{
"tm": "1RB0LF_0RC---_1RD0RA_1LE0RC_0LA0LE_1LE1LB",
"rank": 8,
"class_sheet": "Sync bouncer counter",
"class_guess": "Sync bouncer counter, spread-digit variant (binary counter whose digits sit inside the bouncer body)",
"confidence": "med",
"summary": "Bouncer carrying a binary counter whose digits sit in its body; each overflow inserts a new digit ~4x farther out",
"mechanism": [
"Bouncer: the head shuttles from the left edge into the tape; each trip adds one (010) block to the left lead a.",
"The (100) body holds 7-cell digits 0b10001; each trip is a binary +1 (run to the first 0-digit, set it, clear the 1s).",
"Right end frozen. At overflow (all 1s) a long pause cuts a new lowest digit from the lead, ~4x farther out."
],
"diagrams": [
{
"mode": "custom rows: one per +1",
"png": "img/counter_bits.png",
"html": null,
"steps": 17409,
"caption": "One row per +1: bit columns blink every 1,2,4,8,16,32 rows",
"title": "One row per +1: six bit columns",
"why": "One row per +1. Count the rows between colour changes in each of the six bit columns, left to right.",
"primary": true,
"start": "constructed: 0^inf A> 0 (010)^6 0 0010001 (100)^5 0010001 (100)^4 0010001 (100)^3 0010001 (100)^3 0010001 (100)^3 0010001 0^inf (= K(a=6; bits 000000; gaps 5,4,3,3,3); bit cells at 21, 43, 62, 78, 94, 110)",
"rows": "the start, then one per +1 (each time A reaches a new left edge): 64 rows, steps 0..17,409 (1 row = 6 px tall)",
"window": "cells -189..115, 1 px = 1/3 cell (1 cell = 3 px)",
"legend": "white = 1, black = 0 or never visited, green = head at the new left edge; the columns that blink are the 6 bit cells (21, 43, 62, 78, 94, 110)",
"style": "bbchallenge-default"
},
{
"mode": "default --fit",
"png": "img/counter_ruler.png",
"html": null,
"steps": 882,
"caption": "Each +1 sweeps to the lowest 0 bit: depths 1,2,1,3,1,2,1,4",
"title": "Eight +1s up close, every step",
"why": "Eight +1s, every step. Note where each right sweep turns back, against the bit cells (21, 43, 62, 78).",
"primary": true,
"start": "constructed: 0^inf A> 0 (010)^6 0 0010001 (100)^5 0010001 (100)^4 0010001 (100)^3 0010001 (100)^3 0010001 (100)^3 0010001 0^inf (= K(a=6; bits 000000; gaps 5,4,3,3,3); bit cells at 21, 43, 62, 78, 94, 110)",
"rows": "every step, 0..882 = 8 increments (1 step = 2 px tall)",
"window": "cells -24..115, 1 px = 0.5 cells (1 cell = 2 px)",
"legend": "white = 1, black = 0 or never visited, red/green = head after a right/left move; each right-going sweep turns at a bit cell (21, 43, 62 or 78)",
"style": "bbchallenge-default"
},
{
"mode": "records:L --frame right",
"png": "img/records_L_3e6.png",
"html": "img/viewer.html",
"steps": 3000000,
"caption": "Real run, right edge fixed: new digit columns appear farther left",
"title": "Real run from blank, right edge pinned",
"why": "Real run from blank, right edge pinned. Watch for new thin vertical lines and where each one appears.",
"primary": true,
"start": "blank",
"rows": "the start, then one per new leftmost cell (2,056 rows, steps 0..2,999,327); not evenly spaced in time, and overflow pauses add no rows",
"window": "cells -2,055..11, 1 px = 1 cell (right edge pinned to the last column; it is cell 11 from row 66 = step 1,527 on)",
"legend": "white = 1, black = 0, green = head at the new left edge. Grey texture = the period-3 tape (010.../100...) at 1 px per cell; each thin vertical line = one 7-cell digit block 0b10001; the dense strip at the right = packed high digits",
"style": "bbchallenge-default"
},
{
"mode": "blaze",
"png": "img/blaze_1e7.png",
"html": "img/viewer.html",
"steps": 10000000,
"caption": "Span ~ sqrt(t); the notch is the overflow pause 1.0e6-2.85e6",
"title": "Blaze, 10 million steps",
"why": "The span grows like sqrt(t); the notch at 1.0e6-2.85e6 steps is one overflow pause.",
"start": "blank",
"rows": "Blaze time blocks of 16,384 steps (611 rows, each averaged), stretched to 500 px (1 px ~ 20,000 steps)",
"window": "cells -5,536..11, 1 px = 6.9 cells (each px shows one 4-cell block)",
"legend": "white = 0, orange = 1; pale orange = a mix (each pixel averages 4 cells x 16,384 steps)",
"style": "bbchallenge-blaze"
},
{
"mode": "default",
"png": "img/default_site.png",
"html": "img/viewer.html",
"steps": 10000,
"caption": "bbchallenge view: lead grows left, right end frozen",
"title": "bbchallenge default view, first 10,000 steps",
"why": "The site's view: the lead grows to the left while the right end stays frozen.",
"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"
}
],
"history": {
"skeleton": "0^inf 0, bj: 0->1)",
"steps": "6a + 6(g1+...+gj) + 24j + 9",
"cases": "j = lowest 0 bit; needs some bi = 0 (else Ovf). Holds for every a>=1, gi>=1, 1-6 digits",
"validated": {
"instances": 400,
"passed": 400
},
"source": "manual"
},
{
"name": "Ovf-insert (overflow pause, long lead)",
"from": "0^inf = g'+6, g' = 2044 - 2g1 - 4g2 - 8g3 (k=3; general 2^(2k+5)-4-sum 2^i g_i matches all 4 real inserts). R* = real R at step 114113163",
"validated": {
"instances": 30,
"passed": 30
},
"source": "manual"
},
{
"name": "Ovf-short (overflow pause, short lead)",
"from": "same as Ovf-insert",
"to": "0^inf F gives 1RB0LF_0RC---_1RD0RA_1LA0RC_0LA0LE_1LE1LB; only D0 differs: ours 1LE, template 1LA",
"applies": "no",
"note": "Template LInc/RInc0, mirrored: 10/10 on the template, 0/10 on ours. Same idea (binary counter + unary sync), but our digits are spread through the unary body, not packed in a 4-cell-digit counter."
},
"strategy": "Family proof in the SBCv2 spirit but with new shapes: (1) Inc as an ind-lemma over a 'spread counter' (digits 0b10001 between (100)^g gaps; shift rules over (100)^g via es/sideRLs); (2) map the overflow pause into exact sub-rules (insert / short-lead / R growth), not yet done; (3) multistep_nonhalt + progress_nonhalt_cond with an invariant on (a, k, gaps, counter value), like SBCv2's P(k,n).",
"risks": [
"Overflow pause internals are unmapped: R growth and multi-insert pauses (step 1.1e8 inserted 1028, 4097 and 7). They are most of the proof.",
"Size: nested counters plus an arithmetic invariant; expect 30-80 KB, well over the 15 KB target.",
"Only 4 real overflows exist in 1e10 steps (the next is far beyond reach), so the long-term rules rest on synthetic-config probes."
],
"checkpoint_questions": [
{
"text": "Fig 1: do the six bit columns toggle every 1, 2, 4, 8, 16, 32 rows, i.e. a binary counter inside the bouncer body?",
"figs": [
0
]
},
{
"text": "Fig 2: does each right sweep turn back at the lowest 0 bit (depths 1, 2, 1, 3, 1, 2, 1, 4)?",
"figs": [
1
]
},
{
"text": "Fig 3: at each overflow, does a new digit line appear farther left than the last (a spread counter that inserts digits)?",
"figs": [
2
]
}
],
"discord_check": null,
"stats": {
"simulated_steps": 10000000000,
"cells": 181589,
"nonzeros": 60536,
"growth": "span ~ t^0.5 (17.9k cells at 1e8, 50.2k at 1e9, 181.6k at 1e10); right edge fixed at 11 since step 1527"
},
"status": "CHECKPOINT_A",
"status_reason": "Mechanism found and core rules validated (Inc 400/400, overflow branches 30/30 and 12/12); arithmetic is linear, not Collatz-like; sheet has no notes or claims; on mxdys's UBRRBA_TODO list (Dennis: fair game)."
}