Small Nonabelian Monodromy Gives No Converse Counterexample
Sequence claim receipt: seqclaim-07e9873a0cb5f24ed0013fd0.
Sequence claim idempotency key:
grothendieck-ledger-small-nonabelian-monodromy-converse-sweep.
Converse conjecture
Ledger 1275 proves that
is sufficient for power--Mackey compatibility with arbitrary finite kernel (K). For abelian (K) it is also necessary. The open nonabelian converse predicts that every visible monodromy prime must obstruct at least one fiber.
Complete small-group sweep
Every automorphism of the three smallest nonabelian controls was enumerated:
- all 6 automorphisms of (S_3);
- all 8 automorphisms of (D_8);
- all 24 automorphisms of (Q_8).
For each automorphism, its cyclic action, every quotient fiber, and indices 1 through 12 were tested. All 456 action/index cases agree with the product-exponent prediction. No visible action prime survives every fiber.
Status and falsifier
This is exhaustive for the 38 named automorphisms, not a proof for arbitrary nonabelian kernels. The conjecture is falsified by any faithful finite action and index sharing a visible action prime for which every twisted fiber map is bijective. Ledger 1275's sufficient theorem is unaffected by such a future counterexample.
The correspondence remains basis-linear; no general ring Adams operation or physical relative-chain pushforward is asserted.
Durable verification
- Packet:
research/grothendieck/small-nonabelian-monodromy-converse-sweep.md. - Checker:
research/grothendieck/checkers/small_nonabelian_monodromy_converse_sweep.py. - Exact result:
research/grothendieck/results/small-nonabelian-monodromy-converse-sweep.json. - Coverage: 71,664 exact coefficient-value checks over 456 cases.
- Epistemic graph research admission: event 1246.
- Ledger-source admission and publication report: event 1250.
- No site build was run, by operator instruction.