module module high

`IndisputableMonolith.NumberTheory.ZetaLedgerBridge`

The ZetaLedgerBridge module constructs a zeta-defect sensor carrying unit charge at multiplicity one. Researchers assembling the RS-derived Riemann Hypothesis proof cite it to connect the Euler product to the sensor framework. The module imports EulerInstantiation and UnifiedRH to define the sensor and its charge properties without introducing independent proofs.

claimThe sensor constructed from the zeta defect with multiplicity one carries charge one.

background

This module sits in the Recognition Science number theory layer that instantiates the abstract RS carrier and sensor framework via the Euler product of the Riemann zeta function. The upstream EulerInstantiation module shows that the Euler product of ζ(s) realizes the RS cost structure from AnnularCost and CostCoveringBridge. The upstream UnifiedRH module supplies the structured T1-bounded realizability architecture that replaces the earlier total annular cost bound.

proof idea

This is a bridge module that imports EulerInstantiation and UnifiedRH to define zetaDefectSensor and prove its charge properties. It assembles the unit-charge result for multiplicity one by direct instantiation of the imported sensor framework, together with supporting lemmas on non-physicality and zero locations.

why it matters in Recognition Science

The module supplies the concrete zeta-ledger sensor required by the RH certificate chain in RH_Certificate and the argument-principle bridge in ArgumentPrincipleSensor. It fills the remaining gap identified in ProxyPhysicalizationBridge and supplies the exact ingredients for the RS physical thesis decomposition. It thereby connects the Euler product realization to the T1-bounded architecture used in the full RH proof from the recognition composition law.

scope and limits

Does not prove the Riemann Hypothesis.
Does not address zeros with multiplicity greater than one.
Does not extend the sensor construction to Re(s) less than one.
Does not incorporate the completed zeta function or gamma factor.

used by (4)

From the project-wide theorem graph. These declarations reference this one in their body.

IndisputableMonolith.NumberTheory.ArgumentPrincipleSensor module_import
IndisputableMonolith.NumberTheory.ProxyPhysicalizationBridge module_import
IndisputableMonolith.NumberTheory.RH_Certificate module_import
IndisputableMonolith.NumberTheory.RSPhysicalThesisDecomposition module_import

depends on (2)

Lean names referenced from this declaration's body.

IndisputableMonolith.NumberTheory.EulerInstantiation module_import
IndisputableMonolith.Unification.UnifiedRH module_import

declarations in this module (17)

theorem zetaDefectSensor_charge_one L52
theorem zetaDefectSensor_charge_ne_zero L58
theorem nonzero_charge_not_physical L66
theorem unit_sensor_not_physical L75
theorem strip_zero_gives_nonphysical_sensor L87
def RSPhysicalThesis L115
theorem no_strip_zeros_from_rs L131
theorem zeta_ne_zero_re_ge_one L141
theorem rh_right_half_from_rs L154
theorem gammaR_ne_zero_of_nontrivial_zero L165
theorem completedZeta_zero_of_nontrivial_zero L177
theorem zeta_one_sub_zero_of_zero L191
theorem rh_from_rs_thesis L213
theorem rh_certificate L250
theorem rh_right_half_certificate L258
theorem witnessed_sensor_not_physical L278
theorem witnessed_physical_contradiction L286