{
"tm": "1RB0LF_1LC0LA_---1RD_1RF1RE_1LF1RD_1LB0RE",
"rank": 35,
"class_sheet": "Bouncer + Chaotic Edge",
"class_guess": "Bouncer + Chaotic Edge: period-10 bulk on a left wall, 7-bounce junction, chaotic edge identical to #13's",
"confidence": "low",
"summary": "Exact period-10 bouncer and 7-bounce junction; every 7th bounce stirs a chaotic edge Z, the same edge as #13.",
"mechanism": [
"Bulk 0^inf Phi(Z) independent of n (2077/2077 matches with the 1e9 run). Phi is chaotic: |Z| 143-563 over 5e6 visits (~5e15 steps), no repeat, no halt.",
"Z is cell for cell #13's tail (#13 tail at bounce c-6 = fixed 58-cell word + our Z at bounce c, 1,952/1,952 visits). Halting needs 0 0 0 E> 0; 38,720 near misses 1 0 0 E> 0, all in the edge. Bounces 0-300 (period-5 junction) are plain simulation."
],
"diagrams": [
{
"mode": "default",
"png": "img/default_1e5.png",
"html": "img/viewer.html",
"steps": 99999,
"caption": "Site view: bulk grows left, ragged edge on the right",
"title": "Site view of the first 99,999 steps",
"why": "Compare the smooth left boundary with the ragged right side; the grey stripe band between them is the bulk.",
"primary": true,
"start": "blank",
"rows": "every step; 99,999 steps squeezed into 500 rows (site bilinear view)",
"window": "cells -200..199, 1 px = 1 cell",
"legend": "white = 1, black = 0 or unvisited, red/green = head after a move R/L",
"style": "bbchallenge-default"
},
{
"mode": "records",
"png": "img/records_1e7.png",
"html": null,
"steps": 10000000,
"caption": "One row per record: smooth left stair, ragged right edge",
"title": "Left/right records to 10 million steps",
"why": "One row per new leftmost or rightmost cell. Compare the left boundary with the right boundary and its noisy band.",
"primary": true,
"start": "blank",
"rows": "left/right records (one row per new leftmost or rightmost cell), 2,428 rows to step 10,000,000",
"window": "cells -1342..1085, 1 px = 1 cell",
"legend": "white = 1, black = 0 or unvisited, red/green = head moving R/L",
"style": "bbchallenge-default"
},
{
"mode": "custom: every 28 bounces, junction frame",
"png": "img/zone_every28.png",
"html": null,
"steps": 1000000000,
"caption": "Every 4th edge visit: fixed stripes, then the chaotic band",
"title": "Bulk, junction and edge, every 28 bounces",
"why": "The frame follows the junction. Left: bulk and junction columns. Right: the edge band and its sawtooth right end.",
"primary": true,
"start": "blank",
"rows": "every 28 bounces (every 4th edge visit), bounces 315..14,819 of the 1e9-step run, 519 rows, each taken at a left record",
"window": "cells -60..539, 1 px = 1 cell; cells counted from the junction frame, which moves 12 cells right per row (3 per edge visit)",
"legend": "white = 1, black = 0, slate = right of the visited span",
"style": "custom"
},
{
"mode": "every:1 (explore colours)",
"png": "img/cycle1_explore.png",
"html": null,
"steps": 262,
"caption": "One bounce up close: fast right sweep, slow zigzag left sweep",
"title": "One bounce, cell by cell",
"why": "Top: right sweep over 4 bulk blocks to the junction. Then the slow zigzag left sweep back to the wall.",
"start": "constructed: 0^inf r",
"steps": "4",
"cases": "any r (here r = (1101101101)^n ...)",
"validated": {
"instances": 80,
"passed": 80
},
"source": "manual"
},
{
"name": "right sweep",
"from": "E> (1101101101)^n",
"to": "(1011110110)^n E>",
"steps": "12n",
"cases": "any context",
"validated": {
"instances": 80,
"passed": 80
},
"source": "manual"
},
{
"name": "left sweep",
"from": "(0111101101)^n 0",
"to": "halt",
"steps": "4 (E0 F0 B0 C0)",
"cases": "the only route seen near halting: 38,720 near misses 1 0 0 E> 0 to 1e9, all in the edge; the A1 route (000 1 RC (1+i), which needs the edge to be eventually periodic in i; ours is chaotic, so RInc has no analogue. InfiniteRect_v1.v needs eventually periodic crossing streams per column, which the edge never reaches. A closed-language certificate (CTLCertv1.v / CTL62 solve_cert) is the only formal route seen."
},
"strategy": "Same reduction as #13: wall + bulk sweeps (ind, 12n and 50n) + 6 exact junction bounces reduce non-halting to the edge map Z -> Phi(Z). That edge is #13's edge, so any closed language found for #13 transfers here (and likely to #34, #36, R6). No such language is known.",
"risks": [
"The edge lemma is the whole problem and is the one #13 was parked on (SFT_k refuted k<=36, n-gram CPS fails n<=26 there).",
"|Z| is bounded only empirically (143-563 over 5e6 edge visits); a long transient could still reach 0 0 0 E> 0.",
"Proving the six junction bounces and Phi's n-independence in Rocq needs LongN/InfiniteRect-style side plumbing (15-30 KB)."
],
"checkpoint_questions": [
{
"text": "Fig 3: left of the noisy band, do the stripes stay perfectly vertical all the way down (bulk plus a fixed junction), with all the disorder in the band on the right?",
"figs": [
2
],
"kind": "check"
},
{
"text": "Fig 2: is the left boundary a smooth stair while only the right edge is ragged?",
"figs": [
1
],
"kind": "check"
},
{
"text": "This edge is #13's edge cell for cell. Park #35 with #13, or should we fund one shared edge-language stage for the whole family (#13, #34, #35, #36, R6)?",
"figs": [
2
],
"kind": "decision"
}
],
"discord_check": null,
"stats": {
"simulated_steps": 1000000000,
"cells": 21748,
"nonzeros": 15177,
"growth": "lo ~ -0.47 sqrt(t), hi ~ +0.22 sqrt(t) at 1e9; edge map run 5e6 visits (~5e15 machine steps), |Z| 143-563, no repeat, no halt"
},
"status": "CHECKPOINT_A",
"status_reason": "Bouncer, junction and edge visit found and validated; the chaotic edge is identical to #13's (parked), not arithmetic, so not a cryptid. No non-halting argument for the edge: confidence low, proof work waits for Dennis."
}