IndisputableMonolith.Verification.CprojDerivationCert
Verification certificate module that packages the coercive-projection (Cproj) derivation against the CPM Law of Existence A/B/C skeleton. Auditors and framework maintainers cite it to confirm that projection-defect control, coercivity factorization, and aggregation are wired into one checkable artifact. The module is largely an import-and-bundle layer over LawOfExistence rather than a deep new proof.
claimA derivation certificate for the coercive projection under the Coercive Projection Method: (A) projection-defect inequality, (B) coercivity factorization so an energy gap controls the defect, and (C) aggregation of local tests into membership.
background
Recognition Science uses the Coercive Projection Method (CPM) to turn abstract existence claims into quantitative control: a projection map, a defect measuring failure to land in the target set, and an energy or cost that forces the defect down. The upstream Law of Existence module states this generically in three parts: A (projection-defect inequality), B (coercivity factorization: an energy gap controls the defect), and C (aggregation: local tests imply membership).
This verification module sits in the Verification domain and imports that CPM core together with Mathlib. Its role is not to redefine J-cost, the phi-ladder, or the forcing chain T0-T8, but to certify that a concrete Cproj derivation is an instance of the A/B/C pattern, so downstream physics claims that rely on projection control can point at a single certificate object.
proof idea
Definition and certificate packaging module, not a standalone deep proof. It imports the generic Law of Existence A/B/C formalization and exposes a named certificate (CprojDerivationCert) that records the Cproj instance against those three obligations. Argument structure is: reuse A/B/C interfaces, specialize them to the projection setting, and bundle the resulting obligations into one verifiable artifact. No independent tactic script beyond that wiring is indicated at module scope.
why it matters in Recognition Science
In the Recognition framework, coercive projection is how existence and selection principles become quantitative (defect bounds rather than pure non-emptiness). This module earns its place as the verification-facing certificate that the Cproj derivation matches the CPM Law of Existence skeleton, so auditors can treat projection control as discharged rather than informal. Used-by edges are empty at present: it is a leaf certificate for human and CI audit, not an intermediate lemma feeding a named parent theorem in the supplied graph. It closes a scaffolding-style gap between the generic CPM core and any physics claim that assumes a well-controlled projection step.
scope and limits
- Does not prove the generic Law of Existence A/B/C; that lives upstream.
- Does not derive mass, alpha, or forcing-chain (T0-T8) constants.
- Does not supply a numerical Cproj algorithm or executable projector.
- Does not claim downstream physics theorems; used_by is empty.
- Does not replace domain-specific defect or energy definitions.