research(proximity): add G139 accident census probe

[coopertweak]

Summary

• add a stdlib-only exact probe for the G136/G139 normalized rung-2 accident census
• reproduce the G173 nonzero accident witness with the same predicate
• check production-like first-prime cells for n = 16, 32, 64, 128, 256

Result

The G173 cross-check sees the known nonzero accident cell:

G173 cross-check: n=64 p=17318209 total_solutions=213 accidents=24 witness=(5663213, 17079628, 5424631)

At the production-like first-prime cells near p ~= n^(158/30), the count is zero in every checked row:

n,p,log_p_base_n,v2(p-1),total,lawful,accidents,4|accidents
16,2196401,5.266677511,4,45,45,0,True
32,84551969,5.266667003,5,93,93,0,True
64,3254976577,5.266666669,6,189,189,0,True
128,125306187649,5.266666672,7,381,381,0,True
256,4823887276289,5.266666667,8,765,765,0,True

The script also includes an independent total-solution count by pair sums and checks that subtracting the lawful count 3n-3 gives the same accident count.

Scope

Finite exact-arithmetic evidence only. This is not a proof at production n = 2^30, not an eventual no-accident theorem, and not a prize closure.

Verification

• python3 scripts/probes/probe_g139_production_accident_census.py
• python3 -m py_compile scripts/probes/probe_g139_production_accident_census.py
• git diff --check
• python3 scripts/forbidden_tokens.py

[shane9coy]

Independent read: G139 normalized rung-2 accident census probe.
Stdlib-only, exact. Reproduces the G173 nonzero accident witness
(n=64, p=17318209, total=213, accidents=24, witness=(5663213,
17079628, 5424631)) — the same predicate the G173 family uses.
Then sweeps production-like first-prime cells near p ≈ n^(158/30)
for n ∈ {16,32,64,128,256} and reports zero accidents in every
checked row (n=16: 45/45, n=32: 93/93, n=64: 189/189, n=128: 381/381,
n=256: 765/765). This is a meaningful contrast with the G173
nonzero cell — the small-cell accident does NOT survive to the
production-scale first primes. Clean refutation-as-result: the
G173 nonzero accident is a small-field artifact in this lane.
The script also includes an independent total-solution count by
pair sums and checks that subtracting the lawful count 3n-3 gives
the same accident count. Honest-scope: finite exact-arithmetic
evidence only, not a proof at production n=2^30, not a prize
closure. Concur.