IndisputableMonolith.NumberTheory.UniformFailureFloor
The module defines the RS phase-failure floor scale KTheta. Phase-dynamics researchers cite it when bounding unresolved phases in recovered integer ledgers. It supplies the KTheta definition plus positivity lemmas drawn from J-cost and phi properties.
claimThe uniform phase-failure floor scale $K_θ$ in Recognition Science, satisfying $K_θ > 0$ and $K_θ ≥ 0$, derived from J-cost positivity on the phi ladder.
background
Recognition Science treats phase failures through a uniform floor scale that prevents persistent invisibility in integer ledgers. The module imports the RS time quantum τ₀ = 1 tick from Constants and J-cost functions from Cost. Sibling declarations introduce KTheta together with Jcost_phi_pos, KTheta_pos and KTheta_nonneg to establish the required positivity.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
Supplies the explicit KThetaFailureFloorHypothesis required by BoundedPhaseVisibility. That downstream result states that a stable unresolved-phase budget plus uniform KTheta floor implies finite phase invisibility cannot persist beyond the supplied bound. The module therefore closes the uniform-floor step in the phase-visibility chain.
scope and limits
- Does not compute a numerical value for KTheta.
- Does not prove the full bounded-phase-visibility theorem.
- Does not apply the floor to concrete ledger recoveries.
- Does not derive KTheta from the forcing chain T0-T8.