{ "tm": "1RB0LD_0RC1RA_1LD1RC_1LE0RF_---1LA_1LF0LA", "rank": null, "holdout_line": 593, "triage_rank_among_pair": 1, "class_sheet": "Bouncer + Chaotic Edge", "class_guess": "Bouncer with period-51 bulk and unresolved irregular boundary", "confidence": "low", "summary": "Exact reserve model and local proofs completed; the infinite bound for the 81-bit seed remains open.", "mechanism": [ "The uniform 51-cell bulk roundtrip is formally proved for every n>=0, with arbitrary exterior tapes. A separate counted composition gives exactly 906n+2881 transitions.", "The exact normal form N(k,w)=A>0(011)^k w accounts for every terminating virtual-core case, including zero-reserve halts and safe F escapes. It reproduces all 792 saved primitive records.", "At step 5104 the observed orbit reaches reserve 1 and an explicit 81-bit residual word. Its next 380 observed pairs all satisfy the common-domain reserve bound; no infinite bound has been proved. Uniform constructed families with arbitrarily long common prefixes have opposite halting outcomes. Fixed-prefix tests and the specified small additive potentials cannot establish the needed global safety invariant." ], "diagrams": [ { "mode": "every:100", "png": "img/first-200k.png", "html": null, "steps": 200000, "title": "Early bounces, first 200,000 steps", "caption": "Early bounces, first 200,000 steps", "why": "Follow the moving head and compare the two outer edges.", "primary": true, "start": "blank", "rows": "every 100 steps: 0..200000, 2001 rows; time runs downward", "window": "cells -128..372, 1 px = 1 cells; sampled columns when scale exceeds 1", "legend": "white = 1, black = 0 or unvisited, red = head after a right move, green = head after a left move", "style": "bbchallenge-default" }, { "mode": "every:10000", "png": "img/first-10m.png", "html": null, "steps": 10000000, "title": "Growth through 10 million steps", "caption": "Growth through 10 million steps", "why": "Compare regular bands with the irregular boundary region; rows and columns are sampled.", "primary": true, "start": "blank", "rows": "every 10000 steps: 0..10000000, 1001 rows; time runs downward", "window": "cells -324..2868, 1 px = 2 cells; sampled columns when scale exceeds 1", "legend": "white = 1, black = 0 or unvisited, red = head after a right move, green = head after a left move", "style": "bbchallenge-default" }, { "mode": "default", "png": "img/default-10k.png", "html": null, "steps": 10000, "title": "First 10,000 steps, site view", "caption": "Initial trace in the standard site view", "why": "Compare the initial widening trace before the much larger sampled views.", "primary": false, "start": "blank", "rows": "steps 0..9999 squeezed to 500 display rows; each row blends source rows 20y+9 and 20y+10", "window": "cells -200..199, 1 px = 1 cell", "legend": "white = 1, black = 0 or unvisited, red/green = head after a right/left move; pale colors are blended", "style": "bbchallenge-default" } ], "history": { "skeleton": "Observed span and snapshot compression; no invariant skeleton established", "vars": [ "lo", "hi", "K64_tokens" ], "rows": [ { "step": 1000000, "values": [ -212, 876, 34 ] }, { "step": 10000000, "values": [ -324, 2868, 24 ] }, { "step": 100000000, "values": [ -792, 9156, 33 ] } ] }, "rules": [ { "name": "Uniform bulk roundtrip", "from": "G W C> P^n T 0^8", "to": "=0; fixed words defined in study.md; arbitrary untouched left context", "validated": { "instances": 112, "passed": 112 }, "source": "manual" }, { "name": "Left 00 repair", "from": "A> 0 (011)^k 00 v", "to": "A> 0 (011)^(k+1) 1 v", "steps": "10k+12", "cases": "k>=0; final head two cells left; arbitrary untouched v; blank cells on left", "validated": { "instances": 560, "passed": 560 }, "source": "manual" } ], "template": { "file": null, "module": null, "machine": null, "diff": null, "applies": "unknown", "note": "Preflight found no existing machine-table conjugacy or current open-PR overlap. No proof template selected." }, "strategy": "Retain checked local components. Further mathematical progress needs an ordered invariant for the record-32 seed; repeated generic simulation or bounded-prefix rules do not close the gap.", "risks": [ "No global invariant excludes the zero-reserve A-return halt on the actual blank orbit.", "The executable normal form has extensive exact finite checks but its full general correctness is not yet formalized.", "The local Rocq theorems and finite entrance do not imply blank-start nonhalting; no whole-machine kill gate has run." ], "checkpoint_questions": [], "discord_check": null, "stats": { "simulated_steps": 1846460530, "cells": 42193, "nonzeros": 31455, "growth": "Expanding span in the measured prefix; no asymptotic law established." }, "status": "STUCK", "status_reason": "Completed bounded follow-up: exact finite-reserve normal form and formal local components; the infinite reserve bound for the blank orbit remains unproved.", "accelerator": { "endpoint": { "ev": "end", "reason": "max_loops", "loops": 100000, "step": 1846460530, "steps_exact": true, "nonzeros": 31455, "rules": 2103, "rules_by_level": { "1": 2103 }, "collatz_rules": 0, "failed_proofs": 0, "macro_moves": 90164, "chain_moves": 7733, "rule_moves": 2103, "block_size": 51, "seconds": 4.046 }, "rule_statistics": { "count": 2103, "types": { "Diff_Rule": 2103 }, "uses": { "1": 2103 } } }, "updated_utc": "2026-10-14T20:48:23.681626+00:00", "recommendation": "Retain checked local components. Further mathematical progress needs an ordered invariant for the record-32 seed; repeated generic simulation or bounded-prefix rules do not close the gap.", "halt_precursor": "E is entered only by D0=1LE. Thus D reading 0 with a 0 immediately to its left reaches E0, the undefined transition. Excluding this state-sensitive pattern globally remains unproved.", "stop_reason": "The funded invariant study is complete; its global safety obligation remains open.", "arithmetic_recurrence": "An exact word-dependent reserve map exists, with debit d+[exit=A]-c and explicit threshold/boundary cases. No closed arithmetic recurrence or infinite reserve bound has been proved.", "provenance": { "agent": "GPT-6 Astra (OpenAI)", "direct_engine": "existing tools/sim/tmsim", "formal_checker_run": false }, "study": "invariant-study-20261014/study.md" }