7 Production providers and final threshold split
Trust tier: HEAVY+EF+PF-U. The closed Chapter-14 proof supplies ‘LargeOddSmoothedInput‘. Its exact current transitive boundary contains external finite-computation atoms; the formerly native certificate families have been retired.
Apply the closed large-odd endpoint pointwise. The explicit trust-family edges are an audit summary of the fresh transitive axiom closure; exact atoms and equations are linked in the appendices.
Trust tier: EF-U. Helfgott–Platt Theorem 4.1 supplies ‘FiniteOddGoldbachInput‘.
The source-shaped external theorem already returns the exact ‘PrimeTripleFor‘ witness required by the finite contract.
Trust tier: HEAVY+EF+PF-U. Every odd natural number \(n\ge 7\) is a sum of three primes.
Instantiate the base-trio conditional threshold split with the production large-odd and finite providers.
The finite provider is precisely Helfgott–Platt Theorem 4.1. The large provider is the closed major/minor/tail construction above. The final proof term merely supplies those providers to the conditional threshold split.