Product-Integral Invariants of Exponent Sets: Subset-Sum Algebra, Stability Bounds, and a Prime-Indexed Limit
Year: 2026
Type: preprint
Abstract: This preprint introduces a product-integral invariant of finite and directed exponent sets, F_S = ∫_0^1 ∏_{n ∈ S}(1 - u^n) du. The paper develops its exact subset-sum expansion, monotonicity and stability bounds, signed-cube interpretation, and a prime-indexed directed limit. It includes Lean 4 formalization support and a formally certified rational sandwich computation for the prime limit. Lean formalization repository: https://github.com/alerad/productinvariants
Author: Radisic, Alejandro
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7162324732
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