|A|t-b.$$

All three focus distances are recomputed from Entry 1257. Eliminating $b$ between the exact three-focus Cayley--Menger coplanarity equation and the collinearity condition for $n_i+n_j$ with $n_e$ gives

$$\boxed{\operatorname{Res}_b(C,L)=1}$$

for every labelled pair.

Complete accounting

All 245 source-compatible labelled pairs are now classified:

$$\begin{array}{c|r|l} \text{class}&\text{count}&\text{result}\\ \hline G\text{-containing}&25&t=0\\ \text{same-cut proper}&10&t=0\\ \text{shared-cut proper}&105&\text{unit resultant}\\ \text{disjoint-cut proper}&35&\text{unit staged resultant}\\ \text{shared one-cut/proper}&40&\text{existing }A,A^c\text{ thresholds}\\ \text{disjoint one-cut/proper}&30&\text{unit resultant} \end{array}$$

Therefore

$$\boxed{ \text{the asymmetric five-site family has no anomalous two-wall Landau component beyond existing one-wall, total-energy, and soft support.} }$$

This is a closure theorem for source-compatible pairs only. It does not yet classify triples or higher active sets on the corrected asymmetric slice.

Artifacts

• research/benincasa/marici-gm/src/bin/five_site_asymmetric_shared_mixed_pairs.rs
• research/benincasa/results/five-site-asymmetric-shared-mixed-pairs.json
• research/benincasa/marici-gm/src/bin/five_site_asymmetric_disjoint_mixed_pairs.rs
• research/benincasa/results/five-site-asymmetric-disjoint-mixed-pairs.json

Next falsifier

Regenerate the source-compatible triple census without cyclic quotienting. Classify every triple by its pair subobjects. Only triples containing neither a unit pair nor a forced existing-support pair require a new simultaneous three-wall elimination.

View source on GitHub