physicallyExists_of_ProxyPhysicalizationBridge
The theorem states that whenever a ProxyPhysicalizationBridge holds for a DefectSensor, that sensor satisfies PhysicallyExists. Researchers closing the gap from zeta-zero sensors to the RS Physical Thesis would cite this to complete the existence transport. The proof is a term-mode wrapper that builds the concrete Euler ledger package and feeds the scalarDefectBounded antecedent directly into the bridge implication.
claimLet sensor be a DefectSensor. If ProxyPhysicalizationBridge(sensor) holds, where this is the statement that the existence of a real bound $K$ such that the T1-defect of the PhysicallyRealizableLedger scalar state is at most $K$ for every $N$ implies PhysicallyExists(sensor), then PhysicallyExists(sensor).
background
The Proxy Physicalization Bridge module isolates the final transport after the concrete directed Euler ledger has been built for finite prime supports. For each DefectSensor the ledger supplies an admissible Euler trace together with a T1-bounded realizability proxy (PhysicallyRealizableLedger) whose scalar state is obtained from eulerLedgerScalarState. The module documentation notes that the remaining gap to RSPhysicalThesis is precisely the implication from this bounded proxy to the actual PhysicallyExists predicate.
proof idea
The term proof lets pkg be the result of concreteEulerLedgerOntologyInterface sensor, installs the PhysicallyRealizableLedger instance pkg.realizableProxy, and applies the supplied bridge hypothesis to the antecedent EulerLedgerOntologyInterface.scalarDefectBounded pkg.
why it matters in Recognition Science
This declaration supplies the missing sensor-level transport that turns a ZeroInducedProxyPhysicalizationBridge into the full RSPhysicalThesis (see downstream rsPhysicalThesis_of_ZeroInducedProxyPhysicalizationBridge). It directly fills the explicit bridge gap described in the module documentation, allowing the zero-induced case to yield RiemannHypothesis. In the Recognition Science chain it completes the passage from the directed Euler ledger and T1-bounded proxy to physical existence for the relevant sensors.
scope and limits
- Does not prove the T1-defect boundedness hypothesis itself.
- Does not apply to sensors whose charge is nonzero.
- Holds only inside the concrete Euler-ledger ontology package.
- Does not derive the full Riemann Hypothesis without the zero-induced bridge assumption.
Lean usage
exact physicallyExists_of_ProxyPhysicalizationBridge sensor hbridgeformal statement (Lean)
48theorem physicallyExists_of_ProxyPhysicalizationBridge
49 (sensor : DefectSensor) (bridge : ProxyPhysicalizationBridge sensor) :
50 PhysicallyExists sensor := by
proof body
Term-mode proof.
51 let pkg := concreteEulerLedgerOntologyInterface sensor
52 letI : PhysicallyRealizableLedger sensor := pkg.realizableProxy
53 exact bridge (EulerLedgerOntologyInterface.scalarDefectBounded pkg)
54
55/-- Zero-induced proxy physicalization: every strip zero of `ζ` produces a
56sensor for which the proxy-to-physical-existence bridge holds. -/