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IndisputableMonolith.NumberTheory.MinimalVisibilityEngine

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The module defines a minimal visibility engine limited to the KTheta floor hypothesis and a stable budget with no visibility field attached. Number theorists working on the Erdős-Straus conjecture in the Recognition Science setting cite it to reduce the engine to its essential inputs for phase-budget derivations. The module composes directly from the VisibilityFromFloorBudget breakthrough and the PhaseBudgetEngineFromRS conversion, yielding the stripped carrier required by the residual proof chain.

claimThe minimal visibility engine is the structure carrying only the uniform failure floor $K_θ > 0$ and a stable budget $B$ that obeys the Recognition Composition Law accumulation bound, with no visibility field present.

background

This module sits in the NumberTheory domain and supplies the carrier for the minimal engine used in reciprocal-ledger arguments. The KTheta floor is the uniform positive failure threshold per gate; the stable budget is the T1/RCL-bounded total that prevents unbounded accumulation of defects. Upstream, VisibilityFromFloorBudget derives that some admissible gate must succeed for every nonidentity reciprocal ledger once the floor and budget are fixed, while PhaseBudgetEngineFromRS converts that bounded engine into the phase-budget form consumed by the Erdős-Straus residual chain.

proof idea

This is a definition module, no proofs.

why it matters in Recognition Science

The module supplies the minimal carrier that feeds the phase-budget engine already consumed by the Erdős-Straus residual proof chain. It closes the scaffolding step that follows the VisibilityFromFloorBudget breakthrough by removing the visibility field while retaining the KTheta floor and stable budget. In the Recognition framework it supports the direct passage from T1/RCL budget bounds to concrete number-theoretic applications.

scope and limits

depends on (2)

Lean names referenced from this declaration's body.

declarations in this module (5)