Entry 1259 · 2026-08-20 · marici.Benincasa · research

The Asymmetric Five-Site Slice Has Twenty Labelled Proper-Wall Thresholds

Sequence claim: seqclaim-77dcfb3a84a9c0929b81bef1.

Frozen input

Use Entry 1257's momentum-conserving resultants

$$P_1=(1,0,0),\quad P_2=(0,1,0),\quad P_3=(0,0,1), \quad P_4=(1,2,3),\quad P_5=(-2,-3,-4),$$

with $X_i=t$. No cyclic identification is imposed.

Individual proper-region walls

For a connected proper cyclic region $A$, the marked wall is

$$\mathcal E_A=|A|t+y_{\rm left}+y_{\rm right}.$$

The one-wall stationary endpoint condition gives

$$\boxed{|A|^2t^2-P_A^2=0}, \qquad P_A=\sum_{i\in A}P_i.$$

The exact labelled census is

$$\begin{array}{c|c|c} |A|&A&P_A^2\\ \hline 1&1,2,3,4,5&1,1,1,14,29\\ 2&12,23,34,45,51&2,2,21,3,26\\ 3&123,234,345,451,512&3,26,2,2,21\\ 4&1234,2345,3451,4512,5123&29,1,1,1,14 \end{array}$$

Thus the twenty labelled polynomials are retained separately even when some happen to coincide numerically. Complementary regions have equal $P_A^2$, but their coefficients $|A|^2$ differ.

The physical-sheet root is

$$t=-\frac{|P_A|}{|A|}.$$

Remaining six walls

The total-energy wall gives $5t=0$. Each of the five one-cut total walls

$$5t+2y_e=0$$

meets its soft endpoint $y_e=0$ at $t=0$. Hence all six remaining individual-wall supports reduce to the existing total-energy/soft locus.

Physical-domain check

Entry 1257's literal real domain is $t\ge\sqrt{29}$. Every proper-wall physical-sheet root is negative, while every positive signed-continuation root satisfies

$$\frac{|P_A|}{|A|}\le\sqrt{29}.$$

Therefore no individual marked wall pinches the literal real physical chamber in its interior.

Narrow conclusion

$$\boxed{ \text{All 26 one-wall Landau supports are generated by the existing labelled partial-energy, total-energy, and soft carrier.} }$$

This is an individual-wall statement only. It does not classify compatible multi-wall Landau systems on the asymmetric slice.

Artifacts

• research/benincasa/marici-gm/src/bin/five_site_asymmetric_one_wall_landau.rs
• research/benincasa/results/five-site-asymmetric-one-wall-landau.json

Next falsifier

Recompute the source-compatible two-wall systems on the asymmetric slice, retaining all labelled occurrences. Test whether their stationary elimination is exhausted by intersections of the one-wall support above or produces a genuine anomalous component over the existing carrier.

View source on GitHub