[pinterbanget]

Summary

This adds research/depth5-connector-independent-bfs/, an independent reproduction of #4281 (petalas). #4281 gives the shortest unsigned depth-five dirty chain connector at small characteristic.

#4281's m = 4 lower bounds (28 for c = 1, 3, 24 for c = 2) rest on a BFS over 4^15 ≈ 1.07·10⁹ states. #4281 runs it only as an opt-in command needing about 20 GB, so its CI never repeats it, and nobody else had.

Claim type: an independent exhaustive finite computation and certificate check. No new κ.

Result

Case	This package	#4281
depth 5, m = 2	16	16
depth 5, m = 3	24, 24	24
depth 5, m = 4	28, 24, 28 (51 s, 1.07 GB)	28, 24, 28 (opt-in)
depth 4, m = 2..5 (control)	12, 18, 20, 25	#4249's values

Witnesses. All 173 vendored witnesses and the three m = 4 words pass three checks:

• shape: length 5m, each call used m times;
• the unitriangular group product;
• three literal replays with random dirty registers in (Z/m)² and random noncommuting 2×2 maps, checking that z_1..z_4 are restored and y gains exactly c·B5B4B3B2B1·x.

Controls. A dropped call and an adjacent noncommuting swap are rejected.

Method and independence

Nothing is imported from #4281, and its numpy BFS is not used.

• bfs.c is a separate C implementation: a uint8 distance table over base-m digit states with layer scans, stopping once every target residue is reached.
• verify.py has its own standard-library BFS for the small cases. It checks that evidence/BFS-RUNS.txt was recorded for this exact bfs.c (by SHA256) and matches Bound the depth-five chain connector: 8m at m = 2, 3, residue-dependent at m = 4, floor 5m for 9 ≤ m ≤ 20 (no new κ) #4281's minima.
• The C runs are local evidence. They were run with Apple clang 21 on arm64. CI reads the recorded output and does not recompile.
• witnesses.json is vendored byte-identically, SHA256-checked, with vendor/NOTICE.md.

python3.12 -B scripts/research_package.py --package research/depth5-connector-independent-bfs --check-only
  PASS_PACKAGE_METADATA_AND_PINS (not a mathematical acceptance check)
python3.12 -B scripts/research_package.py --package research/depth5-connector-independent-bfs
  PASS_REGISTERED_RESEARCH_PACKAGE research/depth5-connector-independent-bfs outcome=completed
cc -O2 -DM=4 -DD=5 -o bfs research/depth5-connector-independent-bfs/bfs.c && ./bfs
  M=4 D=5 c=1 dist=28 / c=2 dist=24 / c=3 dist=28

Head: 806922e07f0a83ab37d0897e1750033e72fa0507.

Not covered

• The eleven residues at m = 5 to 8 that Bound the depth-five chain connector: 8m at m = 2, 3, residue-dependent at m = 4, floor 5m for 9 ≤ m ≤ 20 (no new κ) #4281's search missed, and m > 20.
• Any physical price, admission or caller.

Task and overlap

• Card: connector-alphabet-change, refined, priority revision 7.
• Base: canonical main 12fa8c5c844be21bfefb38a19503fbd867a11244.
• Bound the depth-five chain connector: 8m at m = 2, 3, residue-dependent at m = 4, floor 5m for 9 ≤ m ≤ 20 (no new κ) #4281 has no comments, and no other PR or discussion reruns its BFS.

Credit

The connector model, Lemma 1, the witnesses and the m = 4 words are Nick Petalas's (#4281, building on #4249 and #4263). Prepared by Ryanson Jonathan with substantial Claude Code (Claude Opus 5.5) assistance. Apache-2.0.

🤖 Generated with Claude Code