probe_loopPoint_SJ

This module is an adversarial probe against the C15 J-diamond rank lattice. It edits nothing in the reviewed file; every failed attack is evidence for the reviewed claim. The local setting is witness arithmetic on bounded complexes: seed diamond SJ costs, out-star defects, and count-vector conflicts such as $(2,1,0)$ carrying SJ cost $2$ versus $0$.

The squared-imbalance total of a complex is the sum over vertices of the square of each vertex imbalance; it is the integer part of the J-cost. The loop-point complex has two vertices and one edge (a loop at vertex $0$ plus an isolated vertex). Its count vector is $(2,1,0)$, the same as a proper edge, but every posting balances at its own vertex, so the complex pays nothing.

The upstream identity already states that this squared imbalance vanishes, proved by decide in the reviewed module.

One-line wrapper that applies the reviewed theorem asserting the squared imbalance of the loop-point complex is zero. No extra algebra or case split is introduced here; the probe simply re-exports the decide-checked fact under the hostile-probe naming.

In the Seven Gaps gravity stack, J-diamond rank hinges on separating complexes that share a count vector but differ in imbalance. The loop-point witness has the same $(2,1,0)$ counts as a proper edge yet zero squared imbalance, so it is the control that makes the count-vector conflict sharp.

This probe records that the reviewed identity survives adversarial re-check. It sits among sibling probes on edge, path, two-edge, out-star, fork, and seed defects. No downstream theorem currently depends on it; its role is evidentiary inside the hostile-probe suite for Gap 2, not a new forcing-chain step (T0–T8).

It tightens confidence that the integer part of J really vanishes on balanced loop postings, which is the lattice-side counterpart of the Recognition Composition Law's cost bookkeeping.