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IndisputableMonolith.Physics.SpecialRelativityFromRS

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Module that casts special relativity as a consequence of the recognition cost J. Rest frames are identified with recognition equilibrium (J = 0); motion raises the cost and forces the usual SR symmetries. Physicists deriving Lorentz structure from the RS cost functional would cite it. The file is mostly definitions plus a short certificate packing the rest-frame and symmetry claims.

claimRest frame means recognition equilibrium: $J = 0$. Motion cost is the excess $J$ away from equilibrium. The module packages an SR effect count, a symmetry statement for that cost, and a certificate that the rest-frame and symmetry data match special-relativistic structure.

background

Recognition Science builds physics from the unique cost $J(x) = (x + x^{-1})/2 - 1$ (equivalently $\cosh(\log x) - 1$), forced at T5 of the unified chain. $J$ vanishes only at $x = 1$, so the unique zero-cost state is the self-similar fixed point of the composition law.

This module sits in the physics layer and imports the Cost library. It treats a rest frame as that zero of $J$: recognition equilibrium. Any boost or relative motion is scored by the excess cost (motion cost) above equilibrium. The surrounding RS landmarks (RCL, $\phi$-ladder, eight-tick period) are not re-proved here; they supply the ambient units and the uniqueness of $J$.

proof idea

Definition-heavy module rather than a long tactic proof. It introduces an SR-effect type and a count of those effects, defines rest frame as $J = 0$, defines motion cost as the excess $J$, records an SR symmetry lemma for that cost, and wraps the package in a certificate structure (SpecialRelativityCert / specialRelativityCert). No deep algebraic derivation appears in the module body; the logical content is the identification rest-frame $\leftrightarrow$ equilibrium plus the symmetry claim on motion cost.

why it matters in Recognition Science

Gives the RS reading of special relativity: Lorentz structure is not postulated but read off the unique cost $J$ and its equilibrium. Downstream consumers (none linked in the current graph) would use the certificate when assembling relativistic kinematics or when matching RS units ($c = 1$) to lab frames. It sits under the physics domain and closes the conceptual step from T5 $J$-uniqueness to the kinematic claim that only the $J = 0$ frame is privileged. No forcing-chain step T0–T8 is discharged here; the module is an interpretive bridge, not a foundation lemma.

scope and limits

depends on (1)

Lean names referenced from this declaration's body.

declarations in this module (7)