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Bounded Object

Abstract

The actual bounded-integer-sequence condensed abelian group. Its presheaf consists of integer-measure sections with a single bound on all coordinates. Sheafification is left exact, so its inclusion in integer measures is a genuine monomorphism. No derived realization or projective-resolution assumption is used. New proofs, Apache-2.0. Research construction: Juan Esteban Rodríguez Camargo, Notes on Solid Geometry, Lemmas 3.3.3–3.3.4, and root’s immutable checked realization response. The retained supplier and official Mathlib attributions are unchanged.

Theorem 1.1 (bounded Integer Sections restrict).

Lean statement: D5/S3/HomologicalAlgebra/Solid/BoundedObject.boundedIntegerSections_restrict

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

Source. Repository-derived.

Commentary.

The exact declaration is supplied by the compiled Lean source. The actual bounded-integer-sequence condensed abelian group. Its presheaf consists of integer-measure sections with a single bound on all coordinates. Sheafification is left exact, so its inclusion in integer measures is a genuine monomorphism. No derived realization or projective-resolution assumption is used. New proofs, Apache-2.0. Research construction: Juan Esteban Rodríguez Camargo, Notes on Solid Geometry, Lemmas 3.3.3–3.3.4, and root’s immutable checked realization response. The retained supplier and official Mathlib attributions are unchanged.

Theorem 1.2 (free Section Equiv coordinate).

Lean statement: D5/S3/HomologicalAlgebra/Solid/BoundedObject.freeSectionEquiv_coordinate

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

Source. Repository-derived.

Commentary.

The exact declaration is supplied by the compiled Lean source. The actual bounded-integer-sequence condensed abelian group. Its presheaf consists of integer-measure sections with a single bound on all coordinates. Sheafification is left exact, so its inclusion in integer measures is a genuine monomorphism. No derived realization or projective-resolution assumption is used. New proofs, Apache-2.0. Research construction: Juan Esteban Rodríguez Camargo, Notes on Solid Geometry, Lemmas 3.3.3–3.3.4, and root’s immutable checked realization response. The retained supplier and official Mathlib attributions are unchanged.

References