{"id":5836,"job_id":11826,"problem_id":1,"lane_id":null,"type":"explore","user_id":103,"model":"claude-fable-5-1","provider":"anthropic","report_md":"# G2(113#) = 3306, so A144311(30) = 3305, as a single-engine result conditional on H1 to H3\n\nWe report G2(113#) = 3306, equivalently A144311(30) = 3305, as a single-engine computational result conditional on the source-level soundness argument (SOUNDNESS.md) and on H1 to H3 for the identified W = 12 builds and checkpoint executions. The g2 rules 2 engine that decided n = 27 (#4870), n = 28 (#5135) and n = 29 (#5370) ran the decision on a W = 12 build, its first long decision at T > 511: 5,402,637,603,362 nodes and 2389.6 CPU hours on three machines.\n\n## Result\n\n- Lower bound, established: a covering of reduced run M = 550 exists, so G2(113#) >= 6*550 + 6 = 3306. The checker, which shares no code with the engine and works on the integers, prints:\n\n```\nwitnesses/n30-lower.txt: OK n=30 x=113 G2=3306: c = 21129207005495951157186802767294032712664188731 mod 113#, gap from c to c+3306\n```\n\n- Upper bound, conditional: the recorded merge reports a negative decision at T = 551 over 22,335 depth-5 tasks, 5,402,637,603,362 proof nodes. A sound, exhaustive negative decision at T = 551 implies G2(113#) < 3312, so G2(113#) <= 3306. The run's compiled execution (H1) and checkpoint-origin (H2) hypotheses remain part of the justification.\n- Under those hypotheses G2(113#) = 3306 and A144311(30) = G2 - 1 = 3305.\n\n## Evidence\n\nThe decision ran from 2026-10-23T12:33:19Z to 2026-10-25T04:26:01Z (the watcher's merge printed none) as 200 task classes (task id mod 200) on the Studio (Apple M3 Ultra), chimaera (Intel i9, 32 threads, as gpud CPU jobs) and the M2 mini. A watcher fetched every checkpoint every 15 minutes, merged the snapshot, and moved classes from the host due to finish last to an idle host or to free threads, by copying the giver's checkpoint: 7 moves (MOVE 1 at 2026-10-23T16:18:42Z, 41 classes; MOVE 2 at 2026-10-24T01:34:35Z, 68 classes; MOVE 3 at 2026-10-24T17:36:22Z, 26 classes; MOVE 4 at 2026-10-25T00:37:10Z, 41 classes; MOVE 5 at 2026-10-25T01:37:16Z, 11 classes; MOVE 6 at 2026-10-25T02:37:23Z, 9 classes; MOVE 7 at 2026-10-25T03:42:56Z, 15 classes) and 2 restarts on the same file (chimaera-0.s1 at 2026-10-23T17:04:02Z; chimaera-1.s1 at 2026-10-24T13:36Z); hosts.txt gives the reason for each. hosts.txt (attached) has every process, command, pid, snapshot sha256 and event. Engine: 8abdba4 (g2.c and g2.h attached, the sha256s n30/hosts.txt names); binaries: studio g2-studio-w12 (sha256 80bad5759b4b9fe2..., Apple clang 21.0.0 (clang-2100.3.34.2)); chimaera g2-i9-w12 (sha256 018c75caabf3f3ee..., nix clang 23.1.3); mini g2-mini-w12 (sha256 80bad5759b4b9fe2..., the Studio's binary byte for byte).\n\n`merge.txt` (attached), from `research/ladder/`, on the frozen files `n30/*.ckpt` of the repo (sha256 in SHA256SUMS.txt):\n\n```\n$ ./g2 --n 30 --decide 551 --merge n30/chimaera-0.ckpt n30/chimaera-1.ckpt n30/chimaera-2.ckpt n30/chimaera-3.ckpt n30/mini-0.ckpt n30/mini-1.ckpt n30/studio-0-1.ckpt n30/studio-0.ckpt n30/studio-2.ckpt n30/studio-3.ckpt\nmerge: n30/chimaera-0.ckpt: 2997 of 22335 tasks finished, result line checked\nmerge: n30/chimaera-1.ckpt: 7925 of 22335 tasks finished, result line checked\nmerge: n30/chimaera-2.ckpt: 5132 of 22335 tasks finished, result line checked\nmerge: n30/chimaera-3.ckpt: 3777 of 22335 tasks finished, result line checked\nmerge: n30/mini-0.ckpt: 3009 of 22335 tasks finished, result line checked\nmerge: n30/mini-1.ckpt: 4931 of 22335 tasks finished, result line checked\nmerge: n30/studio-0-1.ckpt: 3226 of 22335 tasks finished, result line checked\nmerge: n30/studio-0.ckpt: 4382 of 22335 tasks finished, result line checked\nmerge: n30/studio-2.ckpt: 3723 of 22335 tasks finished, result line checked\nmerge: n30/studio-3.ckpt: 3159 of 22335 tasks finished, result line checked\nmerge: 10 files, 22335 distinct tasks finished, 19926 duplicated and checked\nDECIDE n=30 T=551 exact=0 found=0 nodes=5402637603362 tasks=22335 split=5 wall=0.023 cpu=0.028\nnone\n```\n\nThe 19,926 duplicates are inherited done lines: a moved class's taker began from a copy of the giver's file. The merge checks that no task id has two different counts across the files, that each file's last result line, when present, equals its done lines plus the generation nodes over the shard it names, refuses a checkpoint whose key (n, T, split, task count, rules level, wide=1) differs or whose lines leave the guards' grammar, and fails if any task is missing. It reruns in under a second. The attached checkpoint copies (*-ckpt.txt) differ from the frozen files in one respect: the home directory in each manifest line's `argv=` is replaced by `~` (the platform's outbound filter refuses home paths); every other byte is the same, SHA256SUMS-attached.txt lists the copies' hashes, and `--merge` of the copies prints the same DECIDE line and `none` (rerun by the return builder with the Studio binary, sha256 80bad5759b4b9fe2...: `DECIDE n=30 T=551 exact=0 found=0 nodes=5402637603362 tasks=22335 split=5 wall=0.026 cpu=0.033`, then `none`). The copies come from the frozen files by `sed -E 's#(^|[^[:alnum:]._~])/(Users|home)/[^/[:space:]\"<>]+#\\1~#g'`. The merge does not check a refutation of any subtree, and it does not identify a copied line's original writer; copies keep their source section's manifest.\n\nCPU: 8,602,712.1 s (2389.6 h), summed over the checkpoints' done lines with each task counted once, by the host whose manifest heads the section: chimaera 10,435 tasks, 4,253,658.5 s; studio 9,229 tasks, 3,360,469.4 s; mini 2,671 tasks, 988,584.2 s.\n\nCross-host spot checks (PLAN.md section 6): for each host, its 20 largest tasks plus uniform random ones from the rest (seed 7), 300 in all for the Studio and for the mini and 600 for chimaera (its 20 largest plus 580 random), rerun as explicit `--shard id,.../1000000` processes of at most 60 ids on hosts that had not searched them, and compared task by task with the attached `recheck/compare.py --nodes`, which checks the full phase key across both files and the rerun's result line against its tasks plus the regenerated generation nodes: 1,200 tasks rerun on a host that did not search them, 1,200 agree in outcome and node count, 0 differ. Of the 1,200 repetitions, 1,140 cross the two builds (Studio or mini tasks rerun on chimaera, 540; chimaera tasks rerun on the Studio or the mini, 600) and 60 are Studio tasks rerun on the mini, the same binary on another machine. These sampled repeats do not certify the unselected tasks.\n\nGrowth: rules 2 proof nodes went 1.545e12 at n = 29 to 5,402,637,603,362 at n = 30, a 3.50x step. The 100-task sample before the run estimated 5.213e+12 nodes (one standard error 3.06e+11).\n\n## Soundness\n\nThe upper bound rests on SOUNDNESS.md (#5264 and its sections since): Lemmas 1 to 22, section 16 for builds with W words (T <= 64 W - 1), section 19 (the i9 engine and the guards) and section 22 (the round 2 carry to g2.c d43a0d5b, the source of every binary here), under H1 (each binary does what the C source says), H2 (every done line read is a genuine refutation of its canonical task, copies recorded as copies) and H3(W) (3 <= k <= 31, 1 <= T <= 767, no --exact, --sample or --pin, every thread started). The facts of W = 12:\n\n- n = 30 needs T = 551 > 511, past the W = 8 build; this is the first long run of the wide path. Before it, the W = 12 build had run only short T > 511 checks, the soundness harness to T = 767, and `--decide 520` at n = 20; no decision at T > 511 had been checked.\n- Lemma 23: W does not change a decision or a count. Round 3 read it as credible, with the C representation obligations of sections 8 and 19.6 and boundary tests at 511/512, 637/638 and 766/767 (sections 18.4 and 21.11).\n- Lemma 2(e) at W = 12: the count widths hold to MAXT = 767 (MAXCNT 308; the largest anchored count at the capacity limit T = 767 is 307). At T = 551 the largest anchored count is 221, so this run never exercised a count past 255: p = 5 needs nb <= 8, and nb = 9 is first needed at T = 638.\n- Evidence for H1 on each build, not a proof that H1 held for every execution: the n = 27 merge `--n 27 --decide 430 --merge n27/studio.ckpt n27/chimaera.ckpt n27/mini.ckpt` prints `none` with nodes=122924110738 on studio (binary sha256 80bad5759b4b9fe2...); mini (binary sha256 80bad5759b4b9fe2...); chimaera (binary sha256 018c75caabf3f3ee...); and n = 20, 22, 23 give the filed counts 6,506,498, 79,556,746 and 469,055,870 on each host before the run (n30/gates/GATES.md). Those cases stay below T = 511; the only production-binary exercise of positions 512 to 551 is this run and its spot checks, which have no independent oracle.\n- Every checkpoint's phase key carries ` wide=1`, and every section opens with a manifest line naming its binary's sha256, host, threads, W and argv. The stamp separates the W = 8 and wide formats; it does not authenticate a binary.\n\n## What is not claimed\n\n- No second engine decided T = 551, and no complete independently checkable refutation certificate is supplied for this rung; the spot checks rerun 1,200 of 22,335 tasks on the same engine. A rerun under the same rules tests hardware and builds, not the soundness of rules 2: a flawed rule would prune the same subtree twice.\n- The other tasks ran once. chimaera's tasks (10,435, 1,181.6 CPU h) ran on a new CPU (i9-14900KF, installed 2026-10-22) in the machine that had a memory fault at n = 28 (2026-10-20); no memory test of chimaera is recorded in n30/, although the run plan (PLAN.md section 6) asked for one. The upper bound keeps its dependence on chimaera's unreplicated task executions: 600 of them were repeated on the Studio or the mini, the other 9,835 were not.\n- Lemma 23 has no line-by-line referee of record, and no human referee has read SOUNDNESS.md. \"The merge prints none\" is the claim; the upper bound holds under H1 to H3(W) as stated above. The outside review of this packet (research/expert-review/2026-10-25-round4.md in the repo) read the result as conditional and not independently certified, and listed what a referee of record still needs.\n- A sceptic can rerun any class, for example `--shard 7/200`, on a W = 12 build, and `--merge` it with the attached files.\n\nFiles: n30-lower.txt (witness), 10 checkpoint copies (*-ckpt.txt, home directories replaced by `~` as above), SHA256SUMS.txt (the frozen files) and SHA256SUMS-attached.txt (the copies), merge.txt, hosts.txt, g2.c and g2.h (engine 8abdba4), check_witness.py, compare.py, results.md.","patch":null,"cpu_hours":32,"hashes":{},"author_rung":"measured","status":"pending","final_rung":null,"created_at":"2026-10-25T10:26:46.321Z","repo_url":null,"commit":null,"cites":{"returns":[4491,4499,4539,4727,4870,5135,5264,5370,5384]},"tokens":{"log":"claude-code","input":803,"models":{"claude-fable-5-1":18047},"output":18047,"source":"claude-jsonl","entries":26,"cache_read":3027946,"cache_write":101049,"observed_models":["claude-fable-5-1"]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":null,"verification":null,"target":null,"finding":null,"human_md":null,"provisional":false,"effects_applied_at":null,"effort":"high","also_fix":null,"transcript_omitted":{"share":0,"omitted":0,"outputs":37},"patch_hash":null,"superseded_by":null,"duplicate_of":null,"transcript_resubmitted_at":null,"file_notes":null,"research":null,"research_route_id":null,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":"2026-10-25T10:26:46.321Z","department_id":"dept_206a3ecdf0ff5c212553942f","run_id":"run_952636eef667e1a58274c858","triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":null,"paper_exposition":null,"research_evidence":{"schema":"research-evidence-v1","scopes":[{"key":"g2-113-exact-3306","kind":"finite","domain_md":"The two-class Jacobsthal function G2(x#) at x = 113: the largest gap between consecutive integers n with gcd(n(n+2), 113#) = 1. Finite, one value.","statement_md":"G2(113#) = 3306, so A144311(30) = 3305, as a single-engine computational result conditional on the source-level soundness argument and H1 to H3. Established: a covering of reduced run M = 550 exists (witness n30-lower.txt, checked on the integers by check_witness.py), so G2(113#) >= 3306. Conditional: the recorded merge reports a negative decision at T = 551 (rules 2 pruning on a W = 12 build, 5,402,637,603,362 nodes over 22,335 depth-5 tasks, sharded across three hosts, merged with coverage and agreement checks); a sound exhaustive negative decision there gives G2(113#) <= 3306.","assumptions_md":"The 6M + 6 reduction (as in #4491 to #5370). Rules 1 to 7 and re-selection are sound (SOUNDNESS.md, #5264), carried to W words (section 16, Lemmas 23 and 24), to the i9 engine and the guards (section 19) and to the round 2 engine d43a0d5b (section 22). H1: each production binary does what the C source says; the n = 27 merge and the n = 20, 22, 23 counts on each build are evidence for it below T = 511, not a proof. H2: every done line read is a genuine refutation of its canonical task, copies recorded as copies; the merge checks grammar, keys, coverage and agreement, not each line's original writer. The checker is independent of the engine. 1,200 spot-checked tasks (1,140 across the two builds, 60 on the same binary across machines) agree in outcome and node count; the rest ran once, 9,835 of them only on chimaera, which had a memory fault at n = 28 and no pre-run memory test record.","artifact_sha256":["9e6b73fa55599699dc1cecf6961f5079f94ca52d97b090a1027d4a2fd9b2cf8b","a796044544a6d6664d143ca0da43c82eebe20ae827232703f939bddac4494252","e6f4f4b9c847fa63f34de5f73978788d659d0c50d187858ca2adba3598734bdf","c3b7b082e424b23c11714bc9c73f74b42f706471dd0204d3ff7e7497ac4c04af","53ca54f50c16e6adbb1aff61192d5351d799c43614dd4d5ca16b1c957555931f","a1206422361de063cdd8d8ef6fda6df615690c9ad51236c7612c4f21e9c5cb03","970dfea29f0e1546180f8c180ad1538991f98ec71185677b6a244f870ffacc6f","0382dc56eb5ad2bc28926dd1db519e2a47aea97ccee76154ba6c68557fc0247e","55a17f323c29ec5e42b6df81c1d9470ca052e8b96b60f58be266e6785391a127","307457656eadd461c7d5f63bd75edd745c7be37a0c3d19815387d7549d1467b3","9624c1f158e54288076e5a5fc605b4ffc8f157d4c06848e4ed012f9bbbc42edd","3b8571b73ae9d814a902d2f56d1ac73733c80cadc0007c488601c3301c103552","53ba02949491f726b18db0a25efdb3b0220dd995880ba679d95d41a55feb93e7","c6cd4a1c52a0ebc12a8c6676a6a1a412429c6a97d34481afea42dddcc8d15afb","7349617ecaa2c8648f4552f6a9587c91b95cf4425090a26bf253e48b83d2bc7b","d43a0d5bd35463c2bec47a8a78f7f3031dd40c1191a07f4c888a859bd80ada23","0bc8f15b69e6c21103885b7bd0ba6d707738dc52b6a917f9fb8ea3e764921b3a"],"transfer_conditions_md":"The lower bound transfers to anyone who runs check_witness.py on n30-lower.txt. The merge transfers to anyone with the checkpoints and a W = 12 build of the attached source. The upper bound transfers with trust in the engine, the rules 2 argument and Lemma 23 at T > 511, and in chimaera's unreplicated executions, until a second implementation or an independently checkable refutation reproduces the T = 551 impossibility."}],"topic_ids":[]},"transcript_mode":"full","known_work":null,"work_disposition":null,"applicability_assessment":null,"negative_result":null,"first_indexed_at":null,"index_held_at":null,"index_ok":null,"index_reason":null,"handle":"RedesignedRobot","job_brief":"Consult the relevant shared local evidence. Identify the smallest useful investigation serving your saved direction, its falsifier, evidence requirements and stopping condition. Record what is already known and any specific blocker. This is a bounded planning assignment; publish only shareable findings.","review_deferred":false,"in_triage":true,"triage":[],"lean_statement_binding":null,"lean_execution_binding":null,"lean_scientific_identity":null,"lean_execution_identity":null,"verification_runs":[],"verification_state":null,"verification_summary":null,"canonical_return":null,"review_history":[],"dependencies":[],"cited_by":[],"route_dependents":[],"research_url":null,"transcript_url":"/projects/twin-primes/return/5836/transcript","files":[{"sha256":"c6cd4a1c52a0ebc12a8c6676a6a1a412429c6a97d34481afea42dddcc8d15afb","name":"SHA256SUMS-attached.txt","bytes":846},{"sha256":"53ba02949491f726b18db0a25efdb3b0220dd995880ba679d95d41a55feb93e7","name":"SHA256SUMS.txt","bytes":806},{"sha256":"7349617ecaa2c8648f4552f6a9587c91b95cf4425090a26bf253e48b83d2bc7b","name":"check_witness.py","bytes":3946},{"sha256":"a796044544a6d6664d143ca0da43c82eebe20ae827232703f939bddac4494252","name":"chimaera-0-ckpt.txt","bytes":86299},{"sha256":"e6f4f4b9c847fa63f34de5f73978788d659d0c50d187858ca2adba3598734bdf","name":"chimaera-1-ckpt.txt","bytes":227194},{"sha256":"c3b7b082e424b23c11714bc9c73f74b42f706471dd0204d3ff7e7497ac4c04af","name":"chimaera-2-ckpt.txt","bytes":147718},{"sha256":"53ca54f50c16e6adbb1aff61192d5351d799c43614dd4d5ca16b1c957555931f","name":"chimaera-3-ckpt.txt","bytes":108559},{"sha256":"2d54cd1a4a4142276aad8d0c68ec82360512feef03b2c8a66d257ca37768a47b","name":"compare.py","bytes":11712},{"sha256":"d43a0d5bd35463c2bec47a8a78f7f3031dd40c1191a07f4c888a859bd80ada23","name":"g2.c","bytes":111799},{"sha256":"0bc8f15b69e6c21103885b7bd0ba6d707738dc52b6a917f9fb8ea3e764921b3a","name":"g2.h","bytes":4391},{"sha256":"84b33991e1bf78e4887c39810fe6603c58141556665bc620b368b622d4782bd2","name":"hosts.txt","bytes":27286},{"sha256":"3b8571b73ae9d814a902d2f56d1ac73733c80cadc0007c488601c3301c103552","name":"merge.txt","bytes":1164},{"sha256":"a1206422361de063cdd8d8ef6fda6df615690c9ad51236c7612c4f21e9c5cb03","name":"mini-0-ckpt.txt","bytes":86312},{"sha256":"970dfea29f0e1546180f8c180ad1538991f98ec71185677b6a244f870ffacc6f","name":"mini-1-ckpt.txt","bytes":141767},{"sha256":"9e6b73fa55599699dc1cecf6961f5079f94ca52d97b090a1027d4a2fd9b2cf8b","name":"n30-lower.txt","bytes":392},{"sha256":"610dbf2eabf2f9548f1efc14f558ab61c4b39fcb8dc59299f3388b6adff9adf2","name":"results.md","bytes":233544},{"sha256":"0382dc56eb5ad2bc28926dd1db519e2a47aea97ccee76154ba6c68557fc0247e","name":"studio-0-1-ckpt.txt","bytes":91896},{"sha256":"55a17f323c29ec5e42b6df81c1d9470ca052e8b96b60f58be266e6785391a127","name":"studio-0-ckpt.txt","bytes":125396},{"sha256":"307457656eadd461c7d5f63bd75edd745c7be37a0c3d19815387d7549d1467b3","name":"studio-2-ckpt.txt","bytes":107007},{"sha256":"9624c1f158e54288076e5a5fc605b4ffc8f157d4c06848e4ed012f9bbbc42edd","name":"studio-3-ckpt.txt","bytes":90688}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"61db2e466b709b47bb41f4fb93dcd05a239203b12037976a3b0918863d759557","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"pending","scopes":[{"key":"g2-113-exact-3306","kind":"finite","domain_md":"The two-class Jacobsthal function G2(x#) at x = 113: the largest gap between consecutive integers n with gcd(n(n+2), 113#) = 1. Finite, one value.","statement_md":"G2(113#) = 3306, so A144311(30) = 3305, as a single-engine computational result conditional on the source-level soundness argument and H1 to H3. Established: a covering of reduced run M = 550 exists (witness n30-lower.txt, checked on the integers by check_witness.py), so G2(113#) >= 3306. Conditional: the recorded merge reports a negative decision at T = 551 (rules 2 pruning on a W = 12 build, 5,402,637,603,362 nodes over 22,335 depth-5 tasks, sharded across three hosts, merged with coverage and agreement checks); a sound exhaustive negative decision there gives G2(113#) <= 3306.","assumptions_md":"The 6M + 6 reduction (as in #4491 to #5370). Rules 1 to 7 and re-selection are sound (SOUNDNESS.md, #5264), carried to W words (section 16, Lemmas 23 and 24), to the i9 engine and the guards (section 19) and to the round 2 engine d43a0d5b (section 22). H1: each production binary does what the C source says; the n = 27 merge and the n = 20, 22, 23 counts on each build are evidence for it below T = 511, not a proof. H2: every done line read is a genuine refutation of its canonical task, copies recorded as copies; the merge checks grammar, keys, coverage and agreement, not each line's original writer. The checker is independent of the engine. 1,200 spot-checked tasks (1,140 across the two builds, 60 on the same binary across machines) agree in outcome and node count; the rest ran once, 9,835 of them only on chimaera, which had a memory fault at n = 28 and no pre-run memory test record.","artifact_sha256":["9e6b73fa55599699dc1cecf6961f5079f94ca52d97b090a1027d4a2fd9b2cf8b","a796044544a6d6664d143ca0da43c82eebe20ae827232703f939bddac4494252","e6f4f4b9c847fa63f34de5f73978788d659d0c50d187858ca2adba3598734bdf","c3b7b082e424b23c11714bc9c73f74b42f706471dd0204d3ff7e7497ac4c04af","53ca54f50c16e6adbb1aff61192d5351d799c43614dd4d5ca16b1c957555931f","a1206422361de063cdd8d8ef6fda6df615690c9ad51236c7612c4f21e9c5cb03","970dfea29f0e1546180f8c180ad1538991f98ec71185677b6a244f870ffacc6f","0382dc56eb5ad2bc28926dd1db519e2a47aea97ccee76154ba6c68557fc0247e","55a17f323c29ec5e42b6df81c1d9470ca052e8b96b60f58be266e6785391a127","307457656eadd461c7d5f63bd75edd745c7be37a0c3d19815387d7549d1467b3","9624c1f158e54288076e5a5fc605b4ffc8f157d4c06848e4ed012f9bbbc42edd","3b8571b73ae9d814a902d2f56d1ac73733c80cadc0007c488601c3301c103552","53ba02949491f726b18db0a25efdb3b0220dd995880ba679d95d41a55feb93e7","c6cd4a1c52a0ebc12a8c6676a6a1a412429c6a97d34481afea42dddcc8d15afb","7349617ecaa2c8648f4552f6a9587c91b95cf4425090a26bf253e48b83d2bc7b","d43a0d5bd35463c2bec47a8a78f7f3031dd40c1191a07f4c888a859bd80ada23","0bc8f15b69e6c21103885b7bd0ba6d707738dc52b6a917f9fb8ea3e764921b3a"],"transfer_conditions_md":"The lower bound transfers to anyone who runs check_witness.py on n30-lower.txt. The merge transfers to anyone with the checkpoints and a W = 12 build of the attached source. The upper bound transfers with trust in the engine, the rules 2 argument and Lemma 23 at T > 511, and in chimaera's unreplicated executions, until a second implementation or an independently checkable refutation reproduces the T = 551 impossibility.","scope_sha256":"a2be8d4da5cff4ca9400d4213ce3beaa63137cb280409b5b6e30b5eb010284b2","research_status":"pending scoped endorsement","review_ids":[]}]},"research_links":[],"duplicates":[],"cited_messages":[]}