IndisputableMonolith.CrossDomain.JConvexityUniversality
The JConvexityUniversality module assembles algebraic identities and bounds for the J-cost to establish its convexity and sensitivity properties hold across domains. Cross-domain modelers cite it when extending Recognition Science results beyond isolated sectors. The module proceeds as a chain of lemmas derived directly from the squared J-cost form.
claim$J(r) = \frac{(r-1)^2}{2r}$ together with the identities $J(r^2) = 2J(r) + 2J(r)^2$, sensitivity at unity, and the universal sensitivity equation.
background
The module imports the Cost library, which supplies the squared J-cost $J(r) = \frac{(r-1)^2}{2r}$ as the native recognition cost. CrossDomain context applies this cost to inter-domain comparisons while preserving the Recognition Composition Law. Upstream Cost supplies the base algebraic object; the present module adds symmetry, quadratic, and leading-order expansions.
proof idea
This is a definition module, no proofs. The structure is a sequence of named lemmas (jcost_squared_form through JConvexityUniversalityCert) that perform direct algebraic reductions and substitutions starting from the imported squared form.
why it matters in Recognition Science
The module supplies the cross-domain J-cost toolkit required by any theorem that invokes J-uniqueness (T5) or the eight-tick octave (T7) when domains interact. It feeds parent results that close the forcing chain by guaranteeing convexity holds uniformly.
scope and limits
- Does not derive the full T0-T8 forcing chain.
- Does not compute numerical values for physical constants.
- Does not address Berry creation thresholds or Z_cf.
- Does not treat multi-particle or field-theoretic extensions.
depends on (1)
declarations in this module (12)
-
theorem
jcost_squared_form -
theorem
jcost_upper_bound_at_geq_one -
theorem
sensitivity_at_one -
theorem
jcost_at_one_plus_delta -
theorem
jcost_quadratic_identity -
theorem
jcost_log_symmetric -
def
universalSensitivity -
theorem
universalSensitivity_eq -
theorem
leading_order -
theorem
jcost_symmetric_pair -
structure
JConvexityUniversalityCert -
def
jConvexityUniversalityCert