proxyPhysicalizationBridge_iff_charge_zero
The equivalence asserts that a defect sensor satisfies the proxy physicalization bridge exactly when its charge vanishes. Researchers reducing the Riemann hypothesis through Recognition Science would cite it to equate the physical existence predicate with the zero-charge case. The proof is a one-line term composition that transits the proxy-to-existence equivalence with the symmetric ontological dichotomy.
claimLet $s$ be a defect sensor. The statement that bounded T1 defect of the realizability proxy implies physical existence for $s$ holds if and only if the charge of $s$ is zero.
background
The module isolates the transport from the bounded realizability proxy of the concrete Euler-ledger ontology to the PhysicallyExists predicate. A DefectSensor records the multiplicity (charge) of a zeta zero, its real part, and its location in the right half of the critical strip. ProxyPhysicalizationBridge for a sensor asserts that if the T1 defect of the scalar state from PhysicallyRealizableLedger is bounded, then the sensor physically exists.
proof idea
The proof is a one-line term-mode wrapper. It applies transitivity to the equivalence ProxyPhysicalizationBridge sensor ↔ PhysicallyExists sensor and the symmetric form of the equivalence charge = 0 ↔ PhysicallyExists sensor.
why it matters in Recognition Science
This theorem supplies the direct link between the proxy bridge and the charge-zero condition. It feeds the unconditional bridge for zero-charge sensors and the equivalence of the zero-induced bridge to the Riemann hypothesis. In the Recognition Science framework it connects T1-bounded realizability to the ontological dichotomy that underlies the physical thesis and the reduction of RH.
scope and limits
- Does not establish existence of any particular defect sensor.
- Does not prove the proxy bridge for nonzero charge.
- Does not discharge the full Riemann hypothesis reduction.
- Does not supply numerical bounds on T1 defects.
Lean usage
theorem proxyPhysicalizationBridge_of_charge_zero (sensor : DefectSensor) (h : sensor.charge = 0) : ProxyPhysicalizationBridge sensor := (proxyPhysicalizationBridge_iff_charge_zero sensor).mpr hformal statement (Lean)
105theorem proxyPhysicalizationBridge_iff_charge_zero (sensor : DefectSensor) :
106 ProxyPhysicalizationBridge sensor ↔ sensor.charge = 0 :=
proof body
Term-mode proof.
107 (proxyPhysicalizationBridge_iff_physicallyExists sensor).trans
108 (charge_zero_iff_physicallyExists sensor).symm
109
110/-- The bridge holds unconditionally for charge-zero sensors. -/