Phase 1J-B2 (#132) isolates a local theorem: for a fixed pre-cut molecule, a root-visible C-atom mark is a pushforward whose total variation is bounded by the absolute molecule integral, and the inserted observable survives exact Fubini cutting. The mark costs at most a linear eligible-atom factor.
The next theorem-sized gate is global, not local.
Target
Prove a marked analogue of the Deng–Hani–Ma operation-sequence summation that:
- defines the root-visible collision-event map in every signed cumulant/molecule term before cutting;
- carries the mark through every cut, deletion, split, recollision, truncation, geometry, and error subcase;
- retains a uniform summable gain after the eligible-atom factor;
- declares the controlled test class explicitly:
- full bounded L-infinity ball / total variation, or
- an H-adapted clipped family, or
- the Phase 1F smooth/cylinder weak-flux class;
- stops short of physical flux identification unless the actual/truncated/target current residuals are separately proved.
Primary-source audit points
Audit the marked roles corresponding to Proposition 3.25, Proposition 7.5, Proposition 8.18, and the Section 9 final summation of arXiv:2408.07818, subcase by subcase. Proposition 8.14 is only Fubini reorganization, not physical composition after cutting.
Kill conditions
Record failure if any required category:
- has only reciprocal eligible-atom gain;
- loses every positive epsilon power after marking;
- cannot retain the pre-cut event map;
- or only controls a smaller test class than the stated conclusion.
Claim ceiling
No hard-sphere flux identification, logarithmic-tail removal, entropy chain rule, H theorem, rank promotion, or generic API in this gate.
Phase 1J-B2 (#132) isolates a local theorem: for a fixed pre-cut molecule, a root-visible C-atom mark is a pushforward whose total variation is bounded by the absolute molecule integral, and the inserted observable survives exact Fubini cutting. The mark costs at most a linear eligible-atom factor.
The next theorem-sized gate is global, not local.
Target
Prove a marked analogue of the Deng–Hani–Ma operation-sequence summation that:
Primary-source audit points
Audit the marked roles corresponding to Proposition 3.25, Proposition 7.5, Proposition 8.18, and the Section 9 final summation of arXiv:2408.07818, subcase by subcase. Proposition 8.14 is only Fubini reorganization, not physical composition after cutting.
Kill conditions
Record failure if any required category:
Claim ceiling
No hard-sphere flux identification, logarithmic-tail removal, entropy chain rule, H theorem, rank promotion, or generic API in this gate.