IndisputableMonolith.NumberTheory.VisibilityFromFloorBudget
This module defines admissible gates congruent to 3 mod 4 in the explicit form 4i + 3 for i below k. Researchers reconstructing phase budgets in integer ledgers cite it when applying bounded visibility results to RS-physical inputs. The module assembles its gate set directly from the imported BoundedPhaseVisibility and SubsetProductPhase layers without internal proofs.
claimThe admissible gates are the integers $c = 4i + 3$ for $i < k$ satisfying $c ≡ 3 mod 4$.
background
The module sits inside the bounded phase visibility setting: a recovered integer ledger carries a stable unresolved-phase budget while failed gates share a uniform KTheta floor, so that finite phase invisibility cannot persist beyond the supplied bound. It also imports the finite subgroup-generation layer from SubsetProductPhase, which converts a target phase supplied by a square-budget divisor into the explicit gate structure needed for the Erdős-Straus residual argument.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The module supplies the gate set required by MinimalVisibilityEngine, which repackages the bounded visibility engine by replacing the visibility field with the explicit theorem hits_balanced_phase_of_floor_and_budget and retaining only the stable budget and uniform KTheta floor as RS-physical inputs.
scope and limits
- Does not prove the KThetaFailureFloorHypothesis.
- Does not handle infinite or unstable phase budgets.
- Does not construct the full Erdős-Straus unit-fraction decomposition.