research: freeze continuum collision flux H-response budget

[mountain]

Summary

• freeze Phase 1J-B independently from Phase 1J-A as a whole-event-space signed collision-current response contract
• audit Deng--Hani--Ma Theorem 1, Propositions 3.25/6.2, and the molecule deletion/cutting results at their actual bulk-L^1 and iterated-integral boundaries
• derive a conditional clipped/tail H-response budget with trace, marking, truncation, contact-geometry, and kinetic-comparison errors kept separate
• identify a bounded marked-molecule flux lift, with the collision marked before cutting, as the next theorem-sized target
• add nine exact rational measure certificates and update the Sonnet/status ledgers

Exact findings

For the frozen response fixture, ||nu||_TV = 7/16. At clip level K=2, the bounded term is 7/8, the tail overshoot is 9/16, and the full response budget is 23/16. Five separately typed adapter errors add an absolute budget 1/8.

Target dissipation 2 certifies the negative adapted increment -43/80; target dissipation 1 leaves the same response and errors but yields 37/80 > 0.

The unbounded-covector red team has response masses 1/n and covector values n: total variation tends to zero while every pairing remains exactly one.

Primary-source boundary

• Deng--Hani--Ma, arXiv:2408.07818
• Annals acceptance page

The paper supplies bulk correlation/cumulant estimates. Proposition 8.14 is an exact Fubini/iterated-integral identity, and the paper explicitly states that the molecular/physical correspondence breaks after cutting. This PR does not promote cutting to physical history composition or infer a collision trace from bulk L^1.

Verification

• .venv/bin/pytest -q tests/research/test_continuum_collision_flux_response_budget.py tests/research/test_hard_sphere_continuum_adapter_seam.py tests/research/test_weak_collision_history_cell.py tests/research/test_selective_continuation_time_reversal.py tests/research/test_hidden_lyapunov_mode_discovery.py tests/research/test_charted_fibre_lyapunov_calculus.py — 45 passed
• .venv/bin/pytest -q after rebasing onto merged research: add ordered finite collision response cocycle #129 — 701 passed, 25 skipped, 1 pre-existing deprecation warning
• git diff --check — passed

The shared Sonnet README, phase plan, and repository status ledger were reconciled after #129: both independent result sets are retained, while C3 and the marked-molecule flux theorem remain separate.

Boundary and next gate

This is a record-only continuum contract plus exact finite obstruction. It proves no trace/history-to-flux theorem, marked-molecule estimate, logarithmic-tail control, entropy chain rule for a hard-sphere marginal, continuum or microscopic H theorem, molecule objectification, response cocycle, arithmetic-rank promotion, or API.

The next continuum gate is to mark a root-visible collision atom before cutting, push the prescribed-dynamics integral to the weak event space, and prove a bounded-test estimate with mark count, molecule size, recollision rank, truncation, geometry, and kinetic-comparison costs explicit.

Phase 1J-A remains independent in #129; neither PR borrows the other's conclusion.

Advances #127 (Phase 1J-B only; does not close the issue).