Status: executed bounded research attempt, then rejected in part by coordinator self-review. The route remains open at the generator-to-certificate implication. No claim of impossibility or novelty is made.
Input: PR278 at cc33a9a208609ac584a4f1c470d1808153dc8213 and the exact odd-split source blob 395cc0430fd71cf06f24ae1e5f58c80bc8d40734. The full geometric divisor/norm dependency chain was not read in this attempt.
Muse session 01a11bc2-72d0-7593-a8e7-34e88cb8dab3, run 07e1e043-e891-4914-9d7d-3f42b72288da, completed with the configured meta/muse-spark-1.3-contributor model, high reasoning, maximum 20 steps. Shell/write/web tools were disabled. The first sandbox attempt failed before execution because session-lock and Keychain access were unavailable; an authorized escalation used the existing login. No credentials changed. Dollar cost and exact quota are not reported by this runtime.
The raw response is retained in muse-response-extracted.md. It is not an accepted mathematical report. Its useful distinction is that a transcript whose soundness relies on a zero-free hypothesis is not an unconditional Pratt/Pocklington primality certificate. It produced no verified algorithm improving on the existing conditional Miller consequence.
Coordinator corrections to the response:
- An integer-witness cutoff does not by itself justify restricting to prime bases with the same cutoff. For n=3317044064679887385961981 every prime base at most 22 passes strong testing but base 22 fails. The exact modular test below confirms this. This does not refute a prime-base bound separately proved using character/subgroup information at the actual logarithmic cutoff. Such a proof is missing from the response.
- Every finite group generated by a set admits a generating subset of size at most floor(log2 |G|), by adjoining an element outside the subgroup until generation is complete. Thus the response's claim that there is no size bound is false. Finding the subset and efficiently verifying generation are distinct algorithmic questions, not a proof of logical circularity or impossibility.
- The supplied odd-split source itself has 4Nqg=2Nq(q-1)(N-2), giving g=1 at (q,N)=(3,3) and g=6 at (5,5), not the response's 2 and 8. The claimed absence of an oracle-free implementation also does not follow from unread divisor/norm sections. Those are unverified leaves.
- The elementary coefficient bounds 3*6^3=648 and 5*10^5=500000 are correct; they alone do not lower the proposition's characteristic threshold.
The serious falsification therefore rejected an unsupported shortcut and part of the model's route-closure reasoning. It did not refute the upstream theorem or exhaust the algorithmic route. Given the two more concrete surviving routes, further effort here is deferred until the full odd-degree dependency chain is available or a precise certificate mechanism is proposed.
Reproduce the numerical checks with the repository Python: python falsify.py. All decisions are exact integer arithmetic. The one large integer is not claimed to have a newly determined factorization.