IndisputableMonolith.CPM.Examples
CPM.Examples supplies concrete model instances that confirm the generic CPM inequalities hold in the trivial zero-functional case and related constructions. A working physicist would cite it to sanity-check the projection-defect inequality, coercivity factorization, and aggregation principle before scaling to physical models. The module proceeds by defining each model then verifying the properties directly against the imported LawOfExistence framework.
claimThe module defines models $M$ (trivial, subspace, rs-cone, eight-tick) such that the CPM conditions hold: projection-defect inequality, coercivity factorization (energy gap controls defect), and aggregation principle (local tests imply membership).
background
The upstream LawOfExistence module supplies the generic, domain-agnostic formalization of the Coercive Projection Method (CPM) in three parts: A the projection-defect inequality, B the coercivity factorization where energy gap controls defect, and C the aggregation principle that local tests imply membership. This examples module imports that framework and supplies specific models to test the inequalities. The trivial model sets all functionals to zero, making the inequalities hold vacuously.
proof idea
This is an examples module that defines models (trivialModel, subspaceModel, rsConeModel, eightTickModel) and verifies the CPM properties case by case, including direct computation of minimum values such as rs_cone_cmin_value and eight_tick_cmin_value.
why it matters in Recognition Science
This module feeds the CPM framework by providing validation examples for the LawOfExistence theorems. It supports the Recognition Science approach by confirming the core inequalities in simple cases before scaling to physical models.
scope and limits
- Does not establish the general CPM theorems, which reside in LawOfExistence.
- Does not include models from other domains beyond the listed siblings.
- Does not provide proofs for arbitrary functionals, only specific examples.