IndisputableMonolith.Education.MasteryDesignFromJCost
The module instantiates the canonical J-cost band for the education domain to support mastery design certificates. It forms part of the master cert chain where each domain proves matched-zero and nonnegativity of the J function. Physicists and mathematicians working in Recognition Science cite it when building domain-specific applications of the six-clause template. The module contains no proofs and relies entirely on the imported CanonicalJBand structure.
claimThe education mastery design asserts $J(1)=0$ and $J(x)geq 0$ for all $x>0$, where $J(x)=(x+x^{-1})/2-1$, as the core of the six-clause J-cost template.
background
Recognition Science derives all structures from the J-cost function satisfying the Recognition Composition Law J(xy)+J(x/y)=2J(x)J(y)+2J(x)+2J(y). The upstream CanonicalJBand supplies the reusable six-clause template for J-cost on ratios, applied across the master cert chain for B-tier whole-science openings and Plan v7 domain certs. This module sets the education-domain context by importing that band and declaring the sibling objects MasteryDesignCert and masteryDesignCert as the education-specific instances that inherit matched-zero and nonnegativity.
proof idea
This is a definition module, no proofs. It organizes the mastery design by importing the CanonicalJBand template and declaring the education-specific certificates that inherit the J-cost properties.
why it matters in Recognition Science
The module feeds into the master cert chain for B-tier whole-science openings and the Plan v7 domain certificates. It applies the J-uniqueness from the forcing chain (T5) to the education domain. By providing the template instantiation, it enables the full set of domain certs in Recognition Science.
scope and limits
- Does not establish the full set of J properties such as the composition law.
- Does not provide explicit definitions for the J function itself.
- Does not include any numerical verification or examples of mastery design.
- Does not connect to downstream results beyond the cert chain.