Keyboard shortcuts

Press ← or → to navigate between chapters

Press ? to show this help

Press Esc to hide this help

Value elimination and reconstruction

Abstract

Value elimination and reconstruction.

Theorem 1.1 (normalized value forest reconstruction).

Lean statement: D5/S3/FiniteGroups/NikolovSegal/Equation47ValueElimination.normalized_value_forest_reconstruction

Proof. Machine-checked in Lean as D5/S3/FiniteGroups/NikolovSegal/Equation47ValueElimination.normalized_value_forest_reconstruction (✓ std3). ∎

Source. Repository-derived.

Commentary.

Under the genuine value leaf order, solving one residual equation at every powered-component root reconstructs all normalized vertex targets.

Theorem 1.2 (corrected value forest reconstruction).

Lean statement: D5/S3/FiniteGroups/NikolovSegal/Equation47ValueElimination.corrected_value_forest_reconstruction

Proof. Machine-checked in Lean as D5/S3/FiniteGroups/NikolovSegal/Equation47ValueElimination.corrected_value_forest_reconstruction (✓ std3). ∎

Source. Repository-derived.

Commentary.

The reconstructed normalized values give genuine corrected q-powered factor tuples with all prescribed cycle-base scalars.

Nikolov and Segal, On finitely generated profinite groups, I: Strong completeness and uniform bounds, Annals of Mathematics 165 (2007), 171-238, DOI 10.4007/annals.2007.165.171, Section 8, Lemma 8.3 and Proposition 8.4, Section 9, Proposition 9.1 (pages 223-226), and Section 10, Proposition 10.2 and equations (45)-(50) (pages 228-232). Part II: Products in quasisimple groups, Annals of Mathematics 165 (2007), 239-273, DOI 10.4007/annals.2007.165.239, Theorem 1.2 and Lemma 4.1 (pages 247-248). These are formal adaptations and conditional consequences of published mathematics, with elementary finite-set growth supporting bounded-small coverage; no originality claim or redistribution of the papers is made. Large-simple scalar PRODUCT existence, quasisimple central covers, all-length Proposition 10.2, uniform width and restricted Burnside bounds, and full strong completeness remain unproved.

References