IndisputableMonolith.Physics.ClimatePhysicsFromRS
Module that casts climate energy balance as vanishing of the Recognition cost functional: equilibrium means J = 0. It introduces climate-feedback bookkeeping and a ClimatePhysicsCert wrapper. Climate or RS-thermodynamics workers would cite it when tying planetary energy balance to the J-cost. The module is definitional scaffolding plus a thin certificate, not a deep derivation.
claimClimate energy balance is identified with vanishing of the Recognition cost, $J = 0$. The module defines a climate-feedback type, a feedback count, an energy-balance predicate, and a climate-physics certificate packaging those objects.
background
Recognition Science measures mismatch by the cost $J(x) = \frac{x + x^{-1}}{2} - 1$ (equivalently $\cosh(\log x) - 1$), forced unique by the T5 step of the unified forcing chain and obeying the Recognition Composition Law. Equilibrium configurations are those with $J = 0$, i.e. $x = 1$ in the dimensionless ratio that $J$ scores.
This module sits in the Physics domain and imports only Mathlib and the Cost layer. It treats planetary energy balance as that same $J = 0$ condition, then layers climate-specific bookkeeping (feedback channels and a count of them) on top of the cost language rather than re-deriving radiative transfer from scratch.
proof idea
Definition and certificate module, not a proof-heavy development. It introduces ClimateFeedback and climateFeedbackCount as structural types, states energy_balance as the predicate $J = 0$, and packages the package into ClimatePhysicsCert / climatePhysicsCert. No substantial tactic proof is required beyond whatever trivial certificate construction the Cost import already supplies.
why it matters in Recognition Science
Gives Recognition Science a named landing zone for climate energy-balance claims without inventing a second cost functional. Downstream work that wants to say "RS implies climate equilibrium when $J$ vanishes" can point here rather than re-open the Cost module. No parent theorems currently depend on it (used_by is empty), so it is an interface stub for later climate or Earth-system certificates rather than a link in the T0–T8 forcing chain or the mass/alpha ladder.
scope and limits
- Does not derive radiative transfer, greenhouse forcing, or GCMs from RS axioms.
- Does not prove uniqueness of climate equilibrium beyond the bare $J = 0$ identification.
- Does not compute numerical climate sensitivity or feedback gains.
- Does not connect to the eight-tick octave, D = 3, or the alpha band.
- Does not supply a used_by parent theorem yet; the certificate is currently a leaf.