Jcost_regularity_cert in IndisputableMonolith.CostUniqueness
(1) In plain English: This noncomputable definition builds a RegularityCert structure for the Jcost function. It asserts that Jcost is continuous on the positive reals, strictly convex on the positive reals, and calibrated so that the second derivative of (Jcost composed with exp) at 0 equals 1.
(2) Why it matters in Recognition Science: The certificate supplies the regularity conditions required for the T5 uniqueness theorem. It lets any cost functional meeting symmetry, unit normalization, strict convexity, and calibration be shown equal to Jcost on (0, ∞), which underpins the derivation of physical constants from the single Law of Logic.
(3) How to read the formal statement: The declaration has type IndisputableMonolith.Foundation.ClosedFramework.RegularityCert Cost.Jcost. Its body is a structure literal that fills three fields: continuous receives the proof from the local lemma establishing continuity on Ioi 0; strict_convex receives the strict-convexity property; calibration receives the normalized second log-derivative result. The noncomputable keyword indicates the definition may rely on non-executable mathematical objects such as derivatives.
(4) Visible dependencies or certificates: The definition directly uses the lemma Jcost_continuous_pos for the continuous field. It also references Cost.Jcost_strictConvexOn_pos and CPM.LawOfExistence.RS.Jcost_log_second_deriv_normalized for the remaining fields. These regularity facts are consumed by the surrounding uniqueness results T5_uniqueness_complete and unique_cost_on_pos.
(5) What this declaration does not prove: It does not prove the full uniqueness statement (handled separately by T5_uniqueness_complete and unique_cost_on_pos). It does not derive the functional-equation or convexity properties from scratch, nor does it address empirical validation against measured constants or extensions to the broader forcing chain.