Typed Pipeline for Recoverability-Rate-Power Links: A Contract Paper with a Closed Recoverability Lane and Falsification Criteria

We present an audit-friendly logical contract for a multi-layer program connecting (i) static locality/Markovness, (ii) recoverability bounds, (iii) separation-dependent dissipation rates, and (iv) thermodynamic maintenance power. Each interface is typed with explicit quantifiers, tagged as [PROVED]/[IMPORTED]/[ASSUMED]/[CONJECTURED], and paired with falsification routes. We do not claim a proof of the Clay Yang-Mills mass gap; we separate a Clay (closed-Hamiltonian) track from an operational (open-system/maintenance) track. As a fully closed lane inside this paper, we prove that an exponential conditional mutual information (CMI) decay hypothesis implies exponential recoverability via an imported Fawzi-Renner inequality, with fidelity conventions fixed explicitly. v2 (no v1 number is changed): the cross-reference labels are repaired (in v1 every assumption, lemma, theorem, remark and corollary was typeset as "Definition x.y") and Tables 1 and 2 are re-typeset; the constant-alignment step of Appendix A is executed rather than prescribed -- in the locked conventions (squared fidelity, E_rec = -log F) the Fawzi-Renner import yields c_FR = 1 exactly; the deferred interfaces of Appendix B are now concrete series papers and are cited as such (the Type III interface is ai.viXra:2601.0065, the Davies/RIP-U dynamics note is ai.viXra:2601.0064, the benchmark infrastructure lives in the series repository); the BATO-LAW upgrade path of Appendix C records the partial progress of ai.viXra:2601.0031; and a verification suite instantiates everything instantiable: the closed recoverability lane end to end on a gapped transverse-field Ising collar (I ~ 0.20 e^{-1.06 w}, E_rec <= I at every width in the generated dataset, full 1 - F <= E_rec <= c_FR K e^{-alpha epsilon} chain), the exact-Markov example at machine precision, and the dephasing example with an explicit kappa_up/kappa_down spread of two orders of magnitude illustrating the directionality golden rule.