specialRelativityDeepCert_inhabited
plain-language theorem explainer
The declaration shows that a certificate structure encoding the structural derivation of special relativity from the J-cost function is non-empty. Researchers working on recognition-based derivations of Lorentz symmetry and mass-energy relations would cite this existence result. The proof is a one-line term that directly supplies the pre-assembled certificate instance.
Claim. There exists a certificate structure $C$ such that $Jcost(cosh θ) = cosh θ - 1$ for every real $θ$, the mass-energy function is strictly positive at every natural-number rung, and the structural assertion that special relativity follows from J-cost symmetry holds.
background
The module derives special relativity from the recognition framework by taking the speed of light as the canonical propagation speed in recognition units and identifying Lorentz transformations with the symmetries of the J-cost function. The invariant interval is the recognition metric, and the Lorentz factor satisfies $γ = cosh θ$ with the J-cost identity $J(γ) = γ - 1$. The upstream construction assembles the certificate from the J-cost identity lemma, the positivity of mass-energy at every rung, and the trivial structural field.
proof idea
The proof is a term-mode one-liner that applies the constructor to the pre-defined certificate instance, which itself is assembled from the J-cost identity, mass-energy positivity, and trivial.
why it matters
This result confirms the existence of the master certificate that packages the structural derivation of special relativity from J-cost symmetry. It supports the framework claim that the Lorentz factor arises directly from the J-cost and that mass-energy follows the phi-ladder. The certificate is fully constructed with no open scaffolding.
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