IntegerLedgerState
plain-language theorem explainer
Positive integers are the states of the multiplicative integer ledger. Number theorists grounding the arithmetic base for the RH bridge in Recognition Science cite this when defining ledger atoms prior to Euler weighting. The definition is a direct abbreviation of the standard positivity predicate on natural numbers.
Claim. The predicate on a natural number $n$ holds precisely when $n > 0$, identifying positive integers as the states of the multiplicative integer ledger.
background
The module grounds the arithmetic ledger used by the RH bridge, with primes as irreducible postings of the multiplicative positive-integer ledger. Positive integers occupy the states of this ledger before any weighting into the Euler product occurs. Upstream structures calibrate the J-cost on the positive reals and supply the active edge count per fundamental tick at D=3.
proof idea
Direct definition as the standard positivity predicate on natural numbers. No lemmas or tactics are applied; the body is the one-line abbreviation 0 < n.
why it matters
This supplies the arithmetic base predicate that feeds PrimeLedgerCert and the theorem establishing every prime is a positive ledger state. It fills the initial step of the prime ledger atom construction before primes are weighted into the Euler ledger, consistent with the framework's separation of classical arithmetic from the Recognition Science forcing chain.
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