Second-Law Grounding from Closure Record Refinement, Hidden History, and the Structural Preconditions of Thermodynamic Irreversibility Paper 78 of the NEMS Suite

This paper develops the second-law grounding arc of the NEMS program. Its purpose is precise: to identify the record-theoretic asymmetries already forced by closure-compatible refinement, prove the relevant monotonicity theorems in Lean, and clarify how these results supply the structural preconditions of a second-law-style arrow. The paper does not claim a full reduction of thermodynamics to record theory, nor a full derivation of the thermodynamic second law from closure alone. The thermodynamic interpretation is conceptually supported but not fully reduced. Two distinct monotonicity directions are established. Track 1 proves record-resolution monotonicity: the number of observational equivalence classes visible at a stage cannot decrease under refinement. Track 2 proves hidden-history fiber monotonicity: the size of a fiber over a later visible class cannot exceed the size of the corresponding earlier fiber under the forgetful map, and strict refinement yields strict decrease for at least one fiber. Together with the previously proved theorem of structural irreversibility from closure, these results show that closure grounds irreversibility directly and entropy only indirectly, through the structure of record refinement. The formal contribution is exact and limited. Structural irreversibility is already established in the ArrowOfTime stack. Record-resolution monotonicity and hidden-history fiber monotonicity are now connected to the unified closure architecture. The thermodynamic interpretation remains one level above the formal core: what is proved here is the structural ground beneath a second-law-like arrow. This overview presents the core NEMS theorem engine and selected applications; stronger domain-specific derivation and ontological synthesis claims belong to separate release surfaces with their own premise bundles and formal artifacts. Trust boundary. Machine-checked content lives in nems-lean (ArrowOfTime, RecordEntropy) . Thermodynamic entropy gloss is interpretive and not claimed identical to the record monotones; see .