planckConstantCert
plain-language theorem explainer
Recognition Science pins the Planck constant at ℏ = φ^{-5} with coherence exponent fixed at 5 in native units, together with G = φ^5/π and κ = 8φ^5. The definition constructs the certificate structure by reflexivity on the exponent equality and direct assignment of the positivity and Einstein-relation fields. A physicist auditing zero-parameter derivations of the SM constants would cite it to confirm algebraic consistency once k=5 is forced at D=3.
Claim. The RS constants satisfy the Planck-constant certificate: coherence exponent equals 5, $0 < ℏ_{RS}$, $0 < G_{RS}$, $0 < κ_{RS}$, and $κ_{RS} = 8π G_{RS}$.
background
The module derives A1 SM constants from Recognition Science, stating ℏ = φ^{-5} in RS-native units, G = φ^5/π, and κ = 8φ^5. These follow once the coherence exponent k=5 is forced at D=3 by the Fibonacci route 2^D - D =5 and the integration route D+2=5. The certificate structure requires the exponent equality, positivity of the three RS constants, and the Einstein relation κ_RS = 8π G_RS.
proof idea
The definition constructs the structure record. It sets the exponent field by reflexivity on coherenceExponent =5 and assigns the three positivity fields to the corresponding RS positivity lemmas together with the Einstein relation field to the upstream relation lemma.
why it matters
The declaration certifies the key constants required by the zero-parameter gravity model and the thermal-conductivity regimes. It closes the algebraic derivation from the forcing chain (T5 J-uniqueness through T8 D=3) once the exponent is pinned at 5. The module records zero sorry and zero axiom.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.