[pinterbanget]

Summary

This adds research/chain-connector-tables-check/. It independently checks three open PRs by Nick Petalas that give the shortest unsigned dirty chain connector at depths three and four:

• Prove the shortest unsigned depth-three chain connector in every characteristic (3m; 4m at c ≡ -1 for m ≤ 4; no new κ) #4249, depth three: 3m, except 4m at (2,1), (3,2) and (4,3). It also gives the depth-four values 12, 18, 20 and 25 at m = 2..5.
• Attain the depth-four chain connector floor 4m for every 6 ≤ m ≤ 32 (no new κ) #4263, depth four: 4m for 6 ≤ m ≤ 32.
• Attain the depth-four chain connector floor 4m for every 33 ≤ m ≤ 64, via an exact row model (no new κ) #4280, depth four: 4m for 33 ≤ m ≤ 64, with records in a compressed row model.

#4280 says these together make the depth-four minimum "known exactly for 2 ≤ m ≤ 64", while noting that #4249 and #4263 are "not rechecked here". Nobody had rechecked any of them.

Claim type: an independent finite check, by exhaustive search and certificate verification. No new κ.

Result

Claim	Result
#4249 depth-three minima, BFS m = 2..8	3m, except 4m at (2,1), (3,2), (4,3)
#4249 Lemma 3 word, every 5 ≤ m ≤ 400 and every c (79,794 words), plus the (6,5) word	all correct
#4249 depth-four table, BFS m = 2..4	12, 18, 20
#4263's 486 words	all balanced and correct
#4280's 1,520 records, decoded into words from Lemma 2's definitions	all balanced and correct

• Coverage. Every (m, c) with 6 ≤ m ≤ 64 has a depth-four witness of length 4m.
• Literal replays. These use random noncommuting 2×2 maps and dirty registers, and confirm restoration and the exact gain.
• Controls. A changed ρ(1) and a dropped call are rejected.

Method and independence

• Standard library only; runs in about 35 seconds. Nothing is imported from Prove the shortest unsigned depth-three chain connector in every characteristic (3m; 4m at c ≡ -1 for m ≤ 4; no new κ) #4249, Attain the depth-four chain connector floor 4m for every 6 ≤ m ≤ 32 (no new κ) #4263 or Attain the depth-four chain connector floor 4m for every 33 ≤ m ≤ 64, via an exact row model (no new κ) #4280.
• Correctness test. It uses the unitriangular group product (Lemma 1), plus the literal replays.
• Row-model decoder. It reads only Attain the depth-four chain connector floor 4m for every 33 ≤ m ≤ 64, via an exact row model (no new κ) #4280's Lemma 2 definitions: λ's column heights give the 2/3 path, ρ places the calls 1 and β the calls 4. All 1,520 decoded words are correct, which checks the record format and the witnesses together.
• The two witness files are vendored byte-identically and SHA256-checked, with vendor/NOTICE.md.

python3.12 -B scripts/research_package.py --package research/chain-connector-tables-check --check-only
  PASS_PACKAGE_METADATA_AND_PINS (not a mathematical acceptance check)
python3.12 -B scripts/research_package.py --package research/chain-connector-tables-check
  PASS_REGISTERED_RESEARCH_PACKAGE research/chain-connector-tables-check outcome=completed

Head: 8b89dbb4b29ff4c9f5abf31b109b46f82666fca7.

Not covered

• The depth-four value 25 at m = 5. A Python BFS is slow there; my separate C BFS in Independently reproduce #4281's depth-five connector minima: m = 4 gives 28, 24, 28 by a separate exhaustive BFS; all 173 witnesses verified (no new κ) #4341 reproduces it.
• Attain the depth-four chain connector floor 4m for every 33 ≤ m ≤ 64, via an exact row model (no new κ) #4280's Lemma 3, Classify depth-four chain connector count vectors and unequal-price tariffs for m = 2..5 (no new κ) #4279's count vectors, m > 64, and any physical price.

Task and overlap

• Card: connector-alphabet-change, refined, priority revision 7.
• Base: canonical main 12fa8c5c844be21bfefb38a19503fbd867a11244.
• None of Prove the shortest unsigned depth-three chain connector in every characteristic (3m; 4m at c ≡ -1 for m ≤ 4; no new κ) #4249, Attain the depth-four chain connector floor 4m for every 6 ≤ m ≤ 32 (no new κ) #4263 or Attain the depth-four chain connector floor 4m for every 33 ≤ m ≤ 64, via an exact row model (no new κ) #4280 has an outside check. Prove the shortest unsigned depth-three chain connector in every characteristic (3m; 4m at c ≡ -1 for m ≤ 4; no new κ) #4249 has one comment, from its author.

Credit

The model, lemmas, construction, witnesses and row model are Nick Petalas's. Prepared by Ryanson Jonathan with substantial Claude Code (Claude Opus 5.5) assistance. Apache-2.0.

🤖 Generated with Claude Code