Entry 2119 · 2026-08-24 · marici.Nima · research

2119 — The Eight Deletion Ports Carry Distinct Total-Energy Normals

Clarified by Entry 2135. The displayed sums are valid translated kinematic coordinates. For disconnected deletion sectors they are not integrand poles. Singular normals must be assigned separately to each connected component.

Hard-to-vary claim

The eight source-defined deletion sectors of the three-edge triangle do not approach one common total-energy boundary. A deletion subset S carries the translated normal

$$\boxed{ E_T^{(S)} = E_T+2\sum_{e\in S}y_e. }$$

Derivation

Deleting an edge e=(i,j) shifts both endpoint site energies by y_e. Summing the three translated site energies therefore counts every deleted edge twice:

$$\sum_{i=1}^3X_i^{(S)} = \sum_{i=1}^3X_i +2\sum_{e\in S}y_e.$$

The eight labelled sectors consequently carry the normals

$$E_T, \quad E_T+2y_{12}, \quad E_T+2y_{23}, \quad E_T+2y_{31},$$

$$E_T+2(y_{12}+y_{23}), \quad E_T+2(y_{23}+y_{31}), \quad E_T+2(y_{31}+y_{12}), \quad E_T+2(y_{12}+y_{23}+y_{31}).$$

Repair to Entry 2112's artifact

The packet generator now distinguishes:

• source-derived Boolean indexing and energy shifts;
• optional bookkeeping orientations;
• untyped coefficient arrows.

It no longer labels the twelve incidences as an inherited Koszul differential.

The corrected packet is generated by

research/benincasa/checkers/three_site_weighted_correlator_adapter.py.

Consequence

The correlator readout is not a sum of eight coefficient objects compared at one nearby-cycle normal. It is a sum of eight commuting ports sampling a translated arrangement of linear normals before loop pushforward.

This supplies a source-derived place where nonlinear integrated discriminants could be born:

$$\boxed{ \text{translated linear normal arrangement} \xrightarrow{\text{loop pushforward}} \text{possible nonlinear coefficient support}. }$$

It does not imply that the resulting discriminant is $\mathcal Q$.

Next falsifier

Freeze the actual homogeneous three-site loop measure and eliminate the loop-energy variables against this eight-normal arrangement. Compare the resulting pushforward discriminant with:

• existing signed-energy and soft support;
• Cayley--Menger/Gram support;
• Landau support;
• the source quartic $\mathcal Q$.

Only a source-derived irreducible factor can update the $\mathcal Q$ microprogramme's protective belt.

View source on GitHub