JOURNAL DRAFT 10 REFERENCE EXECUTION REPORT
==================================
Date: 2026-08-23
Platform: Windows x64 reference host
Julia: 1.12.6 (Juliaup release channel)
Parallel Julia threads reported: 16
External Julia package dependencies in proof scripts: none

RESULTS
-------
[PASS] d<=8 regression self-test
  Command: julia +release overlap_U_search.jl --selftest
  Final line: SELFTEST PASSED.

[PASS] exhaustive general search, 9<=d<=32
  Command: julia +release -t auto overlap_U_search.jl --start=9 --stop=32 --out=run_d9_d32_final --resume=false
  Started: 2026-08-23T03:18:57.406
  Finished: 2026-08-23T03:19:08.249
  Result: every manuscript row d=9,...,32 reproduced exactly.

[PASS] independent arithmetic verifier, 9<=d<=32
  Command: julia +release verify_overlap_U_output.jl run_d9_d32_final
  Result: Verification passed; 96 reported incidences checked.
  The verifier recomputed n, phi(n), lambda(n), L, kappa, H, P, c,
  deterministic primality of reported prime factors, divisibility conditions,
  and DONE-file output hashes.

[PASS] d=33 reduced kappa=1 certification
  Command: julia +release certify_d33_reduced.jl
  Result: all 29 remaining kappa=1 parameter branches exhausted; no solutions.
  The two omitted kappa=1 branches are exactly the two eliminated analytically
  by the 2-adic parity lemma in the manuscript.

[PASS] d=33 kappa>1 certification
  Command: julia +release -t auto certify_d33_noncar.jl
  Result: all 135 kappa>1 parameter branches exhausted; exactly
    1047619, 2210671, 3494701, 15197491, 25158871, 93755971
  were found. The script then verified the six factorizations and the
  (kappa,H,j,lambda,L) invariants displayed in the paper.

[PASS] prime-mass minimization through d=33
  Command: julia +release prime_mass_d33_check.jl
  Output:
    generic mass = 0.97018597188211062026285264731291330049308018665623587048...
    minimum non-perfect-power mass = 0.96704268058658268861160528653168362432789595850908773080...
    minimizing squarefree part = 2
    tail certificate G-R2 > G/1331 = true

VALIDATION FIXES DISCOVERED BY THE REFERENCE RUN
------------------------------------------------
Three Julia-execution defects in Draft 7 were found and repaired before this
archive was frozen:
1. a local variable named `local` (a Julia keyword) was renamed local_factor;
2. Python-style enumerate(iterable, start) was replaced by Julia enumerate plus
   an explicit line-number offset in the independent verifier;
3. top-level soft-scope assignments in the density checker were made explicit.
The kappa>1 d=33 certifier was also parallelized across independent branches.

All hashes in SHA256SUMS.txt refer to the post-fix frozen files.


DRAFT 10 STATUS NOTE
--------------------
The proof-critical programs and captured successful reference runs are unchanged
from the frozen 2026-08-23 computation. Journal Draft 10 adds a formal proof that
the implemented support, ratio, overlap-budget, and final-prime pruning rules are
necessary, and clarifies that verify_overlap_U_output.jl is an arithmetic verifier
of reported solutions rather than a second search implementation. No algorithmic
change requiring a new search run was made.
