def
definition
def or abbrev
unified_rh_cert_of_bridge
show as:
view Lean formalization →
formal statement (Lean)
635noncomputable def unified_rh_cert_of_bridge
636 (bridge : EulerBoundaryBridgeAssumption) : UnifiedRHCert where
637 t1_barrier := t1_cost_barrier
proof body
Definition body.
638 admissibility := euler_trace_admissible
639 realizability := euler_physically_realizable
640 realized_collapse := realizedDefectCollapseBoundaryApproaching_of_nonzero_charge
641 t1_no_boundary_crossing := by
642 intro sensor
643 letI : PhysicallyRealizableLedger sensor := euler_physically_realizable sensor
644 exact physicallyRealizableLedger_not_boundaryApproaching sensor
645 boundary_bridge := bridge
646 divergence := nonzero_charge_cost_divergent
647 rh := unified_rh bridge
648
649/-! ## §9. Structural obstruction analysis
650
651The `EulerBoundaryBridgeAssumption` demands that collapse of the realized
652defect family (proved for `charge ≠ 0`) transports to `BoundaryApproaching`
653for the bounded Euler proxy. But the bounded proxy is proved NOT boundary-
654approaching. Therefore the bridge, if true, completes a contradiction chain.
655
656The following theorems make the structural tension explicit:
657- The realized collapse scalar approaches `0` (proved).
658- The Euler scalar proxy does not approach `0` (proved).
659- These are **distinct** scalars, so transport between them is nontrivial.
660- No single scalar can simultaneously collapse and remain T1-bounded (proved:
661 `not_realizedDefectCollapseScalar_t1_bounded`).
662
663The bridge hypothesis asks for a *semantic* connection: the physical meaning
664of cost divergence (which drives the collapse scalar toward `0`) must also
665force the realizability proxy toward `0`. This is not a pure inequality; it
666requires relating the annular-cost growth (a topological winding count)
667to the carrier-derived proxy (a normalized Euler stiffness ratio).
668
669**Equivalent classical formulations** of this bridge:
6701. Primes in short intervals: `π(x+x^θ) - π(x) ~ x^θ / log x` for θ < 1/2.
6712. Ledger stiffness: Carleson-type energy of `log ζ⁻¹` bounded at all scales.
6723. Bandlimited explicit formula packing.
673Each of these is known to be **equivalent to RH** (see Fundamental Theorem
674of Classical Obstruction in `planning/RH_UNCONDITIONAL_CLOSURE_PLAN.md`). -/
675
676/-- The bridge hypothesis, combined with proved results, yields a complete
677contradiction for nonzero charge. This lemma isolates the logical core:
678any scalar path that is simultaneously boundary-approaching and not-boundary-
679approaching is absurd. -/