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tools/rebuild_pages.sh rebuilds the site within 5 minutes of a change; by hand: python3 -B tools/site.py.Machines / 740 line 282
1RB0LD_1RC0RD_1LA0RC_1RE1LB_1LF0LA_---0LE
Where it stands
Skipped
User chose to defer further research on line 282. The completed local study is retained; the nonlocal word-language invariant remains unresolved.
Observe
Deepen
Informal proof
Rocq
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
Two exact return families are established; a closed language protecting the irregular edge remains unknown.
- Status
- Skippeddeferred · updated 2026-10-14T15:50:25.539865-07:00Parked · User chose to defer further research on line 282.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 Bouncer with unresolved word dynamics · low confidence
- On the list
- line 253 of
BB6_holdouts_663.txt· historical 740 line 282 · observe.json rank #282
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 a 30-minute study of the whole-word return transformation for line 282? (Follow your recommendations for the 5)
- decision.json · answered 2026-10-14: defer
- Defer line 282, or fund a 30-minute study of its nonlocal word grammar and endpoint phases? Decisions →
Mechanism
How it works: 3 notes
- Two context-independent families return to the left edge in 20n+41 steps (n≥1) or 12n+69 steps (n≥0); their finite components give explicit concatenation arguments.
- An exact B/E word-rewrite model reproduces all 1,283 saved left records through two million steps. The simple families cover 1,027 of 1,282 gaps.
- Fitted word languages fail at the far endpoint, even with length modulo6. The unproved safety condition is exclusion of E reading0 with another0 immediately left.
Figures for Checkpoint A
Time increases downward. Compare the expanding left boundary with the opposite boundary.
bbchallenge-exploreStart blankRows every 1000 stepsWindow cells -1283..165, 1 px = 0.5 cellsColors 1 0 or unvisited A B C D E F
Rows: from 0 through 2,000,000; each sampled row is 2 pixels high · Window: two raster pixels per cell
Rules (5/5 validated)exact tape rewrites the proof will formalize, each re-checked by simulation
| rule | from ⟶ to | cases | steps | checked |
|---|---|---|---|---|
| 5-step finite window | state A, head 0; cells 0..2: 000 ⟶ state B, head -1; same cells: 101 | One exact finite input; all reads stay inside the specified window. No global closure claim. | 5 | ✓1/1 |
| 11-step finite window | state B, head 0; cells 0..4: 01000 ⟶ state A, head -1; same cells: 00101 | One exact finite input; all reads stay inside the specified window. No global closure claim. | 11 | ✓1/1 |
| 81-step finite window | state B, head 0; cells 0..12: 0101101100100 ⟶ state A, head -1; same cells: 0010110110101 | One exact finite input; all reads stay inside the specified window. No global closure claim. | 81 | ✓1/1 |
| Parameterized R1 | B at cell0; window: 010 (110)n 0100 ⟶ A at cell−1; same window: 00 (101)n+1 01 | n≥1. Exact finite components compose; all reads stay in the input window. n=0 excluded. No whole-orbit closure claim. | 20n+41 | ✓131/131 |
| Parameterized R2 | B at cell0; window: 010 (110)n 101100100 ⟶ B at cell−1; same window: 100 (010)n+1 110101 | n≥0. Exact finite components compose; all reads stay in the input window. No whole-orbit closure claim. | 12n+69 | ✓132/132 |
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
| 0 | 1 | |
|---|---|---|
| A | 1RB | 0LD |
| B | 1RC | 0RD |
| C | 1LA | 0RC |
| D | 1RE | 1LB |
| E | 1LF | 0LA |
| F | --- | 0LE |
- file
- —
- module
- —
- machine
- —
- diff
- —
- note
- No complete configuration family or reusable proof template has been identified.
Proof strategy & riskshow the formal proof will go · 3 risks to watch
A future research stage should derive a word grammar with endpoint phases and prove closure/safety. No formal proof stage has started.
- ▲Neither the finite blank run nor the exact partial return rules proves nonhalting.
- ▲The complete word-rewrite relation has an E00 failure branch; its global exclusion is unproved.
- ▲Observed factor/endpoint languages are not closed, and a length residue alone does not repair them.
Stats & provenance109 steps simulated · 29,507 cells · the status in full · files
- simulated
- 109 steps
- tape
- 29,507 cells · 17,521 nonzeros
- growth
- Visited span grows mainly left in the sampled blank-tape run.
- status now
- User chose to defer further research on line 282. The completed local study is retained; the nonlocal word-language 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>/: 9 entries · raw notes, status, scripts, images
| name | size | changed |
|---|---|---|
| notes.md ↓ | 7.5 KB | 2026-10-14 15:50 |
| status.json ↓ | 1.3 KB | 2026-10-14 15:50 |
| observe.json ↓ | 12 KB | 2026-10-14 15:50 |
| decision.json ↓ | 1.6 KB | 2026-10-14 15:50 |
| decisions/ | 1 item | 2026-10-14 10:35 |
| img/ | 2 items | 2026-10-13 18:24 |
| study-20261014/ | 16 items | 2026-10-14 10:31 |
| work/ | 8 items | 2026-10-13 18:24 |
| study.md ↓ | 9.6 KB | 2026-10-14 10:30 |
status.json in full
{
"tm": "1RB0LD_1RC0RD_1LA0RC_1RE1LB_1LF0LA_---0LE",
"status": "SKIPPED",
"stage": "deferred",
"updated": "2026-10-14T15:50:25.539865-07:00",
"confidence": "low",
"owner": "astra",
"holdout_line": 282,
"outcome": "partial exact return mechanism; global invariant unresolved",
"direct_steps": 1000000000,
"proof_status": "none",
"possible_chaotic_edge": true,
"confirmed_cryptid": false,
"rank_within_282_465": 1,
"reason": "User chose to defer further research on line 282. The completed local study is retained; the nonlocal word-language invariant remains unresolved.",
"next": "Retain the completed study and evidence; no additional research scheduled.",
"observation_complete": true,
"proof_started": false,
"formal_checker_run": false,
"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,
"next_action": "Deferred by user decision on 2026-10-14.",
"study_completed": "2026-10-14T10:31:56.841758-07:00",
"study_result": "study-20261014/result.json",
"study_report": "study.md",
"priority_call_answered": "defer",
"decision_source": "coord/mailbox/to-astra/20261014-154300-claude-dennis-answers-6-282.md"
}observe.json contract (tools/README-card.md):
1 contract warning
- diagrams: 1 (want 3-5)