IndisputableMonolith.Physics.FrictionFromJCost
Defines friction coefficients from the Recognition J-cost on positive reals, with a nonnegativity certificate and a canonical positive threshold. Physicists deriving dissipative terms from the RS cost functional would cite it. The module is mostly definitional: domain cost, threshold lemmas, and an inhabited certificate structure.
claimOn the positive reals, a domain cost is built from the Recognition cost $J(x)=(x+x^{-1})/2-1$. The module records $C\ge 0$, a canonical threshold $\theta>0$, and a friction-coefficient certificate packing these facts for downstream use.
background
Recognition Science forces a unique symmetric cost $J$ on ratios (T5): $J(x)=(x+x^{-1})/2-1$, equivalently $\cosh(\log x)-1$. The Recognition Composition Law constrains how $J$ multiplies under products and quotients. Dissipation and friction are read off as excess cost above equilibrium, not inserted by hand.
This module sits in the Physics layer and imports only Constants (RS time quantum $\tau_0=1$ tick) and Cost (the $J$ infrastructure). It introduces a domain-level cost functional, proves it is nonnegative, and fixes a canonical positive threshold against which a friction coefficient can be certified.
Sibling objects include equality-at-equilibrium for the domain cost, positivity of the threshold, and an inhabited FrictionCoeffCert packing the certified data.
proof idea
Definition-heavy module with short supporting lemmas. Domain cost is defined from $J$; nonnegativity follows from the standard $J\ge 0$ fact in Cost. The canonical threshold is a positive constant (positivity is a one-line inequality). FrictionCoeffCert is a structure bundling the coefficient with the cost and threshold witnesses; cert and cert_inhabited supply a concrete inhabited instance rather than a deep derivation.
why it matters in Recognition Science
Friction and other dissipative coefficients must ultimately descend from the same $J$ that forces $\phi$, the eight-tick octave, and $D=3$. Packaging a friction coefficient as a certificate over domain cost keeps later continuum or transport arguments honest to T5 rather than phenomenological.
No downstream edges are recorded yet, so the module is a leaf provider: it supplies domainCost, the threshold, and FrictionCoeffCert for any Physics development that needs a $J$-sourced drag term. It does not itself close a forcing-chain step; it is infrastructure for reading friction off excess recognition cost.
scope and limits
- Does not derive a microscopic Langevin or Navier–Stokes friction term from first principles.
- Does not prove uniqueness of the friction coefficient beyond the chosen certificate packing.
- Does not connect friction to the mass ladder, alpha band, or eight-tick dynamics.
- Does not supply experimental units conversion; constants remain RS-native unless specialized elsewhere.
- Does not claim a measured numerical value for any material friction coefficient.