IndisputableMonolith.Physics.ElectrochemistryFromRS
Module linking electrochemical equilibrium to the Recognition Science cost: equilibrium holds exactly when the J-cost vanishes. It packages process counts, an equilibrium predicate, and a certificate structure for RS-native electrochemistry. Physicists deriving Nernst-type balances from the forcing chain would cite it. Content is definitional scaffolding around J = 0 rather than a deep proof tree.
claimElectrochemical equilibrium in RS units is the condition $J = 0$, where $J(x) = \frac{x + x^{-1}}{2} - 1$ is the unique cost from the Recognition Composition Law. The module introduces process types, a process count, the equilibrium predicate, and a certificate bundling those facts.
background
Recognition Science forces a unique nonnegative cost $J$ on positive reals via the Recognition Composition Law and the T5 uniqueness step: $J(x) = (x + x^{-1})/2 - 1$, equivalently $\cosh(\log x) - 1$. The zero set of $J$ is exactly ${1}$, so $J = 0$ means the dimensionless ratio under consideration sits at the self-similar fixed point (no excess cost).
This module sits in the Physics layer and imports only Mathlib and the core Cost development. It treats electrochemical processes as RS objects whose equilibrium condition is identified with vanishing $J$, rather than with a separately postulated chemical potential balance. Sibling names indicate a process type, a count of such processes, an equilibrium proposition, and a certificate wrapper.
proof idea
Definition and certificate module, not a multi-step derivation. The central identification is the predicate that electrochemical equilibrium holds when $J = 0$. Supporting declarations introduce the process type, a numeric process count, and an ElectrochemistryCert bundle that packages the equilibrium claim for downstream use. No substantial tactic proof is required beyond wiring the Cost import into those definitions.
why it matters in Recognition Science
Gives electrochemistry a direct RS reading: equilibrium is zero cost on the phi-compatible scale fixed by T5–T6, not an extra thermodynamic postulate. That keeps Faraday-type bookkeeping inside the same J-calculus used for masses, couplings, and the eight-tick octave. No downstream consumers are recorded yet in the mirror graph, so the module is presently a leaf that future Nernst, redox, or electrode theorems can import. It does not itself advance the T0–T8 forcing chain; it applies the already-forced $J$ to a classical physics domain.
scope and limits
- Does not derive Nernst equation coefficients or temperature dependence from first principles.
- Does not prove uniqueness of J; that is assumed from the Cost import and T5.
- Does not model kinetics, overpotentials, or non-equilibrium currents.
- Does not connect to alpha, G, or mass-ladder numerics.
- Does not list downstream theorems; the mirror graph shows zero used_by edges.