The Ontology of Statistical Mechanics: Statistics of Constraint Transition Events in Causal Networks

What is statistical mechanics, constitutionally? Standard statistical mechanics defines itself as the grammar of ignorance --- the systematic treatment of uncertainty about microscopic states. EET statistical mechanics defines itself differently: it is the dual-layer discipline of constraint transition events. The Formal Layer (CLOSED-in-EET) derives the structural forms of the Second Law, Third Law, Fluctuation-Dissipation Theorem, and Causal Indifference Principle from the asymmetries of CND v4.0 dynamics --- independent of any Observer's counting operations. The Numerical Layer (STANDARD) instances probability values, effective temperatures, entropy values, and ensemble constructions through the statistical compression of Observer registration records --- dependent on Observer counting operations, executable by instrument Observers without internal models. SM 3.1 explicitly acknowledges that its own numerical outputs are CCN Observer cognitive products. This dual-layer architecture resolves the constitutional tension between SM's claim to universal applicability and its operational dependence on Observer registration data streams. The Formal Layer's theorems carry system-internal conditional necessity under EET's L1 constitutional presuppositions; they do not claim absolute truth (L0-compatible). The Numerical Layer's outputs carry model-internal objectivity anchored in Natural Causality --- probability values are long-term frequencies of registered constraint transition events, not ``objective tendencies'' independent of all observers. {Version 3.1} is a comprehensive constitutional upgrade from v3.0 (v6.0 alignment). The core innovations are: (i) explicit distinction between the Formal Layer (CLOSED, Observer-independent) and the Numerical Layer (STANDARD, Observer-dependent); (ii) full v6.1 constitutional alignment (L0--L5+ layer renumbering, Barrier Asymmetry conditionalized, ``Constraint + Being'' correction, CD v3.1 → CND v4.0 upgrade); (iii) integration of Observer v2.4 (new core definition: detection → registration) and Measurement v2.1 (six-stage energy ledger, dark data boundary, five-channel noise decomposition); (iv) the No-Equilibrium Theorem established as CLOSED-in-EET --- a constraint network with N ≥ 1 can never reach classical statistical equilibrium, guaranteed by four independent mechanisms; (v) the Five-Channel Complete Constraint Second Law (CND v4.0 III-C.2, CLOSED-in-EET) adopted as the constitutional architecture for all non-equilibrium statistical mechanics in EET; (vi) the η-generalized Fluctuation-Dissipation Theorem registered as WORKING HYPOTHESIS; (vii) the data completeness boundary established --- SM statistics apply only to registered events, with Transient-only events (dark data) lying outside SM's statistical scope; (viii) sixteen academic priority registrations across the major foundational controversies in statistical mechanics; and (ix) all v3.0 constitutional content preserved with corrections and version updates applied. {Constitutional Governance:} Five-Channel Complete Constraint Second Law (CLOSED-in-EET). No-Equilibrium Theorem (CLOSED-in-EET). Five-path Third Law derivation (CLOSED-in-EET). $C(t)$ constitutional identity (≡ Iplastic, CLOSED-in-EET). η = 1 ≠ equilibrium clarification (CLOSED-in-EET, triple citation: CND v4.0 + Entropy v3.3 + Inverse Entropy v3.3). All contents carry system-internal conditional necessity under EET's L1 constitutional presuppositions and the L0 Sole Meta-Axiom (Absolute Truth is Unreachable). {Keywords}: Statistical mechanics; Constraint transition events; Dual-layer architecture (Formal Layer / Numerical Layer); Five-Channel Complete Constraint Second Law; No-Equilibrium Theorem; η-generalized Fluctuation-Dissipation Theorem; $C(t)$ statistical mechanics; Data completeness boundary; Dark data; Observer v2.4 integration; Measurement v2.1 integration; Non-equilibrium statistical mechanics; Energy-Efficiency Theory