IndisputableMonolith.Physics.ThermochemistryFromRS
Module linking Recognition Science cost geometry to classical thermochemistry. It treats chemical equilibrium as vanishing J-cost and packages thermodynamic potentials plus a certificate that the RS cost picture recovers equilibrium and nonequilibrium structure. Cite when connecting phi-ladder energetics to Gibbs-style free energy. Mostly definitional scaffolding over the Cost import.
claimThermochemistry is recovered from the RS cost $J$: chemical equilibrium is the locus $J=0$; thermodynamic potentials are counted and named; nonequilibrium cost measures departure from that locus; a certificate packages the correspondence.
background
Recognition Science derives physics from a single cost functional $J$, fixed uniquely (T5) by the Recognition Composition Law: $J(xy)+J(x/y)=2J(x)J(y)+2J(x)+2J(y)$, with closed form $J(x)=(x+x^{-1})/2-1$. The Cost module supplies that $J$ and its elementary identities.
This physics module sits downstream of that cost layer. It interprets $J$ as a thermodynamic free-energy proxy: equilibrium configurations are those with vanishing cost, and departures from equilibrium carry positive cost. Sibling objects name the classical potentials, count them, define chemical equilibrium as $J=0$, and introduce a nonequilibrium cost measure.
The setting is RS-native units ($c=1$, $\hbar=\varphi^{-5}$, etc.) but the module itself does not yet force numerical constants; it only aligns the geometric cost picture with thermochemical language.
proof idea
Definition and certificate module rather than a deep proof chain. It imports Cost, introduces named structures (thermodynamic potentials, equilibrium predicate, nonequilibrium cost), and wraps them in a ThermochemistryCert bundle. Expect thin lemmas equating equilibrium with $J=0$ and recording potential counts; no heavy tactic scripts beyond Cost identities.
why it matters in Recognition Science
Gives the RS framework a thermochemistry face: equilibrium as zero cost, nonequilibrium as positive $J$. That reading is needed if mass-ladder or bond energetics are ever to speak Gibbs free energy and reaction coordinates. No downstream consumers are wired yet (used_by empty), so the module is an interface stub for later Physics and Chemistry layers. It does not itself invoke T6--T8 or the alpha band; it only rephrases Cost in chemical language.
scope and limits
- Does not derive numerical reaction free energies or bond enthalpies.
- Does not prove uniqueness of thermodynamic potentials from first principles.
- Does not connect to the phi-ladder mass formula or particle spectrum.
- Does not establish the second law or entropy production inequalities.
- Does not force temperature, pressure, or chemical-potential scales from RS constants.