IndisputableMonolith.NumberTheory.CompositionDivergence
The CompositionDivergence module introduces the Composition Closure Hypothesis asserting that defects of off-critical-line zeta zeros diverge under iterated RCL self-composition and must be absorbed by a finite carrier budget. Researchers deriving the Riemann hypothesis from recognition-science cost symmetries would cite it. The module organizes the hypothesis statement together with divergence and cascade lemmas without containing a completed proof.
claimThe Composition Closure Hypothesis states that for each nontrivial zero $ρ$ with $Re(ρ) ≠ 1/2$, the $n$-th iterate of the RCL self-composition on the defect $d(ρ)$ produces a sequence $d_n$ that remains bounded by the carrier budget scale $B$ from the AnnularCost framework.
background
The module sits in the NumberTheory domain and imports the J-cost functional, the Recognition Composition Law (RCL) from ZeroCompositionLaw, the ξ(s)–J(x) symmetry bridge, and the zeroDefect map. Upstream, ZeroLocationCost defines zeroDeviation $ρ = 2(Re ρ − 1/2)$ and zeroDefect $ρ = defect(exp(zeroDeviation ρ))$. XiJBridge records that $ξ(s) = ξ(1−s)$ translates under the defect-coordinate map $x = e^{2(Re s − 1/2)}$ into the J-symmetry $J(x) = J(1/x)$, with the critical line mapping to the unique minimum at $x=1$.
proof idea
This is a definition module with no internal proofs. It declares the CompositionClosureHypothesis as a Prop, introduces supporting notions of composition iterates and budget absorption, and lists sibling lemmas on exponential and doubly-exponential cascade growth that are proved elsewhere.
why it matters in Recognition Science
The module supplies the central hypothesis that feeds rh_from_composition_closure and CompositionRHCertificate, advancing the Recognition Composition Law toward a cost-based proof of the Riemann hypothesis. It closes the loop on how off-line zeros would violate the finite-budget constraint implied by T5 J-uniqueness and the eight-tick octave.
scope and limits
- Does not prove the Composition Closure Hypothesis itself.
- Does not compute explicit numerical bounds for any specific zero.
- Does not address trivial zeros or the functional equation directly.
- Does not derive physical constants such as α or G.