{
"tm": "1RB1LF_0RC0RB_0LD1LA_1LC0LE_0LA---_1LA1LF",
"rank": null,
"class_sheet": "Bell eats counter",
"class_guess": "Bell eats counter: BECv5 TM1/TM2's counter with F1 = 1LF; the counter alternates std / packed encodings, with dirty transients",
"confidence": "med",
"summary": "BECv5 TM1/TM2 counter; F1=1LF packs the top pair. Halting only at rare dirty overflows, avoided by >= 0.29 m.",
"mechanism": [
"K(w,n,m) = w 1, zeros to its right; F1 = 1LF lets a carry pass 11) and moves one 10 from n to m. At n = 0 the right side eats the counter's low end (template ROv).",
"The counter comes back shifted one cell and recounts, so it alternates encodings: std(N) -> pk(2k+b) -> std(2r+b) ... In 2.8% of cycles the overflow sees a dirty word, still shifted.",
"Halting needs an odd landing at a dirty overflow ending 01/11 (or 10, nested). None in 17M cycles (~5e22 steps), gap >= 0.29 m. No 740 holdout shares the table; 349 is equivalent (TM518) to it started in F."
],
"diagrams": [
{
"mode": "default",
"png": "img/default_site.png",
"html": "img/viewer.html",
"steps": 10000,
"caption": "bbchallenge default view, first 10,000 steps",
"title": "bbchallenge default view, first 10,000 steps",
"why": "The site's view. The right edge holds the (10) block; the left edge is the counter being eaten and rebuilt.",
"primary": true,
"start": "blank",
"rows": "10,000 steps squeezed into 500 px rows (1 px row = 20 steps; the site blends steps 20y+9 and 20y+10)",
"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 rows: one per overflow configuration",
"png": "img/counter_rows.png",
"html": null,
"steps": 604697267,
"caption": "The counter word at each of the first 400 overflows",
"title": "Counter word at each overflow",
"why": "One row per cycle. Read the colour strip on the right, then compare the leftmost lit cells row to row.",
"primary": true,
"start": "blank",
"rows": "one per overflow configuration K(w,0,m) = w 100 (abstract rules), bar height = sqrt of count",
"window": "x = (N-m)/m from 0 to 1.6, 1 px = 0.004",
"legend": "blue = std counter, light blue = std N odd, orange = pk N even, yellow = pk N odd, purple = parity broken, white tick = bound of invariant I, grey dotted tick = N = 2m+4 (halting possible for N even), dark grey = band background",
"style": "custom"
}
],
"history": {
"skeleton": "0^inf w 0^inf",
"to": "0^inf 1 = 1; phi(w): last cell 0 -> 1, else the last 00 pair (0^inf counts) -> left cell 1, all cells right of it 0 (random w up to 14 cells)",
"validated": {
"instances": 200,
"passed": 200
},
"source": "manual"
},
{
"name": "R2 overflow, q even",
"from": "0^inf w pk",
"from": "0^inf std(N) = 2^(L+1); k = 0: std(b); else dirty phi^b(std(k)0)",
"validated": {
"instances": 200,
"passed": 200
},
"source": "manual"
},
{
"name": "B pk -> std",
"from": "0^inf pk(N) 0, clean iff 2r+b >= 2^L; k a power of 2: std(k+b); k = 0 (all ones): reset, then std(b+1), m = b+1; else dirty phi^b(pk(k)0)",
"validated": {
"instances": 200,
"passed": 200
},
"source": "manual"
},
{
"name": "phi^j acceleration",
"from": "w",
"to": "phi^j(w)",
"steps": null,
"cases": "cells below the lowest 1 at an odd offset count in binary on their even offsets; when full, the next step lands above",
"validated": {
"instances": 200,
"passed": 200
},
"source": "manual"
}
],
"template": {
"file": "BECv5.v",
"module": "TM1",
"machine": "1RB1LF_0RC0RB_0LD1LA_1LC0LE_0LA---_1LA0RB",
"diff": "F1: 1LF here vs 0RB (TM1) / 1LB (TM2)",
"applies": "partly",
"note": "Kept: LC0, R n m, LInc0, LIncs, RIncs, ROv for std counters. New: a packed counter pk with its own ROv/increments, the shifted-counter orbit (replaces LIncs': H0 -> pk(2k+j) / std), dirty transients, reset R3, and the invariant."
},
"strategy": "Find an invariant on (type, N, m) at overflow, plus the dirty state, that keeps b' off the odd landings ending 01/11/10 (measured gap >= 0.29 m). Then copy BECv5 TM1's LC0/R/RIncs/ROv, add pk lemmas and the dirty-orbit lemma, and close with progress_nonhalt_cond.",
"risks": [
"No invariant yet: the halting branch is real in the abstract system, so a proof must pin down N vs m tightly enough.",
"Dirty orbits need a recursive word description (binary sub-counters on even offsets) that is heavier to formalize than BinInc.",
"R3 resets (hit once, near misses at distance 2) put non-standard words into the next overflow; the invariant must cover them."
],
"checkpoint_questions": [
{
"text": "Counter word at each overflow: do the rows read as one binary counter whose encoding flips every cycle (blue/orange strip), with rare red dirty rows?",
"figs": [
1
],
"kind": "check"
},
{
"text": "One cycle vs TM1: the panels agree until the second bounce, where this machine's cyan F keeps sweeping left over 1s (F1 = 1LF) and TM1 turns back. Is that the only split you see?",
"figs": [
2
],
"kind": "check"
},
{
"text": "Mechanism is closed and validated, but non-halting needs an invariant not yet found (gap >= 0.29 m in 17M cycles). Fund one stage to hunt the invariant, or park?",
"kind": "decision"
}
],
"discord_check": null,
"stats": {
"simulated_steps": 10000000000,
"cells": 4934,
"nonzeros": 2462,
"growth": "span ~ 2.3\u00b7steps^(1/3) cells (4,934 at 1e10); m ~ 1.14\u00b7steps^(1/3); abstract rules: 17,000,000 cycles (m = 4.25e7, ~5e22 steps)"
},
"status": "CHECKPOINT_A",
"status_reason": "Observe done, confidence med: rules closed and validated, non-halting invariant open (decision.json)"
}