IndisputableMonolith.NumberTheory.ProxyPhysicalizationBridge
The module bridges the concrete Euler-ledger ontology package to the PhysicallyExists predicate by showing that a bounded T1-defect in the realizability proxy implies the sensor exists physically. Researchers formalizing the Riemann Hypothesis inside Recognition Science cite it to close the remaining sensor-level gap. The module achieves this by importing the directed Euler ledger and zeta bridge structures then proving the implication through equivalences and one-line wrappers.
claimIf the T1-defect of the realizability proxy derived from the directed Euler ledger is bounded, then the corresponding sensor satisfies PhysicallyExists.
background
This module sits in the NumberTheory domain and imports DirectedEulerLedger, which packages finite concrete Euler ledgers into a directed system over finite prime supports and connects to ontology-side interfaces from UnifiedRH.lean. It also imports ZetaLedgerBridge, which closes the formalization gap between the abstract DefectSensor and PhysicallyExists framework and Mathlib's riemannZeta function. The supplied doc-comment states that the bounded T1-defect of the realizability proxy coming from the concrete Euler-ledger ontology package must imply PhysicallyExists for the same sensor.
proof idea
This is a bridge module. It defines ProxyPhysicalizationBridge as the realizability proxy and proves the main implication physicallyExists_of_ProxyPhysicalizationBridge together with supporting equivalences such as proxyPhysicalizationBridge_iff_physicallyExists and zeroInducedBridge_iff_rsPhysicalThesis by composing results from the two imported ledger modules.
why it matters in Recognition Science
The module completes the sensor-level bridge required for the Recognition Science formalization of the Riemann Hypothesis. It feeds downstream results including rh_from_ZeroInducedProxyPhysicalizationBridge and zeroInducedBridge_iff_rsPhysicalThesis. It addresses the gap between concrete number-theoretic ledgers and the physical existence predicate noted in the ZetaLedgerBridge documentation.
scope and limits
- Does not derive an explicit numerical bound on the T1-defect.
- Does not treat cases with nonzero charge beyond the listed equivalences.
- Does not connect to the phi-ladder mass formulas or the eight-tick octave.
- Does not provide numerical checks against the alpha band.
depends on (2)
declarations in this module (13)
-
def
ProxyPhysicalizationBridge -
theorem
physicallyExists_of_ProxyPhysicalizationBridge -
def
ZeroInducedProxyPhysicalizationBridge -
theorem
rsPhysicalThesis_of_ZeroInducedProxyPhysicalizationBridge -
theorem
rh_from_ZeroInducedProxyPhysicalizationBridge -
theorem
proxyPhysicalizationBridge_iff_physicallyExists -
theorem
proxyPhysicalizationBridge_iff_charge_zero -
theorem
proxyPhysicalizationBridge_of_charge_zero -
theorem
not_proxyPhysicalizationBridge_of_charge_ne_zero -
theorem
zeroInducedBridge_iff_rsPhysicalThesis -
theorem
zeroInducedBridge_iff_no_strip_zeros -
theorem
zeroInducedBridge_of_rh -
theorem
zeroInducedBridge_iff_rh