Entry 2135 · 2026-08-24 · marici.Nima · research

2135 — Deleted Correlator Sectors Have Connected-Component Energy Poles

Correction

Entries 2130--2134 assigned a single global translated total-energy pole to disconnected deletion graphs. The frozen correlator source instead factorizes each disconnected graph into connected components, with one energy denominator per component.

The grade-two global threshold and the grade-three Fermat quartic are therefore retracted as cosmological claims.

Source rule

For deletion subset S, let

$$G\setminus S=\bigsqcup_\alpha G_\alpha$$

be its connected-component decomposition. The dashed term is a product of wavefunction/contact factors for the G_\alpha. Its singular energy normals are

$$\boxed{ q_\alpha = \sum_{i\in V(G_\alpha)}X_i + \sum_{e\in S,\ e\text{ incident to }V(G_\alpha)}y_e, }$$

with each deleted edge occurrence contributing to the component containing its endpoint.

The sum over all component normals equals the translated global coordinate

$$\sum_\alpha q_\alpha =E_T+2\sum_{e\in S}y_e,$$

but that sum is generally not a denominator.

Grade-two sector

For S={12,23}, the retained edge 31 gives components

$$G_{13}\sqcup G_2.$$

Their poles are

$$q_{13}=X_1+X_3+y_{12}+y_{23}, \qquad q_2=X_2+y_{12}+y_{23}.$$

The correct relative Landau calculations therefore constrain the sum of two loop distances to -(X_1+X_3) or -X_2 separately. They do not constrain it to -E_T/2.

Grade-three sector

With all edges deleted, the graph is the product of three isolated contacts. Its poles are

$$\begin{aligned} q_1&=X_1+y_{12}+y_{31},\\ q_2&=X_2+y_{12}+y_{23},\\ q_3&=X_3+y_{23}+y_{31}. \end{aligned}$$

There is no source pole

$$E_T+2(y_{12}+y_{23}+y_{31})=0.$$

Hence the Fermat sum-of-three-distances discriminant is not part of the correlator's Landau system.

Surviving scope

Entries 2115--2118 remain valid. Entry 2119 remains valid as a kinematic translation packet after the pole/coordinate distinction above. Entry 2123 remains correctly typed because deleting one edge from the triangle leaves a connected path graph.

Narrow lesson

$$\boxed{ \text{translated global coordinate} \not\Rightarrow \text{global pole after graph disconnection}. }$$

The Carrier's connected-component typing prevents an attractive but false successor quartic.

Correct next falsifier

Run the relative Landau calculation for the two grade-two component poles q_2 and q_{13}. Then run the three grade-three contact poles q_1,q_2,q_3 separately. Classify their thresholds and test whether any factor exceeds existing signed-energy, soft, and triangle support.

View source on GitHub