derivation_status
This definition builds a status string confirming that the core constant relations tau0 squared equals hbar G over pi c to the fifth, the Planck and G relations hold, and units remain self-consistent. A physicist checking the Recognition Science derivation of c, hbar, and G from the functional equation would cite this string to verify closure. The definition is a direct concatenation of the individual theorem status messages ending with an explicit no-holes marker.
claimThe string that reports successful proofs of the relations $τ_0^2 = ℏ G / (π c^5)$, $ℏ_derived = ℏ_codata$, $G_derived = G_codata$, $τ_0 = t_P / √π$, and unit self-consistency with no remaining proof obligations.
background
The module derives the physical constants c, ℏ, and G from Recognition Science primitives, taking CODATA reference values as targets. Key upstream lemmas establish the relations: tau0_sq_eq gives $τ_0^2 = ℏ G / (π c^5)$, planck_relation_satisfied shows the derived Planck constant matches the codata value, and G_relation_satisfied does the same for G. tau0_planck_relation further identifies $τ_0$ as the Planck time divided by √π, while units_self_consistent confirms that positive ℏ', G', c' satisfying the tau0 expression also recover the original constants.
proof idea
The definition is a direct string concatenation of five status lines drawn from the proven theorems tau0_sq_eq, planck_relation_satisfied, G_relation_satisfied, tau0_planck_relation, and units_self_consistent, followed by the literal marker '✓ NO PROOF HOLES'. No tactics or reductions are applied; the body simply assembles the human-readable report.
why it matters in Recognition Science
This definition closes the constant-derivation section by summarizing that every relation required to recover CODATA values from the Recognition functional equation has been discharged. It sits downstream of the LawOfExistence.Constants bundle and the eval bridges from LinearLogicBridge and Scalar, providing a single checkpoint before any further use of the derived c, ℏ, G in the phi-ladder or mass formula. No open questions remain inside the module.
scope and limits
- Does not derive numerical values for the constants.
- Does not prove any of the listed relations itself.
- Does not address the phi-ladder or mass formula.
- Does not extend to higher-dimensional or quantum-field structures.
formal statement (Lean)
255def derivation_status : String :=
proof body
Definition body.
256 "✓ tau0_sq_eq PROVEN\n" ++
257 "✓ planck_relation_satisfied PROVEN\n" ++
258 "✓ G_relation_satisfied PROVEN\n" ++
259 "✓ tau0_planck_relation PROVEN\n" ++
260 "✓ units_self_consistent PROVEN\n" ++
261 "✓ NO PROOF HOLES"
262
263#eval derivation_status
264
265end
266
267end Derivation
268end Constants
269end IndisputableMonolith