IndisputableMonolith.Physics.SpinTorqueFromJCost
Module that packages spin-torque domain energetics in terms of the Recognition Science J-cost. It introduces a nonnegative domain-cost functional, a strictly positive canonical threshold, and an inhabited SpinTorqueCert certificate. Condensed-matter and RS-physics workers cite it when tying torque thresholds to the cost geometry. Content is definitional plus elementary nonnegativity and positivity lemmas over the Cost and Constants imports.
claimA physics package defining a domain cost built from the J-cost $J$, proving that cost is nonnegative and equals its pointwise evaluation, fixing a strictly positive canonical threshold, and bundling these into an inhabited certificate structure for spin-torque claims.
background
Recognition Science measures mismatch with the unique cost $J(x)=(x+x^{-1})/2-1$ (equivalently $\cosh(\log x)-1$), forced by the T5 uniqueness step and obeying the Recognition Composition Law. The Cost import supplies that functional; Constants supplies the RS-native tick $\tau_0=1$ and related units.
Spin torque is the transfer of angular momentum that switches or precesses a magnetic domain. In this module the energetic barrier of a domain is expressed through $J$ rather than an ad-hoc anisotropy energy, so thresholds become pure numbers in RS units.
Sibling objects name the pieces: a domain-cost map, its evaluation identity, nonnegativity, a canonical positive threshold, and a certificate record that packages the numerical claims for downstream physics lemmas.
proof idea
Definition module with light lemma support, not a deep derivation. Domain cost is introduced as a Cost-side functional; a one-line evaluation lemma records that the named map agrees with pointwise $J$-style evaluation. Nonnegativity is inherited from the standard $J\ge 0$ fact on the positive reals. The canonical threshold is a positive Constant-scale quantity; positivity is a direct arithmetic check. SpinTorqueCert is a structure bundling these facts, with an inhabitation witness assembling the pieces.
why it matters in Recognition Science
Gives the RS physics layer a named home for spin-torque thresholds expressed in J-cost geometry rather than phenomenological anisotropy. That keeps magnetic switching and domain energetics on the same ledger as the forcing chain (T5 J-uniqueness, RCL) and the RS unit system ($c=1$, $\hbar=\varphi^{-5}$). No downstream consumers are wired in the graph yet, so the module is a leaf certificate pack: ready for condensed-matter or device-level theorems that need a nonnegative domain cost and a positive torque threshold in native units. It does not itself force $D=3$ or the eight-tick octave; it only consumes Cost and Constants.
scope and limits
- Does not derive microscopic LLG or Slonczewski torque equations from J.
- Does not prove numerical match to laboratory spin-torque switching currents.
- Does not force spatial dimension, phi, or the eight-tick period.
- Does not supply a dynamical evolution law, only cost and threshold data.
- Does not claim experimental falsification bounds beyond the certificate fields.