knet_eight_tick_refined
plain-language theorem explainer
The definition supplies the refined K_net constant as (9/7) squared for eight-tick CPM geometry. Researchers applying the Coercive Projection Method in Recognition Science cite it when normalizing constants tied to the eight-tick octave. The declaration is a direct noncomputable assignment whose companion theorem immediately reduces it to the fraction 81/49.
Claim. The refined eight-tick constant K_net is defined as $(9/7)^2$.
background
The module formalizes the Coercive Projection Method (CPM) in three abstract parts: A) Projection-Defect inequality, B) Coercivity factorization in which the energy gap controls defect, and C) Aggregation principle in which local tests imply membership. The presentation models mass of orthogonal components, defects, and energy gaps at an aggregate level so concrete instances from diverse domains can plug in without heavy measure-theoretic scaffolding. This definition provides one specific numerical constant for the eight-tick geometry inside that framework.
proof idea
The declaration is a direct definition that assigns the real number (9/7) squared. No lemmas are invoked and no tactics appear in the body.
why it matters
The constant feeds the downstream theorem knet_eight_tick_refined_value, which bundles CPM constants for eight-tick geometry. It supplies a concrete value for the eight-tick octave (T7 in the forcing chain) inside the Recognition Science framework. The choice (9/7) squared is presented as an alternative arising from refined eight-tick analysis.
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