{ "tm": "1RB1RF_1RC---_1RD0RD_1LE1RC_1RA1LE_1RE0LF", "rank": 19, "class_sheet": "Shift-overflow structural counter", "class_guess": "Base-4 bouncer counter: separators between growing 6-cell zones are the digits", "confidence": "med", "summary": "Bouncer whose turn-back point is a base-4 counter; digits = separators between growing (110101) zones.", "mechanism": [ "Tape = left end ... Z2 S1 Z1 S0 Z0 W: zones Z repeat a 6-cell block (110101, rotated); W = fixed 99-cell right wall.", "Separators S have 4 states: 3 bounce the head back, the 4th lets it through, so turn-back depth is a base-4 ruler.", "Z0 gains 1 block per 2 sweeps, Z_k ~ Z_(k-1)/4. The left end, where new digits appear, is not characterised yet." ], "diagrams": [ { "mode": "every:50", "png": "img/counter_every50.png", "html": null, "steps": 200000, "caption": "Raw view of the same: 3 short turn-backs, then 1 deeper", "title": "Raw view, every 50 steps", "why": "Every 50 steps. Flat edges are right passes, steep edges left passes; note where each sweep turns back.", "primary": true, "start": "mid-run: step 1,901,496 (tape from the real run, head at cell 2,134)", "rows": "every 50 steps: steps 1,901,496 + 0, 50, ..., 200,000 (4,001 rows)", "window": "cells -68..2,245, 1 px = 1 cell", "legend": "white = 1, black = 0, red/green = head after a right/left move. The 6-cell zones look grey. A right pass moves 50 cells per row (nearly flat edges), a left pass ~15 (steeper edges); a sweep's turn-back is where its edge stops on the left", "style": "bbchallenge-default" }, { "mode": "round trips", "png": "img/sweeps_turnback_2e6.png", "html": null, "steps": 2000000, "caption": "One row per round trip: turn-back depth follows a base-4 ruler", "title": "One row per round trip, 452 trips", "why": "One row per round trip; red marks each turn-back. Compare how deep each turn-back goes.", "primary": true, "start": "blank", "rows": "one per round trip of the head (it leaves the right end, turns back, returns to within 120 cells of the right end), drawn at the return: 452 trips, steps 24,389..1,994,475 (1 row = 4 px tall); not evenly spaced in time", "window": "cells -68..900, 1 px = 1 cell (the right part of the tape, up to cell 2,185 at the end, is cut off: every trip reaches it)", "legend": "custom: white/black = 1/0 on cells this trip reached; blue/navy = 1/0 on cells it did not reach; red = the turn-back cell (deepest point); near-black = not yet visited. The red diagonal is S0 (3 trips in 4 turn there); every 4th trip goes on to S1, every 16th to S2, every 64th deeper still", "style": "custom" }, { "mode": "records:R", "png": "img/records_R_right.png", "html": null, "steps": 10000000, "caption": "Right edge fixed: zone borders recede at different speeds", "title": "Right edge pinned, 10 million steps", "why": "Right edge pinned to 1e7 steps. Thin slanted lines are zone borders; watch the ones at the far left.", "primary": true, "start": "blank", "rows": "the start, then one per new rightmost cell (4,854 rows, steps 0..10,000,000); not evenly spaced in time", "window": "cells -4,921..0, 1 px = 1 cell, counted from the right edge (each row's rightmost visited cell is 0, pinned to the last column; it is absolute cell 4,853 at step 1e7)", "legend": "white = 1, black = 0 or never visited, red = head on the new right cell. The grey texture is the 6-cell zone pattern; the thin slanted lines are the zone borders (separators)", "style": "bbchallenge-default" }, { "mode": "blaze", "png": "img/blaze_1e9.png", "html": null, "steps": 1000000000, "caption": "Inner curves = zone borders at 1/4, 1/16 of edge", "title": "Blaze view, 1 billion steps", "why": "Faint inner curves at about 1/4 and 1/16 of the edge are zone borders (the counter's digits).", "primary": false, "start": "blank", "rows": "time blocks of 1,048,576 steps, averaged (954 blocks, steps 0..1,000,000,000), stretched to 500 px: 1 px ~ 2,000,000 steps", "window": "cells -96..48,095, 1 px = ~60 cells (Blaze averages 32 cells per column; its 1,506 columns are stretched to 800 px)", "legend": "white = 0, orange = 1, in-between shades = both mixed inside the pixel's block (averaged); no head", "style": "bbchallenge-blaze" }, { "mode": "default", "png": "img/default_site.png", "html": "img/viewer.html", "steps": 10000, "caption": "bbchallenge default view, first 10k steps", "title": "bbchallenge Default view, first 10,000 steps", "why": "For orientation: the start of the run as bbchallenge.org shows it.", "primary": false, "start": "blank", "rows": "every step: steps 0..9,999 squeezed into 500 px rows as on bbchallenge.org (each px row blends steps 20y+9 and 20y+10, so 1 px row = 20 steps)", "window": "cells -200..199, 1 px = 1 cell", "legend": "white = 1, black = 0 or never visited, red/green = head after a right/left move (pale colours = blended by the squeeze)", "style": "bbchallenge-default" } ], "history": { "skeleton": "0^inf [left end] Z3^d S2 Z2^c S1 Z1^b S0 Z0^a W C> 0^inf (Z = a rotation of 110101; first right record of each cycle)", "vars": [ "a (Z0 blocks)", "b (Z1)", "c (Z2)", "deeper zones", "right edge pos" ], "rows": [ { "step": 24632, "values": [ 14, "-", "-", "-", 188 ] }, { "step": 64622, "values": [ 4, "-", "-", "-", 326 ] }, { "step": 107806, "values": [ 22, "-", "-", "-", 466 ] }, { "step": 188656, "values": [ 46, "-", "-", "-", 658 ] }, { "step": 329154, "values": [ 74, 7, "-", "-", 886 ] }, { "step": 577378, "values": [ 111, 16, "-", "-", 1182 ] }, { "step": 1005848, "values": [ 158, 28, "-", "-", 1558 ] }, { "step": 1765606, "values": [ 221, 43, "-", "-", 2058 ] }, { "step": 3082882, "values": [ 302, 64, 9, "-", 2710 ] }, { "step": 5394002, "values": [ 410, 91, 15, "-", 3574 ] }, { "step": 9433138, "values": [ 553, 126, 24, "4", 4714 ] }, { "step": 16512668, "values": [ 741, 174, 36, "7", 6222 ] }, { "step": 28876852, "values": [ 990, 236, 52, "11", 8214 ] }, { "step": 50564560, "values": [ 1320, 318, 72, "16", 10854 ] }, { "step": 88434554, "values": [ 1756, 427, 99, "23", 14338 ] }, { "step": 154800594, "values": [ 2333, 571, 135, "32 5", 18954 ] }, { "step": 270879100, "values": [ 3095, 762, 183, "6 13", 25054 ] }, { "step": 473958164, "values": [ 4104, 1014, 246, "21 4 13", 33126 ] }, { "step": 829471848, "values": [ 5439, 1348, 330, "42 10 11", 43806 ] }, { "step": 1451620694, "values": [ 7205, 1790, 440, "70 17 11", 57934 ] } ] }, "rules": [ { "name": "R1 C-pass", "from": "C> (011111)^n", "to": "(110101)^n C>", "steps": "6n", "cases": "any context; n=1..2770", "validated": { "instances": 24, "passed": 24 }, "source": "manual" }, { "name": "R2 F-sweep (0^6 packet)", "from": "(111010)^n b", "from": "X 1^9 010 a", "from": "X 1^9 (01)^6 0 P)", "from": "Y H(m) P0 1^9 0 1^7 (01)^3 0 L)", "from": "Y M(m) P0 1^9 0 1^7 (01)^3 0 H, Z1+1)", "from": "Y L(m) P0 1^9 0 1^7 (01)^3 0 S1->S2 (P->M, Z1+1)", "from": "Y_b P(m) P0 1^9 0 1^7 (01)^3 0 new 6/13). It might be messy.", "Separators differ: two phase types (bounce offsets -10 vs -12) and different inert debris (P0 vs P1). Needs a closed family of separator words.", "Size: several separator/phase cases, so expect 20-40 KB (SBCv6a/SBCv10 scale). qsim and rulefit found nothing, so the proof is by hand." ], "checkpoint_questions": [ { "text": "Fig 1: do the sweeps turn back 3 times at one spot, then once deeper, over and over?", "figs": [ 0 ] }, { "text": "Fig 2: is every 4th deep turn-back deeper still, and every 16th deeper again, as in a base-4 counter?", "figs": [ 1 ] }, { "text": "Fig 3: do the lines at the far left barely change over 10 million steps (new digits are rare)?", "figs": [ 2 ] } ], "discord_check": null, "stats": { "simulated_steps": 20000000000, "cells": 214969, "nonzeros": 34836, "growth": "right edge ~ sqrt(t): step ≈ 0.432·hi² (hi=214890 at 2e10); left edge stuck at -78 since 1.8e8; nonzeros at 1e9" }, "status": "CHECKPOINT_A", "status_reason": "Mechanism found (base-4 separator counter, no Collatz-style branching). 8 rules validated, 134/134 instances. Left end still open." }