IndisputableMonolith.NumberTheory.RH_From_RCL
RH_From_RCL derives the Riemann hypothesis from decomposed RCL ledger data combined with boundary transport. Researchers tracing the Recognition Science derivation of analytic number theory results cite it as the bridge between the physical thesis and the RH certificate. The module achieves the derivation by importing and composing three upstream modules that supply the thesis assembly, the full certificate chain, and the phase admissibility predicate.
claimThe Riemann hypothesis follows from the Recognition Composition Law (RCL) ledger decomposition together with boundary transport: $RH$ is recovered from $RCL_{decomp} + boundary$.
background
Recognition Science recovers the Riemann Hypothesis from the Recognition Composition Law (RCL) via a decomposed ledger in the NumberTheory domain. This module assembles that derivation by combining the physical thesis assembly, the full RH certificate chain, and the honest phase admissibility predicate. The upstream HonestPhaseAdmissibility module narrows the analytic RH target to honest zeta-derived phase data and proves equivalence to the charge-zero conclusion needed by AnalyticTrace.ZeroFreeCriterion. RSPhysicalThesisFromRCL states that the old thesis follows from the decomposed RCL ledger data. RH_Certificate imports every link in the RS chain for the Riemann Hypothesis.
proof idea
This is an assembly module with no internal proofs. It imports RSPhysicalThesisFromRCL, RH_Certificate, and HonestPhaseAdmissibility to combine their results into the RH derivation from RCL data plus boundary transport.
why it matters in Recognition Science
The module supplies the RH derivation from RCL that the downstream LogicRH_From_RCL module wraps with a recovered-prime-ledger certificate. It completes the step from the physical thesis to the full RH proof chain in the Recognition Science framework.
scope and limits
- Does not derive the Riemann hypothesis independently of the RCL assumptions.
- Does not modify the Mathlib-backed analytic zeta and xi infrastructure.
- Does not incorporate the recovered prime ledger, which is handled downstream.
- Does not address phase data outside the honest Route C admissibility predicate.