IndisputableMonolith.NumberTheory.EffectivePrimePhaseInput
The module supplies the EffectivePrimePhaseInput interface that converts a bounded prime phase supply into a concrete subset-product phase hit for every trapped ledger. Researchers closing the Erdős-Straus conjecture through phase-budget arguments cite it as the bridge between distribution and finite generation layers. The module assembles the two imported interfaces into a single package without new theorems.
claimFor every trapped ledger $L$, a bounded prime phase supply $P$ produces a subset-product phase hit on $L$.
background
The module operates in the Erdős-Straus residual setting of Recognition Science. PrimePhaseDistribution supplies the RCL algebra and finite square-budget closure, naming the distribution statement that instantiates BoundedBalancedSearchEngine. SubsetProductPhase isolates the finite subgroup-generation layer that converts a square-budget divisor phase into the required unit-fraction construction.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The module feeds the PhaseBudgetEngine package required by PhaseBudgetToErdosStraus, which composes the phase-budget interface with the already-proved Erdős-Straus RCL closure chain. It thereby supplies the missing prime-phase input that turns the T1/RCL budget and finite gate enumeration into a bounded subset-product hit for every residual trap.
scope and limits
- Does not prove the prime phase distribution theorem.
- Does not construct explicit unit fractions.
- Does not enumerate finite gates or set the uniform failure floor.
- Does not address global equidistribution beyond the bounded case.
used by (1)
depends on (2)
declarations in this module (7)
-
structure
EffectivePrimePhaseInput -
def
primePhaseBoxDistribution_of_effectivePrimePhaseInput -
def
boundedBalancedSearch_of_effectivePrimePhaseInput -
theorem
erdos_straus_residual_from_effectivePrimePhaseInput -
structure
RSPrimePhaseEquidistribution -
def
effectivePrimePhaseInput_of_rsPrimePhaseEquidistribution -
theorem
erdos_straus_residual_from_rsPrimePhaseEquidistribution