{ "tm": "1RB0RF_1RC0LD_1RD0RA_1LE0LC_1LB0LE_0RC---", "rank": null, "class_sheet": "Bell eats counter", "class_guess": "Binary counter at the left wall eats a 6-cell reservoir; each overflow fossilizes the counter's binary residue as junk that the next cycle re-reads", "confidence": "low", "summary": "Left-wall binary counter eats a 010001 reservoir; overflow leaves a binary-residue junk word; spurts are residue-timed", "mechanism": [ "Counter pass (rules P0/P1, 80/80): 0^inf (a+1, b+2^a, c-2^a) while c >= 2^a.", "Overflow (rule O, 24/24): when c < 2^a the whole sea is re-laid as a 3-cell field, 0^inf J (011)^(2b+2c) C>, where J is a junk word of exactly 3a+4 cells (the counter's partial state, i.e. a binary residue). Halting needs A to read 1 with a 1 on its right (A1 -> 0RF, F1 undefined). No halt to 2e10 (span 75,979, 36,061 ones).", "Cycle: J (101)^n B> -> J' (101)^n' B> (n' - n = +28..+72 at the 34k level) or a spurt that doubles the field, 1 0^3 (011)^(2n+12..24) C>. J is the previous counter's residue (c0 + 2^a0) mod 2^A, and it decides which: plateaus of 1, 1, 9, 3 and 31 cycles, spurts at 1.1e7, 3.0e7, 3.3e8, 9.9e8, 1.88e10." ], "diagrams": [ { "mode": "default", "png": "img/default_site_1e4.png", "html": null, "steps": 10000, "caption": "bbchallenge default view, first 10,000 steps", "title": "bbchallenge default view, first 10,000 steps", "why": "The site's view. The tape grows left in steps; the fine stripes are the 3- and 6-cell fields being rewritten.", "primary": true, "start": "blank", "rows": "10,000 steps squeezed into 500 px rows (1 px row = 20 steps; the site blends neighbouring 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", "style": "bbchallenge-default" }, { "mode": "custom", "png": "img/span_logt.png", "html": null, "steps": 20000000000, "caption": "Span against log step to 2e10: plateaus and spurts", "title": "Span vs log(step): plateaus and spurts", "why": "Each flat stretch is many cycles; each steep rise is one spurt cycle. Compare the plateau lengths.", "primary": true, "start": "blank", "rows": "chart, not a tape: x = log10(step) from 6 to 10.3 (vertical gridline at each power of 10), y = span hi-lo+1 at each new record", "window": "cells 0..80000, 1 px = 223 cells (vertical axis = span; chart gridline every 10,000 cells; horizontal axis = log10 step 6..10.3)", "legend": "blue = span (cells visited), grey = gridlines, white = background", "style": "custom" }, { "mode": "every:40000", "png": "img/fieldmap_cycle.png", "html": null, "steps": 30000000, "caption": "One ordinary cycle as a field map, 1 px = 6 cells", "title": "One ordinary cycle: the reservoir is eaten", "why": "Rows go down in time. Watch the orange/blue boundary (the phase defect) move right until blue is gone.", "primary": true, "start": "mid-run: step 110,000,000", "rows": "every 40000 steps (751 rows, 3e7 steps: one cycle plus the start of the next)", "window": "cells -7850..297, 1 px = 6 cells (one 6-cell block per pixel; block colour by content)", "legend": "grey = 3-cell field (011 in any phase); orange = 010001 left of the phase defect; blue = 010001 right of it (the reservoir); green/purple/cyan/olive = 010001 in other phases; red = any other block (junk, defect); black = blank; white = head", "style": "custom" }, { "mode": "every:100000", "png": "img/fieldmap_spurt.png", "html": null, "steps": 66000000, "caption": "The spurt cycle at 2.6e8-3.3e8, field map", "title": "The spurt cycle: the field doubles leftward", "why": "Same colours as the cycle map. Here the left edge advances on every sweep instead of the defect.", "primary": false, "start": "mid-run: step 261,900,000", "rows": "every 100000 steps (661 rows, 6.6e7 steps, through the spurt that ends at step 326,852,586)", "window": "cells -16,778..363, 1 px = 6 cells (one 6-cell block per pixel; block colour by content)", "legend": "grey = 3-cell field (011 in any phase); orange/blue/green/purple/cyan/olive = 010001 in its six phases; red = any other block; black = blank; white = head", "style": "custom" } ], "history": { "skeleton": "0^inf = 2^a; a = 0..9, b = 1..2^a+60, c = 2^a..2^a+300", "validated": { "instances": 40, "passed": 40 }, "source": "manual" }, { "name": "P0 counter pass, 0-defect", "from": "0^inf = 2^a; a = 0..9, b = 1..2^a+60, c = 2^a..2^a+300", "validated": { "instances": 40, "passed": 40 }, "source": "manual" }, { "name": "O overflow (shape only)", "from": "0^inf 0^inf (at the next right record), |J| = 3a+4 cells, J not yet characterised", "steps": null, "cases": "c < 2^a; a = 0..7", "validated": { "instances": 24, "passed": 24 }, "source": "manual" }, { "name": "Cycle map (observed only)", "from": "0^inf J 101^n B> 0^inf", "to": "0^inf J' 101^n' B> 0^inf, n' - n in +9..+75; or spurt 0^inf 1 0^3 011^(2n+k) C> 1 0^inf, k in 12..24", "steps": null, "cases": "which branch: decided by J (a binary residue); not characterised", "validated": { "instances": 0, "passed": 0 }, "source": "manual" } ], "template": { "file": "machines/1RB0RF_1RC0RB_1LD0RA_1LE0LD_1RB0LC_1LA---/1RB0RF_1RC0RB_1LD0RA_1LE0LD_1RB0LC_1LA---.v", "module": null, "machine": "1RB0RF_1RC0RB_1LD0RA_1LE0LD_1RB0LC_1LA---", "diff": "d = 4 (start A); SOMDC_Class1.v nonhalt (1LB---_1RC0RF_1LD1RB_1LE0LD_1RB0LB_1RB0RA, start F) also d = 4", "applies": "no", "note": "W4-3 (ours, killed) is a multi-level counter on 00/11 defects whose fossils are inert (block lengths only matter mod 4). Here the counter's leftover is fossilized as junk J and is re-read: J decides the next cycle's start and whether it spurts. W4-3's RIncs-style scan does not cover a junk word that carries a binary residue. SOMDC_Class1 shares the d = 4 distance only; its rule set (one structural counter) has no overflow-to-junk step." }, "strategy": "A proof needs a closed description of the junk words J and the cycle map (J, n) -> (J', n') or spurt, for every reachable J. That is an arithmetic map on n and a binary residue (c0 + 2^a0) mod 2^A, with the spurt as one residue class. Parked unless that map turns out to be a clean binary rule.", "risks": [ "Residue-driven: the cycle outcome depends on a ~12-bit residue of a slowly growing n; plateau lengths 1, 1, 9, 3, 31 look irregular (possible Collatz-like map).", "The junk J and the junk-processing phase (several sweeps with right records before each counter starts) are not characterised.", "Waves 4 and 5 rejected it; the only fixed-constant rule rulefit found (E1(2n,632-n)) is one finite pass of rule P." ], "checkpoint_questions": [ { "text": "Fig 3: does the orange/blue boundary (the phase defect) move right in passes until the blue reservoir is gone, as rules P0/P1 say?", "figs": [ 2 ], "kind": "check" }, { "text": "Fig 2: plateaus of 1, 1, 9, 3 and 31 cycles between spurts. Park B-4 as residue-driven (STUCK), or fund one 2 h stage to characterise J and the cycle map?", "figs": [ 1 ], "kind": "decision" } ], "discord_check": null, "stats": { "simulated_steps": 20000000000, "cells": 75979, "nonzeros": 36061, "growth": "span doubles in spurts: 1.7k -> 3.5k (1.1e7) -> 7.4k (3.0e7) -> 16.7k (3.3e8) -> 34.2k (9.9e8) -> 75.0k (1.88e10); in between, plateaus grow ~30-190 cells per cycle; no halt to 2e10" }, "status": "STUCK", "status_reason": "Parked at observe (cap 1 h): counter passes and overflow shape validated (104/104), but the cycle map runs on a binary residue fossilized as junk; spurts are residue-timed (plateaus of 1, 1, 9, 3, 31 cycles)." }