[TomZahavy]

Ports the following 11 BB(6) halting and non-halting proofs from the resolved holdouts:

• 1 Halt: M_1RB0RE_1RC0RA_0LD0RB_1LA0LE_1LC1LF_0LCHHH
• 10 NonHalt: M_1RB0LC_1RC0RA_1RD0RF_0LEHHH_1LB1LA_1LD1RA, M_1RB0LE_1RCHHH_0RD0RB_1RE0LA_1RF0LF_1LD1RF, M_1RB0RA_1LC0RE_1LD0LC_1RA0LB_1RA0RF_1LEHHH, M_1RB0RA_1RC0RC_1LD1RF_HHH1LE_1RF0LF_1RA0LE, M_1RB0RC_1LC1RB_0RE1LD_0LC1LA_1RF1RA_HHH0RB, M_1RB0RF_0LCHHH_1LE1LD_1RE0LA_1RA0RD_1LB1RD, M_1RB0RF_1RC0RB_1LD0RA_1LE0LD_1RB0LC_1LAHHH, M_1RB1LF_0RCHHH_1RD1RF_1LE0LF_1LB0LA_1LD0RE, M_1RB1RA_0LC0RA_1RC1LD_0LB1LE_1LF0RC_HHH0LD, M_1RBHHH_1LC0LA_1LD0LC_1RE0LB_1RF0RE_1LC0RD
• And BusyBeaver/Calculi/SegCount.lean which provides segment-counting utilities.

Hygiene and Verification:

• All 73 unused intermediate declarations have been pruned.
• All lines are wrapped to a maximum of 100 columns.
• No autoImplicit or linter.* false overrides are used.
• Verified locally with lake comparator and leanchecker via the default kernel!

Also updates the counts in the READMEs.

[mo271]

Looks great! Checked out the branch and went through SegCount.lean, the 11 new Halt/ and NonHalt/ modules (nice reuse of Counter.does_not_halt_of_conj_stem on the 4 shifted-entry conjugation stems), BusyBeaverChallenge.lean, and comparator/busy_beaver.json (687 -> 698). Formatting and linter hygiene are super clean across all files.

Two tiny non-blocking doc-count nits if you touch the branch (or we can fold them into #29 when rebasing):

• In BusyBeaver/BB6/README.md, line 3 says 191 resolved (32 IsHalt + 159 IsNotHalt in NonHalt/), while lines 1027–1039 say 192 resolved (32 + 160) because the NonHalt table also lists Pomme (M_1RB1LA_1RC1RE_1LD0RB_1LA0LC_0RF0RD_0RBHHH.lean, which lives in BusyBeaver/BB6/).
• Root README.md line 18 still says 180 resolved Halt/ and NonHalt/ (-> 191).

Recommend merging this one before #29 so #29 can rebase cleanly on top. LGTM!

[TomZahavy]

Thanks for the thorough review and check, @mo271!

Confirmed both doc-count items you spotted:

1. BusyBeaver/BB6/README.md (191 vs 192): Confirmed — BusyBeaver/BB6/Halt/ has 32 modules and BusyBeaver/BB6/NonHalt/ has 159 modules (191 across Halt/ and NonHalt/), while the Resolved BB(6) NonHalt Machines table lists 160 rows because it also includes Pomme (./M_1RB1LA_1RC1RE_1LD0RB_1LA0LC_0RF0RD_0RBHHH.lean in BusyBeaver/BB6/). Lines 3 and 1027–1069 should explain that distinction explicitly (191 in Halt//NonHalt/, 192 resolved including Pomme).
2. Root README.md (180 -> 191): Confirmed — the Overview table row for BusyBeaver/ (line 13) still reads 180 resolved Halt/ and NonHalt/ proofs and should be updated to 191.

To avoid invalidating the green ~4h BusyBeaver CI run (since this PR modifies .lean files under BusyBeaver/, any push to this branch re-triggers the full build), we're leaving bb6-new-proofs-batch1 untouched so #28 can be merged cleanly as-is (mergeStateStatus: CLEAN, all checks green). Right after #28 merges, we'll open a tiny docs-only follow-up PR on main to fix both counts (which will skip the 4h BusyBeaver CI build thanks to #26's !BusyBeaver/**/*.md path exclusion)—unless #29 prefers to pick them up directly during rebase.

Ready to merge whenever you are!