Measure Factorization

Abstract

Actual derived factorization of every uniformly bounded integer family through the constructed local reflection of the protected P. The tensor square is proved in BoundedMeasures; no D(Solid) realization is assumed. New proofs, Apache-2.0, following Rodriguez Camargo’s concrete measure argument.

Theorem 1.1 (local PTo Integer Measures unit).

Lean statement: D5/S3/HomologicalAlgebra/Solid/MeasureFactorization.localPToIntegerMeasures_unit

Proof. Machine-checked in Lean as D5/S3/HomologicalAlgebra/Solid/MeasureFactorization.localPToIntegerMeasures_unit (✓ std3). ∎

Source. Repository-derived.

Commentary.

The exact declaration is supplied by the compiled Lean source. Actual derived factorization of every uniformly bounded integer family through the constructed local reflection of the protected P. The tensor square is proved in BoundedMeasures; no D(Solid) realization is assumed. New proofs, Apache-2.0, following Rodriguez Camargo’s concrete measure argument.

Theorem 1.2 (bounded Family Local Lift comparison).

Lean statement: D5/S3/HomologicalAlgebra/Solid/MeasureFactorization.boundedFamilyLocalLift_comparison

Proof. Machine-checked in Lean as D5/S3/HomologicalAlgebra/Solid/MeasureFactorization.boundedFamilyLocalLift_comparison (✓ std3). ∎

Source. Repository-derived.

Commentary.

Every uniformly bounded integer family factors through the actual local reflection of P, with the canonical measure comparison. This is a proved concrete comparison, valid for all light profinite S, not a realization assumption.

References

• Truth anchor: D5/S3/HomologicalAlgebra/Solid/MeasureFactorization.boundedFamilyLocalLift_comparison
• Truth anchor: D5/S3/HomologicalAlgebra/Solid/MeasureFactorization.localPToIntegerMeasures_unit
• Dependency: D5/S3/HomologicalAlgebra/Solid/BoundedMeasures