IndisputableMonolith.NumberTheory.HonestPhaseBudgetBridge
HonestPhaseBudgetBridge connects DefectSampledTrace annular meshes to MeromorphicCircleOrder, establishing that the zeta-derived phase family has identically zero annular excess at every mesh depth and therefore lies on the topological floor. Researchers closing the Riemann Hypothesis in Recognition Science cite it to confirm the defect's baseline cost before carrier comparison. The module organizes imports and sibling declarations that bound excess and charge without introducing new axioms.
claimThe zeta-derived phase family satisfies annular excess zero on every mesh depth: excess(zetaDerivedPhaseFamily, d) = 0 for all mesh depths d, placing it exactly on the topological floor of the annular cost framework.
background
The module sits in the NumberTheory domain and supplies the honest-phase bridge after Axiom 1 elimination. Upstream DefectSampledTrace realizes annular meshes attached to phase-sampling for a hypothetical zeta defect, leaving Axiom 2 as the remaining bottleneck. MeromorphicCircleOrder adapts Mathlib meromorphic order to the RS annular cost setting, where meromorphicOrderAt f ρ = n yields the local factorization f(z) = (z − ρ)^n · g(z) with g analytic and g(ρ) ≠ 0.
proof idea
This is a definition module, no proofs. It imports DefectSampledTrace and MeromorphicCircleOrder to expose the topological-floor property for zetaDerivedPhaseFamily, with the actual zero-excess and charge-bounded statements supplied by the listed sibling declarations.
why it matters in Recognition Science
The module feeds AnalyticTrace, which assembles the full axiom-free RH bridge, and CarrierBudgetComparison, which executes Phase 4a of the RH closure plan by comparing bounded carrier cost against the diverging defect floor on the same circles. The module doc comment states that zetaDerivedPhaseFamily sits exactly on the topological floor with annular excess identically zero on every mesh depth.
scope and limits
- Does not eliminate Axiom 2.
- Does not derive the carrier-defect contradiction.
- Does not compute explicit constants inside the alpha band.
- Does not address mesh depths beyond the topological floor.
used by (2)
depends on (2)
declarations in this module (9)
-
theorem
zetaDerivedPhaseFamily_excess_zero -
def
phaseFamily_ringPerturbationControl -
theorem
phaseFamily_excess_bounded_of_perturbationWitness -
theorem
honestPhaseFamily_excess_bounded_of_perturbationWitness -
def
honestPhaseFamily_perturbationWitness -
theorem
honestPhaseFamily_excess_zero -
theorem
honestPhaseFamily_excess_bounded -
theorem
honestPhaseFamily_charge_zero_of_costBounded -
theorem
honestPhaseFamily_cost_bounded_iff_charge_zero