IndisputableMonolith.NumberTheory.LogicRH_From_RCL
This module assembles RH decomposition data that augments the classical analytic stack with an explicit recovered-prime-ledger component drawn from logic-native atoms. Researchers deriving the Riemann Hypothesis inside Recognition Science from the RCL would cite it to maintain compatibility between the zeta function over Mathlib's ℕ/ℂ and the transported LogicNat ledger. The module is a definition module that imports RH_From_RCL and LogicPrimeLedgerAtom to record the transport equivalence.
claimAn RH decomposition datum equipped with a recovered prime ledger component, where primality statements on LogicNat are transported via the equivalence LogicNat.toNat to ensure compatibility with the classical ℕ-based ledger in the analytic zeta stack.
background
Recognition Science derives the Riemann Hypothesis from the Recognition Composition Law (RCL) via boundary transport data. The upstream RH_From_RCL module supplies the final assembly whose only remaining nontrivial datum is BoundaryTransportCert, the explicit RS physical bridge carrying realized annular collapse to the T1-bounded Euler ledger boundary. LogicPrimeLedgerAtom supplies the first recovered-number adapter: primality is stated directly on LogicNat and recovered to the classical ledger through the transport equivalence LogicNat.toNat.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
This module supplies the data structure required by sibling declarations such as riemann_hypothesis_from_rcl_logicPrime and rh_from_rcl_logicPrime_completion_boundary. It completes the bridge from RS physical thesis data logic to the classical RH assembly by recording the explicit recovered-prime-ledger component, advancing the T1-bounded Euler ledger boundary in the Recognition Science chain.
scope and limits
- Does not prove the Riemann Hypothesis.
- Does not compute explicit zeta zeros or prime counts.
- Retains classical analytic fields without altering the zeta stack.
- Assumes the LogicNat.toNat transport equivalence without new proofs.
- Does not extend the ledger to non-prime or higher-dimensional cases.