IndisputableMonolith.NumberTheory.T1BoundaryExclusion
The T1BoundaryExclusion module asserts that no physically realizable ledger can approach the T1 boundary. Researchers deriving the Riemann Hypothesis from the Recognition Composition Law would cite it when closing the realizability side of the argument. The module imports the three-component T1-bounded architecture from UnifiedRH and exposes the exclusion as a named certificate.
claimNo physically realizable ledger $L$ satisfies $d(L_n) → T_1$ as $n → ∞$, where $d$ denotes defect distance.
background
The module belongs to the NumberTheory domain and imports UnifiedRH, whose doc-comment describes the T1-Bounded Realizability Architecture. That architecture replaces the earlier OntologicalPrimeLedger (which asserted bounded total annular cost and thereby contradicted the proved not_realizedDefectAnnularCostBounded) with a structured three-component setup. The setting therefore concerns nonzero-charge realized defect families whose collapse scalars approach zero while remaining inside the T1-bounded Euler realizability scalar.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The module supplies the exclusion certificate required by the downstream BoundaryTransport module, which the latter doc-comment calls the remaining physical bridge in the RH-from-RCL route. UnifiedRH already shows that nonzero-charge realized defect families possess a concrete collapse scalar approaching zero; T1BoundaryExclusion ensures that scalar transports to the T1-bounded realizability scalar.
scope and limits
- Does not prove existence of any specific realizable ledger.
- Does not supply an explicit positive lower bound on defect distance.
- Does not address non-realizable or non-physical ledgers.
- Does not resolve the full Riemann Hypothesis.