1354 — Intrinsic Primes and Norm Support Are Distinct
Epistemic-graph event: 1378.
The conditional pointed pi_0 construction and regular-fiber norm homology
produce primes in different senses.
On pi_0, the free additive Carrier classifies its endomorphisms and becomes
the initial semiring. Prime elements then arise internally from divisibility
and irreducibility, without an external prime list or degree map. This is
genuine conditional prime formation.
By contrast,
only detects the prime divisors of an already supplied fiber degree. If a
source-derived degree functor identifies that correspondence with dU, then
for d>2
Norm support is therefore a possible downstream realization of intrinsic
divisibility, not its origin. The exceptional H_2=0 shows that homology is
not a faithful prime detector by itself.
Scope: the initial semiring remains conditional on the explicit pointed monoidal relaxation. No full-Carrier lift, Frobenius, Euler product, or physical chain realization follows.
Durable verification:
- Research packet:
research/grothendieck/two-prime-mechanisms-audit.md. - Inputs:
research/nima/phase-i-endomorphism-semiring.md,research/nima/phase-i-intrinsic-primes.md, and Ledgers 1348 and 1350. - Epistemic-graph event: 1378.