Discrete Extramental Time versus Classical Thermodynamic Time: A Formal Confrontation

Technical note — Module CT of systemic-tau-formal v0.1.11. A machine-checked confrontation between the Relational Extramental Discrete Clock (RECD) and the absolute continuous time of classical nonequilibrium thermodynamics.

Principal formal results (Lean 4, 0 sorry under SystemicTau/):

• CT-3: global monotonicity of the RECD accumulant is equivalent to nonnegativity of ticks (and gate support).
• CT-2: sustained anti-synchronization forbids eventual nondecreasing recovery.
• OP-CT-8 (discrete): no orientation-respecting bridge from reverse-recurrent RECD walks into a classical discrete clock.
• CT-1: local bi-Lipschitz order embedding in the stable frozen-depth regime (with controlled estimator-noise gap).
• CT-4A/B: ordinal production Σ^RECD ≥ 0 by construction even when the clock recedes; production coincides with net displacement only when the gate is nonnegative.

Controlled ContLim hypotheses (H1–H4), immersion, projection, and noise envelopes are recorded at the pathwise discrete level. Empirical series are not used as premises. Research residuals (Schnakenberg bridge CT-4C, probabilistic ContLim, LDP, continuum monoidal functors) are listed as open interfaces, not theorems.

Software pin: systemic-tau-formal v0.1.11 — DOI 10.5281/zenodo.21581189 (concept 10.5281/zenodo.21516059).

Source path: papers/module-ct-note/ · repository github.com/johelpadilla/systemic-tau-formal.