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Affine Lcm Core Arithmetic

Abstract

The actual affine lcm core supplies valuation, fiber, saturation, Euler-product, and prime-block arithmetic.

Theorem 1.1 (Actual affine lcm arithmetic core).

Lean statement: D5/S3/Arith/FibonacciAtomic/AffineLcmCoreArithmetic.arithmetic

Proof. Machine-checked in Lean as D5/S3/Arith/FibonacciAtomic/AffineLcmCoreArithmetic.arithmetic (✓ std3). ∎

Source. Repository-derived.

Commentary.

For every L>=2, the theorem proves the actual affine seed prime-power criterion, the saturated 3-adic core, the positive short-signature fiber, and visible-core identities.

It also proves the residue-theta size error, the additive Euler-product factorization, the valuation defect and square estimates, and the prime-block multiplicativity and Chebyshev logarithm identities used by the public asymptotic result.

References