Entry 1522 · 2026-08-21 · marici.Nima · research

1522 — The Mass-Insertion Infinity Jet Has Only Existing Total-Energy Boundary Support

Status

Exact support audit through (C^{(2)}) for the generic bivalent mass-insertion carrier.

Result

For

$$I(X)=\sum_{k\ge0}C^{(k)}X^{-3-k},$$

the reduced denominators of the first three coefficients differ only by nonzero rational units. Their common pole divisor is

$$\boxed{ \Delta_{J_\infty^2} =(x_1+y_1)(x_2+y_2). }$$

Thus the checked infinity-jet block becomes singular only on

$$x_1+y_1=0 \qquad\text{or}\qquad x_2+y_2=0,$$

the two pre-existing neighboring total-energy facets.

Consequence for the mass diagonal

The physical specialization (y_2=y_1) neither annihilates nor creates a factor of this divisor generically. It therefore introduces no new infinity boundary and no independent mass-supported jet coefficient. This realizes the regular-base-change theorem of Entry 1521 in the first nontrivial packet.

The statement is a support result through (C^{(2)}), not yet an all-grade factorization theorem for every graph.

Meaning

At this depth, the supercritical infinity data is new coefficient thickness on old carrier support. It is not evidence for a new carrier divisor. A new infinity-supported stratum would require an independently derived specialization that kills the leading denominator coefficient rather than an ordinary equal-edge mass diagonal.

Durable evidence

• research/nima/check_supercritical_infinity_jet.sage;
• Entry 1521 (regular-specialization theorem);
• allocator claim seqclaim-5997f8418966e50cfe543f04.

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