BB(6) hunt
Machines / 740 line 6

1RB1LD_1LC0RF_0RD0LB_1LB0LE_1LA---_0RA0RF

740 line 6SkippedBouncer + Chaotic Edgebbchallenge ↗Explorer

Where it stands

Skipped

User chose to defer further research on the 6/348 family. The completed local study is retained; the edge-word invariant remains unresolved.

Observe
Deepen
Informal proof
Rocq
space-time diagram, first 10,000 steps from blank
The first 10,000 steps from a blank tape. Time runs down; white is 1.
About this picture

The standard picture (bbchallenge.org's Default view): each row is the whole tape at one step, time runs downward, and the head's path draws the pattern.

bbchallenge-defaultStart blankRows steps 0 → 10,000, top to bottomWindow cells −200..199, left to rightColors 1 0 or unvisited

Overview

In one sentence

Exact sweep rules and tested edge returns are known; the growing edge word still lacks a closed model.

Status
Skippeddeferred · updated 2026-10-14T15:50:25.539865-07:00Parked · User chose to defer further research on the 6/348 family.
idle since Oct 14 15:50 (45 h ago) · status.json 2026-10-14T15:50:25.539865-07:00
Class
Bouncer + Chaotic Edgeours: sheet Bouncer + Chaotic Edge ≠ ours Period-seven bouncer with partially described edge returns · med confidence
On the list
line 5 of BB6_holdouts_663.txt · historical 740 line 6 · observe.json rank #6
eqv ×3sim 1e15UBRRBA
Your calls on file 4
priority call (answered)
defer
next
Retain the completed study and evidence; no additional research scheduled.
2026-10-14 · study
Fund one 30-minute edge-return study for the shared line 6/348 family? (Follow your recommendations for the 5)
decision.json · answered 2026-10-14: defer
Defer 6/348, or fund another 30-minute study of the variable edge-word transformation? Decisions →

Mechanism

How it works: 3 notes
  • Two exact local sweep identities describe the period-seven bulk; a reduced word interpreter matches 122 saved/full endpoint checks through 100 million steps.
  • R1 has an informal universal derivation; two further return families remain candidates. All 124 independent C checks and 31 extra literal checks pass.
  • 473 exact bounded prefix returns explain 22 of 37 observed consecutive edge returns. The growing remainder is not a closed word family.

Figures

Fig 1 · Irregular edge at new records

Compare the short irregular words beside the long periodic region.

Irregular edge at new records
bbchallenge-defaultStart blankRows start, then all 121 new left records through 100,000,000 stepsWindow cells 0..255, 1 px = 1 cellsColors 1 0 or unvisited head moving R/L
Rows: last pictured record at step 10,923,095 · Window: coordinates relative to the current leftmost reached cell
Fig 2 · Long sweeps across the growing tape

Follow the head markers across the reached span; narrow tape details are undersampled.

Long sweeps across the growing tape
bbchallenge-defaultStart blankRows every 100,000 stepsWindow cells -121..13,216, 1 px = 8 cellsColors 1 0 or unvisited head moving R/L
Rows: including step 0 and step 100,000,000; 1001 rows · Window: sampled columns, head marker retained
More figures (1)Fig 3: Initial motion
Fig 3 · Initial motion

Read downward to see the initial sweeps.

Initial motion
bbchallenge-defaultStart blankRows site canvas: output row y blends step rows 20y+9 and 20y+10 equallyWindow cells -200..199, 1 px = 1 cellsColors 1 0 or unvisited head moving R/L
Rows: 500 output rows · Colors: bilinear blends retained
Rules (5/5 validated)exact tape rewrites the proof will formalize, each re-checked by simulation
rulefrom ⟶ tocasesstepschecked
Right run: exact local identity
A>0 1k 0
⟶ 1 0k+1 A>
k>=1; arbitrary exterior unchanged and unread.k+2✓160/160
Left bulk: exact local identity
(1000000)n A>1
⟶ A>1 (1001111)n
n>=0; arbitrary exterior unchanged and unread.17n✓160/160
R1: derived edge family
0∞ A>01001111100101 (1111001)n 0∞
⟶ 0∞ A>0100111101110010 (1111001)n+1 0∞
n>=0; blank exterior; informally derived for every n; head shift -3.48n+73✓42/42
R2: candidate edge family
0∞ A>01001111100101111110010 (1111001)n 0∞
⟶ 0∞ A>0101111100101111111110010 (1111001)n+3 0∞
n>=1; blank exterior; finite-tested, not a universal proof; head shift -2.168n+486✓41/41
R3: candidate edge family
0∞ A>0100111111100101111111110010 (1111001)n 0∞
⟶ 0∞ A>01011100111100101111101111110010 (1111001)n+6 0∞
n>=1; blank exterior; finite-tested, not a universal proof; head shift -4.336n+1410✓41/41
Compressed historynone yet: the tape compressed to a skeleton with growing exponents
—
Template comparisontemplate: unknown · the nearest solved proof, what carries over, and the transitions that differ
01
A1RB1LD
B1LC0RF
C0RD0LB
D1LB0LE
E1LA---
F0RA0RF
file
—
module
—
machine
—
diff
—
note
No existing proof template has been established for the irregular edge.
Proof strategy & riskshow the formal proof will go · 3 risks to watch

Park whole-machine formalization. Any additional funded work should target a closed symbolic update for the variable edge word and its small-bulk exceptions, rather than longer runs or more fixed-prefix examples.

  • ▲R1 has an informal universal derivation; R2/R3 remain candidates, and no closed edge recurrence or Rocq theorem is established.
  • ▲No invariant excludes the halting-sensitive A/111 case in canonical orientation for every future reachable word.
  • ▲The reflected table changes the corresponding start state; both initial configurations remain separate obligations.
Stats & provenance5.3·109 steps simulated · 96,254 cells · the status in full · files
simulated
5.3·109 steps
tape
96,254 cells · 68,673 nonzeros
growth
Observed bulk expansion toward the right; no asymptotic growth law proved.
status now
User chose to defer further research on the 6/348 family. The completed local study is retained; the edge-word invariant remains unresolved. (status.json, 2026-10-14T15:50:25.539865-07:00)
files
observe.json · notes.md · status.json

Proof & checks

No proof work yet.

Files

machines/<tm>/: 8 entries · raw notes, status, scripts, images

namesizechanged
notes.md ↓7.0 KB2026-10-14 15:50
status.json ↓1.2 KB2026-10-14 15:50
observe.json ↓5.9 KB2026-10-14 15:50
decision.json ↓1.5 KB2026-10-14 15:50
decisions/1 item2026-10-14 10:35
evidence/27 items2026-10-14 10:18
img/3 items2026-10-13 18:24
study.md ↓13 KB2026-10-14 10:29
status.json in full
{
 "tm": "1RB1LD_1LC0RF_0RD0LB_1LB0LE_1LA---_0RA0RF",
 "status": "SKIPPED",
 "stage": "deferred",
 "updated": "2026-10-14T15:50:25.539865-07:00",
 "confidence": "med",
 "reason": "User chose to defer further research on the 6/348 family. The completed local study is retained; the edge-word invariant remains unresolved.",
 "next": "Retain the completed study and evidence; no additional research scheduled.",
 "simulation_only": false,
 "observation_completed": "2026-10-13T18:24:18.533813-07:00",
 "updated_utc": "2026-10-14T22:50:25.539865+00:00",
 "study_started": "2026-10-14T10:06:30.232473-07:00",
 "study_deadline": "2026-10-14T10:36:30.232473-07:00",
 "study_budget_minutes": 30,
 "proof_started": false,
 "next_action": "Deferred by user decision on 2026-10-14.",
 "study_result": "study.md",
 "formal_checker_run": false,
 "study_completed": "2026-10-14T10:29:58.650928-07:00",
 "informal_local_derivation": true,
 "evidence_kind": "Local informal derivations and finite checks; no whole-machine invariant or Rocq proof.",
 "priority_call_answered": "defer",
 "decision_source": "coord/mailbox/to-astra/20261014-154300-claude-dennis-answers-6-282.md"
}