{
"tm": "1RB0LD_1RC0RA_1RD1RF_1LA0LE_1RE1LD_0RB---",
"rank": 3,
"class_sheet": "Skelet 1-like Class 2",
"class_guess": "Skelet 1-like Class 2: binary down-counter on a list of (10)^p(01)^q pairs with overflow re-pairing (SBCv6 TM21 family)",
"confidence": "high",
"summary": "Binary down-counter on a list of (10)^p(01)^q pairs; overflow re-pairs the list (TM21-like). 7 rules validated.",
"mechanism": [
"Tape: (10)^h, marker 11001, then pairs (10)^p (01)^q, each ending in a digit block 0001 (=1) or 0010 (=0).",
"Each cycle (3 short bounces + 1 long sweep) subtracts 1 from that binary number; pairs the borrow passes get p+1, q-1.",
"At 0, End adds a tail; at the next 0, Overflow re-pairs the list and adds a pair (net ~1 per 2 epochs: width ~ t^0.5)."
],
"diagrams": [
{
"mode": "custom rows: one per decrement",
"png": "img/cycles_phase_1e7.png",
"html": null,
"steps": 10000000,
"caption": "One row per decrement: edges swap fixed/drifting at most overflows",
"title": "One row per decrement, every 4th cell",
"why": "One row per counter decrement, every 4th cell drawn. Watch the vertical and slanted colour edges, and where they kink.",
"primary": true,
"start": "blank",
"rows": "one per counter decrement: each time A reaches a new left edge with the tape reading (10)^h 11001... (902 rows, steps 8..9,982,476); not evenly spaced in time",
"window": "cells -7,305..132, 1 px = 4 cells (only every 4th cell is drawn; all drawn cells are odd)",
"legend": "white = 1, black = 0 on the drawn cells. The tape is 1010... almost everywhere, so each band is one phase of it and each colour edge is a pair boundary: vertical edge = digit block (fixed), slanted edge = (10)|(01) split (moves 2 cells per borrow). Green = head",
"style": "bbchallenge-default"
},
{
"mode": "explore --fit",
"png": "img/explore_3dec.png",
"html": null,
"steps": 1676,
"caption": "Three decrements: 3 short bounces, then sweep to first 0001",
"title": "Three decrements up close, every step",
"why": "Every step from counter value 12. Compare how far each long sweep reaches over three decrements.",
"primary": true,
"start": "constructed: 0^inf =1, q>=1; any h mod 4; R = remaining pairs + any tail",
"validated": {
"instances": 48,
"passed": 48
},
"source": "manual"
},
{
"name": "DecMerge",
"from": "0^inf 0 digit: fuse with next pair; last pair fuses into tail: (10)^p (01) 0001 (10)^t 1 -> (10)^(p+t+3) 1",
"validated": {
"instances": 36,
"passed": 36
},
"source": "manual"
},
{
"name": "End",
"from": "0^inf =1, q>=1. q=0 (EndLast): last pair becomes tail (10)^(p+4) 1, validated 36/36",
"validated": {
"instances": 36,
"passed": 36
},
"source": "manual"
},
{
"name": "Ov",
"from": "0^inf =1; new counter value 2^(L+1)-2",
"validated": {
"instances": 36,
"passed": 36
},
"source": "manual"
},
{
"name": "X1",
"from": "0^inf 1, plus a 3-state tail automaton (none / (10)^t 1 / (101)^2(01)^k).",
"risks": [
"Invariant: the far end has small margins (a far q shrinks by 3 per 2 epochs); excluding a bad merge (q->0 on a 0->1 digit) needs exact far-end bookkeeping. Simulation only so far (2^48 abstract cycles).",
"Size: TM21-style proof plus a tail automaton and 7 rule shapes, probably 15-30 KB.",
"Class 1 neighbour is being mined from a numbered Sk1 list; unknown whether that list covers Class 2 (memo Q3)."
],
"checkpoint_questions": [
{
"text": "zoom_cycles_annotated: rows 8,319 to 17,139 (between the yellow RE-PAIR bands); each row is the tape at the start of one count-down step. A pair = a run of 10s (blue) then a run of 01s (orange); its digit block = the next 4 cells (purple), 0001 = 1, 0010 = 0. Expected: each purple block stays on the same 4 cells all the way down; only its one light (1) cell moves, one cell left or right, when the digit flips (0001 ↔ 0010): in pair 1's block every row (the zigzag), in pair 2's every other row, and in pair 3's once, at row 10,419. At row 13,983 pair 3 turns into the teal tail. Meanwhile each blue→orange border jumps 2 cells right on some rows: pair 1's on every row, pair 2's on every other row. The magnified box at the top shows one such step cell by cell. Is that what you see? (In Fig 1, zoomed far out, the purple blocks are the vertical edges and the borders the slanted ones.)",
"figs": [
5
],
"kind": "check",
"answer": "yes",
"date": "2026-10-10",
"note": "The purple block is a coherent column, but it shifts internally (light vs dark purple) and translates by one cell partway down; the single-cell checkerboard columns are what Q2 explains. So 'keeps its columns' is not literally true."
},
{
"text": "zoom_cycles_annotated: the two yellow RE-PAIR bands, above rows 8,319 and 19,436. Re-pairing = the tape is regrouped into new pairs and the counter restarts (here at 6); it happens when the counter (right margin) hits 0 for the second time. At the first 0 the step is End instead: it raises the counter (0 → 1 at row 6,366; 0 → 3 at row 13,983) and changes the right end, and the two Ends differ: '+ tail' (row 6,366) adds a 3-cell teal tail after the last pair, while 'pair 3 → tail' (row 13,983) absorbs pair 3 into the tail. Across each band, black dashed lines carry the old blue→orange borders down and purple dotted lines the middles of the old purple blocks. Expected: the dashed lines end on the new purple blocks of pairs 1 and 2, and the dotted lines end 1 cell left of the new borders of pairs 2 and 3 (pair 1's starts next to the old gold marker), so the two kinds of column swap roles. Re-pairing also adds a pair: the new pair 3's orange run takes over the old teal tail, and its purple block (the rightmost) sits just past where the tail ended, so no line leads to it. Is that what you see? (In Fig 1 each swap is a row where the vertical and slanted edges kink.)",
"figs": [
5
],
"kind": "check",
"answer": "yes",
"date": "2026-10-10",
"note": "Black dashed lines carry the old blue→orange borders down; purple dotted lines carry the old purple blocks down: that explains the checkerboard."
},
{
"text": "Fig 2: the long sweeps go deep, shallow, then medium as the counter goes 12 → 11 → 10 → 9. Does the sweep depth read as the borrow chain of a binary down-counter?",
"figs": [
1
],
"answer": "yes",
"date": "2026-10-10"
}
],
"discord_check": "see reports/discord-drafts.md message 2",
"stats": {
"simulated_steps": 1000000000,
"cells": 67343,
"nonzeros": 33665,
"growth": "left edge ~2.1*t^0.5 (doubling epochs); right edge almost static (157 -> 181 cells, 1e8 -> 1e9)"
},
"status": "CHECKPOINT_A",
"status_reason": "Mechanism found: 7 rules, 252/252 random-config checks; they reproduce all 8,374 canonical transitions to 1e9. Not a cryptid (linear arithmetic)."
}