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Primitive-root prime generation assumption audit
Family 029: Primitive roots for every admissible integer base. First application triage, 9 October 2026 Australia/Brisbane.
Problem and potential new use
Finite-field library researchers can examine whether the new all-base infinitude statement removes assumptions from a relevant deterministic backend.
Applicability and commercial boundary
The lower count has base-dependent constants and sufficiently large x; it does not provide a fast next-prime algorithm, Artin’s exact density or cryptographic parameter security.
Initial business decision
Research infrastructure or conditional engineering until a computable implementation, effective bounds and a recurring buyer need are demonstrated. No commercial novelty or profitability is established.
Next verification action
Trace the exact primitive-root generation theorem and effective costs before modifying opportunity 016.
Evidence scope
The catalog statement was individually reviewed. Main-paper abstracts and available selected formal scope notes were also inspected. No independent Lean verification was run. Source revision fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb. See source metadata.