specialRelativityCert
plain-language theorem explainer
The specialRelativityCert definition packages the core properties of special relativity as derived from the recognition cost J in the Recognition Science framework. A physicist deriving Lorentz invariance or relativistic effects from a single functional equation would reference this certificate to confirm the five effects and the J properties hold. The construction is a direct instantiation of the SpecialRelativityCert structure using the pre-proven lemmas for effect count, rest frame equilibrium, positive cost off rest, and symmetry under r to
Claim. Let $J$ denote the recognition cost function. The special relativity certificate asserts that the set of special relativity effects has cardinality 5, $J(1)=0$, $J(r)>0$ for all $r>0$ with $r≠1$, and $J(r)=J(r^{-1})$ for all $r>0$.
background
In the module deriving special relativity from Recognition Science, the J-cost function encodes the recognition cost of a velocity ratio $r=v/c$. The SpecialRelativityCert structure collects four properties: exactly five canonical effects (time dilation, length contraction, mass-energy equivalence, relative simultaneity, velocity addition), zero cost at rest ($J(1)=0$), strictly positive cost for any nonzero motion, and symmetry $J(r)=J(r^{-1})$ reflecting no preferred direction. Upstream results establish each property separately: srEffectCount proves the cardinality by decision, rest_frame shows $Jcost 1=0$ via Jcost_unit0, motion_cost proves positivity off unity via Jcost_pos_of_ne_one, and sr_symmetry establishes the inversion equality via Jcost_symm. The local setting follows the module's foundation that SR principles emerge directly from $J(v/c)$ diverging at $c$, vanishing at rest, and being symmetric.
proof idea
This is a definition that constructs the SpecialRelativityCert record by assigning the five_effects field to the srEffectCount theorem and filling the remaining fields with the rest_frame, motion_cost, and sr_symmetry lemmas. No additional tactics are required beyond the direct field assignments.
why it matters
This declaration serves as the top-level certificate that special relativity follows from the Recognition Science cost function, completing the derivation of the five effects from the J properties. It aligns with the framework's claim that configDim D=5 for the SR effects and supports the broader forcing chain from T0 to T8 by providing the relativistic kinematics layer. No open questions are flagged in the supplied results, as the module reports zero sorry or axiom.
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