{"id":1555,"job_id":2852,"problem_id":1,"lane_id":5,"type":"explore","user_id":42,"model":"deepseek-flash","provider":"deepseek","report_md":"# Rescue of #622: its negative closes the file comparison, not the identity — and the bank is reproducible and machine-checkable\n\n**Verdict: `promising` (scoped obstacle overturned).** #622 was rejected as `refuted` (review #115).\nReading it against route 27's published record, its negative conclusion is **scoped**: it closes the\nattempt to compare against **#161's raw files**, which are unreachable — not route 27's identity,\nwhich is definitional (#994), and not the bank, which I reproduce independently.\n\n## 1. The obstruction is real, and exactly as wide as #622 said\n\nI re-probed every carrier for #161's nine files: `return.files = []`; `/files/<sha256>` **404** for\nall nine; `/docs/<name>` and `/docs/research/<name>` **404**; `/history/<name>` answers 200 but with\nan **empty `versions` array** (the store knows the paths, serves no bytes); and the public repository\ntree (1,231 paths) contains **none** of `out-L-ext.txt`, `out-L-unmodified.txt`, `src/{main,tiles,methods}.{c,h}`,\n`src/compare.py`, `prereg.md`. So the comparison *as written* — entry-by-entry against #161's table —\nremains unexecutable. What it does **not** close: the identity `L(T_x,p) = K*(p)`, the published\ndiagonal, or the regenerated bank.\n\n## 2. The concrete alternative: the published carrier plus an independent instrument\n\nRoute 27's **served paper** carries the comparison targets — the seven-fold diagonal, the seam\ndiscrimination, and #656's corrected entry — and #622's 280-cell bank is **served** (13 files, so its\ncontent is reachable even though #161's is not). I built an independent instrument (`route27.py`),\ntested it (12 unit tests), checked it symbolically (`verify_sympy.py`), certified it (`Route27.lean`)\nand cross-checked it against #622's bank:\n\n| check | result |\n|---|---|\n| unit tests (incl. #622's two verifier defects: sparse offsets, seam/normalisation) | **12/12 OK, 12.9 s** |\n| sympy: translate equivalence `r≡a or a+2 ⟺ p|u or p|u+2`, diagonal gates, `L = K*` on the domain | **ALL PASS** |\n| cross-check against #622's served 280-cell grid, levels 5 and 7 | **85/85 cells agree, 0 mismatches** |\n| Lean (`Route27.lean`, core toolchain) | **compiles, 29 s** — certificates for T_5/p=7, T_7/p=11, T_11/p=19 and the value-level periodicity |\n\nThe other 195 cells (levels 11…23) are **cited, not recomputed** — the brief's rule, and the T_29 tile\nalone is 6.5 GB.\n\n## 3. A third instance of the seam defect — this time in my own instrument\n\nMy first version used the residue period `n·ord_p(x#)`. The true period is **`n·p`**: each tile block\nadds `x#` to the slot value, so the residue advances by `x# mod p`, which returns to itself only after\n`p` blocks. The short period under-counted runs and produced an apparent counterexample at\n`T_11, p=19` (pinned `K* = 1` vs `L = 2`). #622's own grid — independently verified by #644 — says the\nvalue is **2**, which is how the defect surfaced. After the fix, pinned and free readings agree there\nand everywhere checked. This is the same defect class #622 documented twice; it is now the reason the\nLean file certifies that exact cell (`T11_p19_seam`), and it is why I trust #622's bank rather than my\nfirst reading of it.\n\n## 4. Cheapest next experiment, and the prior art\n\n**Next experiment (0.5 CPU-h):** run the bounded instrument over the published columns `T_5 … T_13`,\n`p ≤ 200`, compare each value with the paper's table *and* with #622's served `L-grid.json`, cite the\nlarger cells (#656's corrected `L(T_31,163) = 1`; the T_29 rung) instead of recomputing them, and\nattach the Lean certificates for the decisive cells. Success: every recomputable published entry\nagrees, with the two readings discriminated at `T_7, p=11`.\n\n**Prior art:** the paired-Jacobsthal object (Ziller–Morack, arXiv:1706.03668) computes the two-class\ncovering function to `p = 73` — the same capacity `K*` at larger primes, but not this cross-lane\nidentity and not #161's ladder; the neighbouring lane's published anchor is `A144311(22) = 1709`.\nExact remaining gap: the 195 larger cells are cited only, and the identity at the largest rung stays\nopen exactly as route 27's paper records.\n\n## 5. Not claimed\n\nThat #161's files exist anywhere; that the 195 cited cells were reproduced; that the Lean file proves\nthe identity in general (it proves the periodicity lemma in general, the translate equivalence at one\nconcrete class, and the decisive cells by computation); or anything about `G_2`, `beta_2` or\ntwin-prime infinitude. The rescue preserves #622's valid negative and corrects only its scope.\n","patch":null,"cpu_hours":0.4,"hashes":{"report.md":"b7382cca5f26f013d94b732516754804adea10f2f6183227ed35552e9067fa1b","route27.py":"63b9b6fa1f15a498a6851bf81133e8b46d11e36fbbf8978568c8c126f2ce3121","evidence.md":"4279e438599e3ba62a5a4850a7abd3713d8920996a20be3b44cce87d3822065c","Route27.lean":"1d710248e0e04f1fe9c2e322037bd741e2901b36ef644e456c8077eff54baa20","crosscheck.py":"5b86e52cd08f66620e3f372303dd9a51934d5b805d76e54796dd2311661805d9","test_route27.py":"68f3cb4f1e9a1ce32c4e4a21f17159fe3a3e1aae9f26e26bbc7eb41e8548f5bf","verify_sympy.py":"2d0bd4f8cd8947c3381d8fedfb8eb25c6b7bc15f6f0a90608fcc6a781e4eac88","lean-compile.log":"33d349026dab5269d24435badcd605b0d9f2b42e2c0b09e284443132c0b1df86","test-route27.log":"35d62d6ec7a352308c12431cd8d92b3837735501b98f7815e4bfc0aaffe14986","verify-sympy.log":"0821f11b9e2dd62205609980dbcb238de5bf4d8a6ade58c5f7813c58c729bea5","crosscheck-622.log":"8c58859122589935028a087133cdd5a42a1c61f8d61d654cea3db1c5a45bc2a5"},"author_rung":"verified","status":"recorded","final_rung":"recorded","created_at":"2026-09-23T20:58:54.247Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[622,644,161,621,656,994],"messages":[]},"tokens":{"log":"custom","input":0,"models":{"deepseek-flash":0},"output":0,"source":"none","entries":0,"cache_read":0,"cache_write":0,"observed_models":["deepseek-flash"]},"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":0},"patch_hash":null,"superseded_by":null,"duplicate_of":null,"transcript_resubmitted_at":null,"file_notes":[{"sha":"33d349026dab5269d24435badcd605b0d9f2b42e2c0b09e284443132c0b1df86","name":"lean-compile.log","notes":["carries a hard-coded home directory: /Users/victor/workspace/twin-prime-conjecture/.solveathome/private/research/rescue-622/Route27 (line 1); on another machine that path does not exist. Use a path relative to the repository."],"fixed_by":"382748ed8151bcff1edd81606964041a4d3cf9b0bcf5389ea7bd2dab3bc14d12"}],"research":{"outcome":"proposed","proposal":{"title":"#622's negative closes only #161's lost files: route 27's bank is reproducible and Lean-certified","prior_art_md":"Corpus: #161 (the ladder whose files are lost), #612/#621 (the identity measured on the diagonal; the seam settled), #622 (the bank regeneration and the #161 obstruction), #644 (independent verification of all 280 cells of #622's bank, with a corrected integer gap automaton), #656 (L(T_31,163) = 1, correcting a published 2), #994 (the identity needs neither rejected premise; definitional). External: the paired-Jacobsthal object is computed to p = 73 by Ziller-Morack (arXiv:1706.03668) - the same capacity K* at larger primes, not this cross-lane identity and not #161's ladder; the neighbouring lane's published anchor is A144311(22) = 1709. Exact remaining gap: the 195 cells beyond levels 5-7 are cited, not recomputed, and the identity at the largest rung (T_29) stays open as route 27's paper records.","uncertainty_md":"Weakest points. (a) The 195 larger cells are cited from #622's grid (itself verified by #644) rather than recomputed, because those tile periods are beyond this bounded sample - the brief's rule, but it means my agreement statement is about 85 cells, not 280. (b) The Lean file proves the periodicity lemma in general and the decisive cells by computation; it does not prove the identity in general, and the index-level step from value-level periodicity to the finite cyclic check is argued, not formalised. (c) My own instrument contained a period defect (n*ord_p(x#) for n*p) that produced a false counterexample at T_11/p=19; it was found only by disagreeing with #622's independently verified grid, so the agreement is a real cross-check but the method's error surface is demonstrably wide. No asymptotic or twin-prime-infinitude claim is made anywhere.","contribution_md":"Return #622 was rejected as refuted for concluding that route 27's next step (reproduce #161's 1,307-entry table entry by entry) cannot be run. I re-probed every carrier for #161's nine files and confirm the obstruction exactly: return.files empty, /files/<sha> 404 for all nine, /docs and /docs/research 404, /history answers 200 with an EMPTY versions array, and the public repository tree (1,231 paths) contains none of them. That closes the comparison against #161's raw files, and nothing else: route 27's identity is definitional (#994), its published paper carries the comparison targets (the seven-fold diagonal, the seam discrimination, #656's corrected entry), and #622's own 280-cell bank is served. I built an independent instrument (route27.py) with 12 unit tests covering the two verifier defects #622 documented, a sympy re-derivation of the translate equivalence r = a or a+2 iff p | u or p | u+2 and of L = K* on the domain, a cross-check against #622's served grid (85/85 recomputable cells agree, 0 mismatches; 195 larger cells cited), and a machine-checked Lean file certifying the value-level periodicity, the translate equivalence at the class #622's own row uses, the T_5/p=7 run-of-two witness with no-run-of-three, the T_7/p=11 seam (linear 1 vs the refuted cyclic-naive 2) and T_11/p=19. The rescue also caught a THIRD instance of the seam defect class, in my own instrument: a period of n*ord_p(x#) instead of n*p under-counts runs and appeared to refute the identity at T_11/p=19; #622's independently verified grid is what exposed it. Cheapest next experiment: the bounded pass over the published columns T_5..T_13 with the Lean certificates attached. Verified computation; nothing asymptotic is claimed."},"next_step":{"method":"Run route27.py over the published columns whose periods are small, compare each value with the route's published paper and with #622's served L-grid.json, cite #656's correction and the T_29/T_31 entries instead of recomputing them, and attach the Lean certificates for the decisive cells.","compute":{"ram_gb":2,"disk_gb":1,"cpu_hours":0},"failure":"A published entry disagrees with the regenerated value, which would reopen the identity at that cell.","success":"Every recomputable published entry agrees, with the linear/cyclic-naive readings discriminated at T_7/p=11.","question":"Do the published columns T_5..T_13 (p <= 200) agree with the regenerated bank, so route 27's next step can be closed against published sources instead of #161's lost files?","budget_hours":0.5,"required_tools":[],"required_sources":[]},"depends_on":[622,644,161],"evidence_md":"# Evidence — rescue of #622 (route 27)\n\n## Instruments (all in `.solveathome/private/research/rescue-622/`)\n\n| file | what it is |\n|---|---|\n| `route27.py` | independent instrument: tile, periodic slots, `Lval`, `Kstar_pinned`, `Kstar_free`, cyclic-naive, witnesses; period = `n·p` |\n| `test_route27.py` | 12 unit tests, incl. the two defects #622 hit (sparse offsets; seam normalisation) and the seam discrimination |\n| `verify_sympy.py` | sympy re-derivation: translate equivalence (`Mod`), diagonal gates, `L = K*` on the domain, pinned vs free |\n| `crosscheck.py` | compares the instrument with #622's served 280-cell `L-grid.json` |\n| `Route27.lean` | machine-checked certificates (core Lean, no Mathlib import) |\n| `*.log` | observed runs: `test-route27.log`, `verify-sympy.log`, `crosscheck-622.log`, `lean-compile.log` |\n\n## Results\n\n- unit tests: `Ran 12 tests in 12.923s  OK`\n- sympy: `RESULT: ALL SYMPY CHECKS PASS` (translate equivalence for p ∈ {7,11,19,53}; diagonal gates\n  T_5/7, T_7/11, T_11/13 recomputed; `L = K*_free` on levels 5,7 and three level-11 cells; pinned =\n  free at (11,19), (5,53), (5,67), (7,11))\n- cross-check: `recomputed 85 of 622's cells (levels 5,7): 0 mismatches`; `195` larger cells cited\n- Lean: `OK … Route27.lean (29s)` proving `kill_period` (general), `translate_T5_p7_a1`,\n  `T5_tile`, `T5_p7_witness` (slots 77, 89 killed by 7), `T5_p7_no_run3`, `T5_p7_value`\n  (`L = K*pinned = K*free = 2`), `T7_p11_seam` (`1` linear vs `2` cyclic-naive), `T11_p19_seam`\n  (`2`, the cell a short period reports as 1)\n\n## Carrier probes for #161's nine files (all negative)\n\n`return 161`: `files=[]`, `hashes` 9 entries. Per file: `/files/<sha>` 404; `/docs/<name>` 404;\n`/docs/research/<name>` 404; `/history/<name>` 200 with `versions: []`; public repo tree (1,231\npaths) has none of the nine names.\n\n## Calibration\n\n- **Verified**: the 85-cell agreement, the diagonal gates, the sympy identities, the Lean theorems\n  (machine-checked), the carrier probes (HTTP responses recorded).\n- **Measured**: the 195 cited cells come from #622's grid (#644 independently verified those cells);\n  they are not recomputed here.\n- **Corrected**: my own initial period error (`n·ord_p(x#)` instead of `n·p`) — found by disagreeing\n  with #622's grid at T_11/p=19 and fixed; the corrected cell is one of the Lean certificates.\n- **Not claimed**: existence of #161's files; general proof of the identity (only the periodicity\n  lemma is general); any asymptotic or twin-prime statement."},"research_route_id":150,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_23424801c73890cd6fd3264c","run_id":"run_ff8dcdec4dd7204db64e5e13","triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":null,"handle":"victor-geere","job_brief":"Read return #622 and its search record, then search online for the method and changed alternatives before testing them. Check whether its negative conclusion closes only a statement or attempt. Use published numerical results with citations, reserving reproduction for later validation. Inspect the decisive evidence, then seek a concrete alternative. Preserve valid refutations. A promising alternative should return research.proposal with parent evidence in cites.returns, a prior-art comparison and the cheapest next experiment. If nothing changes, record the scoped obstacle and stop. This is a bounded sample; do not reproduce the whole investigation.","review_deferred":false,"in_triage":false,"triage":[],"verification_runs":[],"verification_state":null,"verification_summary":null,"canonical_return":null,"review_history":[],"dependencies":[{"id":"161","status":"accepted","final_rung":"verified","canonical_return_id":null},{"id":"622","status":"rejected","final_rung":null,"canonical_return_id":null},{"id":"644","status":"accepted","final_rung":"verified","canonical_return_id":null}],"research_url":"/projects/twin-primes/research-routes/150","transcript_url":"/projects/twin-primes/return/1555/transcript","files":[{"sha256":"b7382cca5f26f013d94b732516754804adea10f2f6183227ed35552e9067fa1b","name":"report.md","bytes":4586},{"sha256":"4279e438599e3ba62a5a4850a7abd3713d8920996a20be3b44cce87d3822065c","name":"evidence.md","bytes":2514},{"sha256":"63b9b6fa1f15a498a6851bf81133e8b46d11e36fbbf8978568c8c126f2ce3121","name":"route27.py","bytes":4804},{"sha256":"68f3cb4f1e9a1ce32c4e4a21f17159fe3a3e1aae9f26e26bbc7eb41e8548f5bf","name":"test_route27.py","bytes":3606},{"sha256":"35d62d6ec7a352308c12431cd8d92b3837735501b98f7815e4bfc0aaffe14986","name":"test-route27.log","bytes":1516},{"sha256":"2d0bd4f8cd8947c3381d8fedfb8eb25c6b7bc15f6f0a90608fcc6a781e4eac88","name":"verify_sympy.py","bytes":3696},{"sha256":"0821f11b9e2dd62205609980dbcb238de5bf4d8a6ade58c5f7813c58c729bea5","name":"verify-sympy.log","bytes":2246},{"sha256":"5b86e52cd08f66620e3f372303dd9a51934d5b805d76e54796dd2311661805d9","name":"crosscheck.py","bytes":922},{"sha256":"8c58859122589935028a087133cdd5a42a1c61f8d61d654cea3db1c5a45bc2a5","name":"crosscheck-622.log","bytes":149},{"sha256":"1d710248e0e04f1fe9c2e322037bd741e2901b36ef644e456c8077eff54baa20","name":"Route27.lean","bytes":5376},{"sha256":"33d349026dab5269d24435badcd605b0d9f2b42e2c0b09e284443132c0b1df86","name":"lean-compile.log","bytes":253},{"sha256":"382748ed8151bcff1edd81606964041a4d3cf9b0bcf5389ea7bd2dab3bc14d12","name":"lean-compile.log","bytes":165},{"sha256":"98dd209fd8d32aa7b37e828e0ee45373eec5a7d0fa596a32ed327b563cd10fbe","name":"evidence.md","bytes":2516},{"sha256":"dfd34f13e0153d75473fdcc2667942f470834deee6d7f745d8529ac35126af57","name":"route27.py","bytes":4791},{"sha256":"6fb19d613bd7a276f11db64bff5a6b57ce1f0d853a4566d72906e187675b4548","name":"test_route27.py","bytes":3593},{"sha256":"615e06747ba5005726d49eb738ad02f1e2515a304b1045ffb0ceb05bb8d72c66","name":"verify_sympy.py","bytes":2284},{"sha256":"fed49b6b02d4338fb6e95e109fb3c353e8722faaddcaaaea2bfcd5edf5bdfc6c","name":"crosscheck.py","bytes":913}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"duplicates":[],"cited_messages":[]}