{ "tm": "1RB---_1LC1RE_1LD0LC_1LE1LC_1RF0RE_1RA0RB", "rank": 14, "class_sheet": "Structural counter + counter", "class_guess": "3/2 wall conveyor (rational-base counter) + right-edge counter", "confidence": "med", "summary": "Period-5 tape; 5-state walls drift right x1.5 per level (3/2 conveyor); right-edge counter absorbs them; no halt branch.", "mechanism": [ "Tape = period-5 pattern: B sweeping right turns 11000 into 10111; C sweeping left turns it back (5 steps/block).", "Walls are 5-state gadgets: B bounces once then passes, C twice then passes; each round moves a wall 5 cells right.", "So each wall is crossed 3/2 as often as the one to its left; walls are born at the left, absorbed at the right." ], "diagrams": [ { "mode": "every:8", "png": "img/zigzag_every8_from1139175.png", "html": null, "steps": 16000, "caption": "Nested bounces off walls (from step 1,139,175)", "title": "Raw head path, every 8 steps", "why": "Every 8 steps. Long vertical lines are walls; follow the head's sweeps and where they turn back.", "primary": true, "start": "mid-run: step 1,139,175 (same tape as Fig 2, head at cell -97)", "rows": "every 8 steps: steps 1,139,175 + 0, 8, ..., 16,000 (2,001 rows)", "window": "cells -99..366, 1 px = 1 cell (the whole tape)", "legend": "white = 1, black = 0, red/green = head after a right/left move. Whiter stripes = `10111` (swept right by B), darker stripes = `11000` (swept left by C); the slanted edges between them are the head sweeping, ~8 cells per row", "style": "bbchallenge-default" }, { "mode": "every:100 phase", "png": "img/phase_solid_every100_from1139175.png", "html": null, "steps": 330206, "caption": "Colour = phase: walls drift right, fan out, vanish at right edge", "title": "Phase map: each colour band is a segment", "why": "Every 100 steps; colour edges are walls. Follow one band down: its position, its width, where it starts and ends.", "primary": true, "start": "mid-run: step 1,139,175 (a left record; tape in `cfg_step1139175_pos-97.txt`, head at cell -97)", "rows": "every 100 steps: steps 1,139,200, 1,139,300, ..., 1,469,300 (3,302 rows)", "window": "cells -104..398, 1 px = 1 cell (the whole tape)", "legend": "custom: the tape repeats a 5-cell block (`11000`, or `10111` after a right sweep); colour = which of its 5 shifts a cell is in, so every colour boundary is a wall (a +1 shift). Grey = the period-4 zone at the right barrier; black/white = cells in no pattern (0/1); near-black = not yet visited; head not drawn", "style": "custom" }, { "mode": "default", "png": "img/default_site_1e4.png", "html": "img/viewer.html", "steps": 10000, "caption": "bbchallenge default view, first 10,000 steps", "title": "bbchallenge Default view, first 10,000 steps", "why": "For orientation: the period-5 stripes as bbchallenge.org shows them.", "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" }, { "mode": "records", "png": "img/records_1e8.png", "html": null, "steps": 100000000, "caption": "Records to 1e8: right edge gains 1,586 cells, left 406 (~4x)", "title": "Edge records to 100 million steps", "why": "The right edge gains 1,586 cells, the left edge 406: about 4 to 1.", "primary": false, "start": "blank", "rows": "the start, then one per new leftmost or rightmost cell (1,993 rows, steps 0..100,000,000); not evenly spaced in time", "window": "cells -406..1,586, 1 px = 1 cell", "legend": "white = 1, black = 0 or never visited, red/green = head on a new right/left cell", "style": "bbchallenge-default" }, { "mode": "blaze", "png": "img/blaze_1e8.png", "html": null, "steps": 100000000, "caption": "Blaze 1e8: both edges keep growing, ever slower (span ~ t^(1/3))", "title": "Blaze view, 100 million steps", "why": "Both edges keep growing, ever slower (span ~ t^(1/3)); walls are too fine to see.", "primary": false, "start": "blank", "rows": "time blocks of 131,072 steps, averaged (763 blocks, steps 0..100,000,000), stretched to 500 px: 1 px ~ 200,000 steps", "window": "cells -406..1,587, 1 px = ~2.5 cells (Blaze averages 2 cells per column; its 997 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": "custom", "png": "img/nested_marker_k2p40m9.png", "html": null, "steps": 112, "caption": "Zone system: a marker, then a nested marker", "title": "Marker descent and the nested marker", "why": "Each orange diagonal is a marker sinking one unit per row; the second starts where the first ends.", "primary": false, "start": "constructed: zone of class k = 2^40 - 9 (o = 3) at marker height 46 (deepen7 value form; scripts/deepen8/fig_nested.py)", "rows": "one row per closed-system step (one absorption at the zone bottom), 113 rows from marker height 46 to the next canonical state", "window": "zone units 0..59 from the zone bottom (tape order, left = bottom); 1 unit = 4-5 tape cells, drawn 6 px wide", "legend": "white = 0 digit, black = 1 digit, orange = P unit (the markers), blue = S1 head, magenta = wall head (SP/W), grey = above the zone's top unit", "style": "custom" }, { "mode": "custom", "png": "img/lprime_step_R8_off33.png", "html": null, "steps": 1, "caption": "One representative step stands for every member", "title": "Lemma L′: one step, three marker heights", "why": "Left of each green tick the pair rows match across all three; only the orange marker height differs.", "primary": false, "start": "constructed: value-form zones VF(k, o*2^(k+5), off) at phase 1: representative k = 20, off = 33 (marker height 11); members k = 300, off = 289 (height 35) and k = 581, off = 545 (height 60) (scripts/proof4/fig_lprime.py)", "rows": "three pairs of rows, 10 px each: the zone before one closed-system step (top) and after it (bottom); representative, then the two members", "window": "zone units 0..71 from the zone bottom (tape order, left = bottom); 1 unit = 4-6 tape cells, drawn 6 px wide", "legend": "white = 0 digit, black = 1 digit, orange = P unit (the marker), blue = S1 head, grey = above the zone top, green tick = the cut after digit 7 (after digit 6 in the bottom rows, one digit lost to the landing)", "style": "custom" } ], "history": { "skeleton": "0^inf light", "from": "B> (11000)^n", "to": "(10111)^n B>", "steps": "5n", "cases": null, "validated": { "instances": 140, "passed": 140 }, "source": "manual" }, { "name": "S_L: C sweeps left, light -> dark (C on 0)", "from": "(11110)^n dark (C on 1)", "from": "(10111)^n 0^inf", "to": "1^3 1", "steps": "4", "cases": "C on the blank left of the tape", "validated": { "instances": 140, "passed": 140 }, "source": "manual" }, { "name": "Wall W0 reflects B (wall -> W1)", "from": "B> (11000)^n 0", "to": " Lw1)", "from": "B> (11000)^n 1 (11000)^m", "to": "(10111)^n 1 00111 (10111)^(m-1) B>", "steps": "5n+5m+1", "cases": "m >= 1", "validated": { "instances": 140, "passed": 140 }, "source": "manual" }, { "name": "Wall Lw1 reflects C (-> Lw2)", "from": "1 00111 (10111)^m ", "steps": "10m+11", "cases": null, "validated": { "instances": 140, "passed": 140 }, "source": "manual" }, { "name": "Wall Lw2 reflects C (-> Lw3)", "from": "000111 (10111)^m ", "steps": "10m+11", "cases": null, "validated": { "instances": 140, "passed": 140 }, "source": "manual" }, { "name": "Wall Lw3 lets C pass (-> W0, moved 5 cells right)", "from": "101111 (10111)^m 2x-1, sigma_score_unbounded_nonhalt). From its S1/Inc_a configs our machine hits 0/60 targets and halts 25/60; only its Inductive trip relation P is reusable." }, "strategy": "Prove sweeps with ind and the 5 wall rules with es. Encode the tape as a list of (segment length, wall state) with an Inductive trip relation (CounterCmp_v1 P, BECv7 digit encoding); prove one head trip by induction on the list, then a closed invariant (left gadget + list + right barrier) and finish with progress_nonhalt_cond / multistep_nonhalt.", "risks": [ "Right barrier (0001 zone) is a second counter: last-segment growth per cycle is 4-12 blocks depending on a; needs its own case analysis.", "Exact wall spacings follow a 3/2 rounding orbit; the invariant must bound them, not pin them (200/200 perturbed tapes ran 1e8 steps without halting).", "No proof in this class yet; nested trip induction may give a 30-60 KB file." ], "checkpoint_questions": [ { "text": "Fig 1: do the head's sweeps turn back at the long vertical lines (walls), nesting small zig-zags inside bigger ones?", "figs": [ 0 ] }, { "text": "Fig 2: do the colour bands drift right and get wider as they go?", "figs": [ 1 ] }, { "text": "Fig 2: are new bands born at the left edge, and does each one end in the thin grey strip at the right edge?", "figs": [ 1 ] } ], "discord_check": "see reports/discord-drafts.md message 1", "stats": { "simulated_steps": 1000000000, "cells": 4258, "nonzeros": 2660, "growth": "span ~ t^0.33 (445 / 935 / 1,993 / 4,258 cells at 1e6 / 1e7 / 1e8 / 1e9)" }, "status": "CHECKPOINT_A", "status_reason": "Mechanism found: 3/2 wall conveyor + right-barrier counter. 10 local rules 1400/1400, cycle shape 40/40. No halting branch seen; the 3/2 arithmetic only sets wall spacings, so not flagged cryptid." }