INDEPENDENT kappa=1 PRESCRIBED-INDEX CERTIFICATE, d=34..64
================================================================

Equation certified:
    n - 1 = d * lambda(n)
for squarefree Carmichael n (kappa=1).

The program certify_kappa1_d34_d64.py implements the finite prescribed-index
ratio recursion independently.  It uses the last-two-prime divisor-pair identity
from the manuscript.  Factorization is used only as an untrusted backend:
every returned factor is reconstructed and independently primality-certified.
Below Sorenson-Webster psi_12 it uses the first twelve prime Miller-Rabin bases;
below psi_13 it uses the first thirteen; above psi_13 it uses a recursive
Pocklington certificate after exact factorization of n-1.

The two expensive empty cases were partitioned exactly, not truncated:

    d=34: 15 (s,H) branches, 344,284 last-two-prime prefixes,
          max exact ratio prime bound 2,140,591, no solution.

    d=35: 15 (s,H) branches, 381,524 last-two-prime prefixes,
          max exact ratio prime bound 7,296,343, no solution.

verify_kappa1_split_logs.py sums the non-overlapping captured split logs and
checks these exact totals and all false overflow/certificate-abort flags.
The p2-count TSV files document which second-prime subbranches actually contain
prefixes, so gaps in the split log filenames are zero-prefix regions rather than
unsearched intervals.

For d=36..48 and d=49..64 the captured whole-range logs reproduce the published
Pinch table exactly.  The independently generated nonempty kappa=1 indices in
34..64 are:
    37,39,43,44,45,47,48,49,50,52,53,54,55,60,61.
Pinch is therefore an external cross-check, not a proof dependency.

Historical-log banner note
--------------------------
Some split logs for d=34 and d=35 were captured immediately before a cosmetic
banner was corrected.  Those logs say "factor_backend=GNU coreutils factor".
The source version that generated them already called sympy.factorint in the
batch factorization function; the banner alone was stale.  This does not affect
any acceptance decision because every returned factor was reconstructed and
independently certified.  certify_kappa1_d34_d64_log_version.py is retained so
this provenance is auditable; certify_kappa1_d34_d64.py contains the corrected
banner and identical certification logic plus clearer split-filter options.
