IndisputableMonolith.NumberTheory.CompositionDivergence
The CompositionDivergence module introduces the Composition Closure Hypothesis asserting that defects from off-critical-line zeta zeros under iterated RCL self-composition must be absorbed by finite carrier budgets. Researchers examining cost-based routes to the Riemann hypothesis would cite the setup. The module organizes definitions and supporting declarations around this hypothesis using imported cost and zero-location machinery.
claimThe Composition Closure Hypothesis states: for each nontrivial zero $\rho$ with $\operatorname{Re} \rho \neq 1/2$, the $n$-th iterate of the Recognition Composition Law self-composition on the associated defect is absorbed by a finite carrier budget scale (carrierBudgetScale of a BudgetedCarrier).
background
The module sits in the NumberTheory domain and imports the $\xi(s)$--$J(x)$ bridge, where the completed xi satisfies $\xi(s)=\xi(1-s)$ and $J(x)=J(1/x)$ under the defect map $x=e^{2(\operatorname{Re}s-1/2)}$, with the critical line at $x=1$. ZeroLocationCost supplies zeroDeviation $\rho=2(\operatorname{Re}\rho-1/2)$ and zeroDefect $\rho=\operatorname{defect}(\exp(\text{zeroDeviation}\rho))$. ZeroCompositionLaw records that the Recognition Composition Law induces a composition law on zeta-zero defects. The module then defines the Composition Closure Hypothesis on top of these objects, with the bound parameter drawn from the AnnularCost carrier budget scale.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The module supplies the Composition Closure Hypothesis and related declarations (CompositionClosureHypothesis, rh_from_composition_closure, CompositionRHCertificate) that serve as the interface for cost-based arguments toward the Riemann hypothesis. It connects zero-location cost to iterated RCL defects and the carrier budget, feeding the broader Recognition framework landmarks on J-uniqueness and the critical-line fixed point.
scope and limits
- Does not prove the Composition Closure Hypothesis.
- Does not compute explicit growth rates of iterated defects.
- Does not implement or verify the AnnularCost carrier budget.
- Does not address the functional equation or trivial zeros.
- Does not derive the Riemann hypothesis itself.