IndisputableMonolith.Verification.CminDerivationCert
Verification certificate module packaging a derivation of the minimum cost constant C_min from the Coercive Projection Method. Auditors of the CPM existence pipeline cite it to confirm the certified bound sits on the Law of Existence A/B/C stack. Structure is a thin cert wrapper over the imported CPM core, not a fresh analytic derivation.
claimA verification certificate $C_{\min}\text{DerivationCert}$ asserting a derived lower bound on the minimum recognition cost $C_{\min}$, obtained from the Coercive Projection Method (projection-defect inequality, coercivity factorization, and aggregation).
background
The module lives in the Verification domain and imports the CPM Law of Existence core. That upstream module supplies a domain-agnostic formalization of the Coercive Projection Method in three parts: (A) a projection-defect inequality relating how far a state sits from a projected admissible set; (B) coercivity factorization, in which an energy gap controls the defect; and (C) an aggregation principle that lifts local tests to membership.
$C_{\min}$ is the minimum recognition cost appearing in existence and threshold arguments. In Recognition Science this sits near the cost geometry built from the J-functional and the forcing chain, and is the quantity a cert must pin before downstream existence or mass-ladder claims can quote a concrete floor.
No separate analytic development is introduced here; the setting is certificate packaging of the CPM A/B/C stack for audit.
proof idea
This is a certificate module, not a standalone proof development. It imports Mathlib and the CPM Law of Existence module, then exposes a cert object (CminDerivationCert) whose obligations are discharged by reference to the A/B/C lemmas of that core: projection-defect control, energy-gap coercivity, and local-to-global aggregation. Expect a structure or Prop bundle rather than a long tactic script.
why it matters in Recognition Science
Places a named, auditable certificate on the derivation of $C_{\min}$ so verification pages can point at a single object instead of raw CPM internals. Upstream is the Law of Existence (CPM A/B/C). No downstream used_by edges are recorded in the graph snapshot, so the cert is presently a leaf for external or later verification consumers rather than an in-tree parent theorem. It does not itself re-prove J-uniqueness (T5), $\varphi$-forcing (T6), or the eight-tick/dimension steps; it only certifies the minimum-cost bound extracted from CPM coercivity.
scope and limits
- Does not derive J-uniqueness, phi, eight-tick period, or D=3.
- Does not supply a numerical closed form for C_min beyond the cert interface.
- Does not replace the CPM A/B/C proofs; it only packages them.
- Does not record in-tree downstream consumers in the current graph.