Explain the theorem prime_lattice_minimum from IndisputableMonolith.Mathematics.PrimeCostSpectrumFromJCost.

permalink: https://pith.science/recognition/ask/explain-the-theorem-prime-lattice-minimum-from-indisputablem-bccc8427 · first asked 2026-05-17 · browse all asks

confidence: high in recognition cached

The theorem prime_lattice_minimum asserts Jcost 1 = 0. This is established directly as := Jcost_unit0. In context, it means zero recognition cost at ratio 1, so a prime lies exactly on the lattice. The module uses it to build PrimeCostCert, which pairs this with the count of five regimes from primeDistributionCount. The surrounding claims on zeta zeros and prime counting are noted as MODEL level.

cited recognition theorems

PrimeCostSpectrumFromJCost.prime_lattice_minimum Direct theorem stating Jcost 1 = 0, the core claim to explain
PrimeCostSpectrumFromJCost.primeDistributionCount Supports the PrimeCostCert that incorporates the lattice minimum result

outside recognition

Aspects Recognition does not yet address:

Deeper connections to Riemann zeta zeros and prime counting function interpretations
Actual proofs of prime distribution regimes, which require Zhang-Maynard or deeper RS-prime-cost theory

recognition modules consulted

IndisputableMonolith.Mathematics.PrimeCostSpectrumFromJCost
IndisputableMonolith.Mathematics.PrimeGapFromJCost
IndisputableMonolith.NumberTheory.PrimeCostSpectrum (truncated)
IndisputableMonolith.Mathematics.FundamentalTheoremCalculusFromRS
IndisputableMonolith.Mathematics.GoldbachFromRS

The Recognition library is at github.com/jonwashburn/shape-of-logic. The model is restricted to the supplied Lean source and instructed not to invent theorem names. Treat output as a starting point, not a verified proof.