EBBA_of_rh

formal source

 721
 722/-- RH implies `EulerBoundaryBridgeAssumption`. If no sensor has nonzero
 723charge, the bridge is vacuously satisfied. -/
 724theorem EBBA_of_rh
 725    (hrh : ∀ sensor : DefectSensor, sensor.charge ≠ 0 → False) :
 726    EulerBoundaryBridgeAssumption := by
 727  intro sensor
 728  letI : PhysicallyRealizableLedger sensor := euler_physically_realizable sensor
 729  exact { toLedgerBoundary := fun hm _ => absurd hm (fun h => hrh sensor h) }
 730
 731/-- `EulerBoundaryBridgeAssumption` is logically equivalent to RH.
 732
 733This theorem makes machine-checkable the observation documented in §9:
 734the bridge hypothesis is not weaker than RH — it IS RH expressed through
 735the T1-bounded realizability architecture. -/
 736theorem EBBA_iff_rh :
 737    EulerBoundaryBridgeAssumption ↔
 738      (∀ sensor : DefectSensor, sensor.charge ≠ 0 → False) :=
 739  ⟨unified_rh, EBBA_of_rh⟩
 740
 741/-! ## §11. RS Ontological Route — Direct T1 Exclusion
 742
 743The two-scalar architecture (§§1–10) introduced a carrier proxy and a cost-
 744tracking collapse scalar, then bridged them with `EulerBoundaryBridgeAssumption`.
 745That bridge is logically equivalent to RH (`EBBA_iff_rh`).
 746
 747This section presents the **direct RS ontological route**, which bypasses the
 748proxy entirely.  The argument is:
 749
 7501. **T1 (Law of Existence):**  `J(0⁺) = ∞`.  Near-zero scalars have unbounded
 751   cost.  Proved: `nothing_cannot_exist`.
 752
 7532. **Cost divergence:**  Charge `m ≠ 0` forces annular cost to grow as
 754   `Θ(m² log N)`.  Proved: `nonzero_charge_cost_divergent`.