IndisputableMonolith.NumberTheory.ArgumentPrincipleSensor
A zero of the Riemann zeta function in the right half of the critical strip produces a nonphysical nonzero-charge sensor through the already-proved ontological dichotomy. Researchers formalizing the Riemann Hypothesis inside the Recognition Science framework cite this module to link analytic number theory directly to physical existence constraints. The module assembles the proved argument principle sampling with the zeta-ledger bridge to derive the sensor implication without new axioms.
claimIf there exists $s$ with $Re(s) > 1/2$ such that $zeta(s) = 0$, then a nonphysical nonzero-charge sensor exists, by the ontological dichotomy.
background
The module operates inside the NumberTheory domain of the Recognition Science formalization. It imports ArgumentPrincipleProved, which eliminates the argument_principle_sampling axiom and upgrades the analytic route to witnessed zeta inverse phase-family data, and ZetaLedgerBridge, which closes the formalization gap between the abstract DefectSensor and PhysicallyExists framework from UnifiedRH and Mathlib's concrete riemannZeta function. The doc comment states that a zero of zeta in the right half of the critical strip gives a nonphysical nonzero-charge sensor by the already-proved ontological dichotomy.
proof idea
This is a definition module, no proofs. It defines the charged sensor implication by direct reference to the imported results from ArgumentPrincipleProved and ZetaLedgerBridge.
why it matters in Recognition Science
The module supplies the explicit sensor construction required by RSPhysicalThesisDecomposition, which replaces the opaque RSPhysicalThesis dependency with a structured bundle of ingredients for the RH proof. It advances the Recognition framework by converting zeta zero data into a concrete nonphysicality constraint, supporting the chain that rules out right-half zeros. This closes the formalization gap identified in the upstream ZetaLedgerBridge doc comment.
scope and limits
- Does not prove the Riemann Hypothesis.
- Does not compute or locate any explicit zeta zeros.
- Does not derive the full physical thesis or J-cost relations.
- Does not address zeros on the critical line or in the left half-plane.