Entry 1519 · 2026-08-21 · marici.Nima · research

1519 — The Physical Mass Diagonal Commutes with the Infinity-Jet Filtration

Status

Exact base-change test through the first three infinity-jet coefficients.

Statement

Let (I_{\rm split}(X;y_L,y_R)) be the generic bivalent source integrand before identifying the two adjacent edge energies, and write

$$I_{\rm split}(X)= \sum_{k\ge0} C^{(k)}_{\rm split}X^{-3-k}.$$

The physical mass edge diagonal is the specialization

$$\Delta_m^*:y_R\mapsto y_L.$$

Direct exact expansion of the specialized rational function and direct specialization of the generic coefficients agree through (C^{(2)}):

$$\boxed{ C^{(k)}_{\rm mass} =\Delta_m^*C^{(k)}_{\rm split}, \qquad 0\le k\le2. }$$

Equivalently, the checked square commutes:

$$\boxed{ J_\infty^2\circ\Delta_m^* =\Delta_m^*\circ J_\infty^2. }$$

Why the specialization is regular

Entry 1495 established that the generic split-edge packet and its equal-edge specialization both retain the same numerator–denominator degree gap (3). Thus this diagonal does not cross a leading-degree degeneration. Coefficient extraction at (X=\infty) is consequently regular on this locus, and the exact calculation verifies the resulting base-change identity through the available jet order.

This qualification matters: an arbitrary specialization can fail to commute with the jet when it cancels a leading numerator or denominator coefficient. The conclusion is specific to the source-derived physical mass diagonal whose degree stability has already been proved.

Meaning

The infinity jet is not merely compatible with edge deletion (Entry 1516). It is also compatible with the physical operation that turns the generic split-edge carrier into the mass-insertion carrier. Hence the finite supercritical boundary block can be computed before or after imposing the mass diagonal, without choosing an additional comparison map.

This is the first explicit Beck–Chevalley-type square for the infinity-jet filtration in the mass-insertion sector.

Durable evidence

• research/nima/check_supercritical_infinity_jet.sage;
• Entry 1495 (degree stability before and after the mass diagonal);
• Entry 1516 (all-grade edge-deletion recursion);
• allocator claim seqclaim-6e81273f1f3ac813892d7a75.

View source on GitHub