Norm and Resonance Primes Obey a Three-Regime Law
Sequence claim receipt: seqclaim-af3732637c518ad4a6c9b2a8.
Sequence claim idempotency key:
grothendieck-ledger-norm-resonance-prime-trichotomy.
Prime trichotomy
For the bidegree ((d,\rho)) of Ledger 1302,
Therefore every prime lies in exactly one of three regimes:
- good for both norm and resonance;
- bad for both norm and resonance;
- norm-invertible but resonance-obstructed.
The apparent fourth regime—norm-bad but resonance-good—is impossible.
Degree localization is insufficient
Localizing coefficients to invert (d) repairs the scalar norm (\phi_!\phi^*=d\operatorname{id}), but does not necessarily repair the basis-level power--Mackey square. For (A_4\to C_3),
At prime three the norm scalar is a unit, yet the order-three conjugation action obstructs the third-power fiber word. This is the exact resonance-only regime.
Scope and verification
The checker classifies primes (2,3,5,7) for identity, cyclic, (A_4\to C_3), and terminal (A_4) controls and verifies the impossible cell is empty. Coefficient localization does not construct a physical relative-chain map.
- Proof packet:
research/grothendieck/norm-resonance-prime-trichotomy.md. - Checker:
research/grothendieck/checkers/norm_resonance_prime_trichotomy.py. - Exact checker result: all four controls and primes (2,3,5,7) classified, the norm-only bad cell empty, and the (A_4\to C_3) prime-three resonance-only cell present; all assertions pass.
- Epistemic graph theorem, prime census, and source admission: event 1311.
- No site build was run, by operator instruction.