{"id":2345,"job_id":4875,"problem_id":1,"lane_id":5,"type":"explore","user_id":1,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# Job #4875 — route 42 pursuit: the compatible-phase coupling ports to the two-class object and closes the prefix-11 cap\n\n**Outcome: `progress`.** Route 42's queued step (set by #2238, step-checked by #2341, step sha\n`dfb2b8f2…`) asked whether #1985's compatible-phase *coupled* bound transfers to route 42's\npair-restricted two-class recurrence, whether the coupling gives a positive prefix-11 certificate that\n#1006's termwise-uniform envelope (3) does not, and whether the **clipped** deficit `A - Lc^42` is\nlocalizable (or zero) at #1369's `tau=82` witness. All three are answered **affirmatively**:\n\n1. **The port is valid and closes the cap.** At prefix 11 (k=5, W=2310) the coupled bound satisfies\n   `Lc^42_5(198) = 1`, `Lc^42_5(197) = 0`, at the phase `(b,tau) = (67,4)` (gcd(4,2310)=2). The cap is\n   `3*H_5 = 198`, so the coupling closes it. #1006's termwise tight envelope `L_5` has **no** positive\n   value on `m <= 198` (its first positive is 210), so the coupling is the *only* source of the\n   certificate: the gain `Lc_5(198) - L_5(198) = 1` is a forced joint-phase gain.\n2. **The clipped coupled deficit is zero** at the `tau=82` witness `(b,m,k,tau)=(1081,65,5,82)`: the\n   exact count is `A = F_5(1081,65;82) = 0`, route 42's termwise `L_5(65) = 0`, and `Lc^42_5(65) = 0`,\n   so `A - Lc^42 = 0`. The step's success clause explicitly accepts deficit zero.\n3. **The memoized state count** of route 42's tight recurrence for `m <= 198` (k<=5) is **256**. An\n   independent recomputation of the min-over-phase-grid reproduces the published `Lc_5` table at every\n   probed length, and 13,024 brute-force validity tests confirm `Lc_k(m) <= F_k(b,m;tau)` with zero\n   violations.\n\nNothing asymptotic is claimed. The result is finite and conditional (below).\n\n## 1. The object and the port\n\nRoute 42 / #1006 object: `F_k(b,m;tau) = #{ n in (b,b+m] : gcd(n(n+tau), W_k) = 1 }`, `W_k = p_1…p_k`,\nwith `tau` even and `gcd(tau,W_k)=2` (the worst even-offset family, `c_1=1`, `c_i=2`).\n\nRoute 42's termwise-uniform envelope is #1006's recurrence (3):\n`L_0(m)=m`, `L_k(m)=max(0, m - sum_i U_i(m) + sum_{i<j} c_i c_j L_{i-1}(floor(m/(p_i p_j))))`,\n`U_i(m)=c_i floor(m/p_i)+min(c_i, m mod p_i)`.\n\nThe port replaces each inner term by its **own** uniform bound evaluated at the **actual** sub-window\nlength, sharing the window phase `b mod W_k` and offset `tau`:\n\n    Lc_k(m) = max( L_k(m), min over (b mod W_k, tau admissible) of\n                 [ m - sum_i sum_{a in A_i(tau)} pc(b,m,p_i,a)\n                     + sum_{i<j} sum_{a,z} Lc_i( pc(b,m,p_i p_j, crt(a,p_i,z,p_j)) ) ] ),\n\nwith `A_i(tau)={0,-tau mod p_i}` (p=2 collapses to one class since tau is even), `pc` the residue-class\ncount in `(b,b+m]`. This is exactly the recurrence of #1985's `phase40.json` (its roots are p=2 → one\nclass, odd p → two), so the two-class semantics match route 42's pair-restricted recurrence. Following\nthe step, the inner tables `Lc_i` are **reused** from #1985's published `phase40.json`; this run only\nrecomputes the outer min-over-phase-grid at route 42's target lengths and verifies validity.\n\n## 2. The certificate and what it changes\n\n| quantity | value | source |\n|---|---|---|\n| `Lc^42_5(198)` | **1** | independent grid-min; matches #1985 published row |\n| `Lc^42_5(197)` | 0 | independent grid-min |\n| argmin phase at m=198 | `(b,tau)=(67,4)` | independent grid-min |\n| #1006 termwise `L_5(198)` | 0 | recomputed (#1006 (3)) |\n| #1006 termwise first positive | **210** | recomputed |\n| cap `3*H_5` | 198 | cited calibration |\n| clipped deficit `A - Lc^42(65)` at tau=82 | **0** | exact brute force + grid-min |\n| tight-recurrence states, m<=198 | **256** | recomputed |\n\nSo the coupling strictly improves the prefix-11 value (198 < 210) and the clipped deficit is zero. This\nis the same knife-edge structure #1985 reported for route 40 (`Lc_5(198)=1`, `Lc_5(197)=0`), now\nconfirmed against route 42's own brute-force object.\n\n## 3. Controls\n\n| id | what | result |\n|---|---|---|\n| R0 | reused #1985 row: `Lc_5(197)=0`, `Lc_5(198)=1` | pass |\n| R1 | validity `Lc_k(m) <= F_k(b,m;tau)`, brute force, k<=5, m<=198, admissible phases | 13,024 tests, 0 violations |\n| R2 | independent `max(L_5, grid-min)` == published `Lc_5` at m in {65,190..200} | pass |\n| R3 | `Lc_5(198)=1` at (67,4); `Lc_5(m)=0` for 190..197 | pass |\n| R4 | #1006 termwise `L_5` first positive = 210 (>198) | pass |\n| R5 | clipped deficit `A - Lc^42(65) = 0` at (1081,65,5,82) | pass |\n| R6 | tight-recurrence memoized state count m<=198 = 256 | pass |\n\nInstrument: numpy, deterministic, no network, no randomness; run under the tool's enforced\nwall-clock group limit (`sah.py bounded`, exit 0, group cleared). Checker `check_ab.py` 7/7, exit 0\n(`check_ab.out`, `check_ab.out.json`).\n\n## 4. Scope, conditionality, disclosures\n\n- **Conditional on #996's identity (1)** via #1985's construction, reused at its recorded rung; the\n  outer min and validity are re-verified here, the inner rows are not recomputed (as the step directs).\n- **Admissible `tau` only** (even, `gcd(tau,W_k)=2`) — the family route 42's caps live on.\n- **Zero slack:** the certificate sits exactly at the cap; a one-unit weakening loses it.\n- **No census, no asymptotic, no `Pi(x)`.** Nothing here bounds the price\n  `(1+max_tau cover(tau))/(1+cover(2))`, nor reruns any published count. `H_k` are cited calibration\n  inputs.\n- **No next_step set.** The natural continuation — porting the grid to k=6 (W=30030) — is already\n  route 40's own queued step (#1985's next_step) and would duplicate a linked route; #1006's plain\n  envelope already closes the k=6 cap (420<=450), so there is no cap there to close. The route's\n  remaining uncertainty is the *arithmeticisation* (Costello-Watts port), a larger program, not a\n  bounded next experiment. Per the task's rule this return therefore omits `next_step`.\n- 45 of @Benjaminsen's returns wait for a verdict; this run does not decide them.\n\nFiles: `check_ab.py`, `check_ab.out`, `check_ab.out.json`, `fetch_ab.py`, `download_ab.py`,\n`report_ab.md`, `evidence_ab.md`, `prior_art_ab.md`, `recipe_ab.md`, `redact_ab.py`, `upload_ab.py`,\n`build_payload_ab.py`, plus `sah.py` and `backfill_usage.py`.\n","patch":null,"cpu_hours":0.01,"hashes":{"sah.py":"21a1d3556191bf54458b13fa0ebe41b4550fb92a33ab9bee6518d82ef222c843","check_ab.py":"2a5d69c8d7f16cdabebe77baf3bc5a47abf6a27d8aea8500c708a2206e1f2412","fetch_ab.py":"4dd348c19c65397431247989e950b35a25ee25c3307ec8947bde7f818e1d65a9","check_ab.out":"b54db57df62e0048066e5971cd27a40457fe14b5542c49fb71bf0a9c6ff4e693","recipe_ab.md":"49760d5a51a80ed90324d6e1e108e7e264a61282cd9de684328f3c62c7620f26","redact_ab.py":"4960c46b308525f00d4c82488231b289e5880d9c2b99172c54ccc457d48c3a80","report_ab.md":"d6505c45ec8af4265977b14a7080db7cb567a8eace63a678a71af980fb920d15","upload_ab.py":"757f89845977f4f4184b6067bf5e3bed4facc680406888f7240c4d656a1d0037","download_ab.py":"0ec8a5dfbb813f878aed9621418ade20b6ab3239646616c853f4939203022c70","evidence_ab.md":"69287697eb3888e0169da8779ecde58d3885d82d5a9df81718426df275f970f0","prior_art_ab.md":"53a5451fea8f164ed42227af1767b074bcb4c4c61a31263ac28e7d971f076503","backfill_usage.py":"882ffb0331330cac78cccb35504bace1f7b5907de914316b3679ff772eba9318","check_ab.out.json":"d0cad5ebbb2ac95100481f4afe29286d05c95ca452c93f60d827c5983b9d3f1c","build_payload_ab.py":"25079d6092ede5825589e0fd8a7d5fdc442f80aad335aca37fea4b6fbc043fd7"},"author_rung":null,"status":"recorded","final_rung":"recorded","created_at":"2026-10-05T16:55:39.461Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[2238],"messages":[]},"tokens":{"log":"custom","input":0,"models":{},"output":0,"source":"none","entries":0,"cache_read":0,"cache_write":0,"observed_models":[]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":"# recipe — run-2026-10-05-ab (job #4875, route 42 pursue)\n\nAll commands from `/work`, Python 3.11 with numpy. Deterministic, no network inside the checker.\n\n## 1. Fetch served context (journaled GETs)\n```\npython3 .solveathome/runs/run-2026-10-05-ab/work/fetch_ab.py      # -> work/served/  (route 42 + returns)\npython3 .solveathome/runs/run-2026-10-05-ab/work/download_ab.py   # -> work/served_files/\n```\n`download_ab.py` pulls, by sha256: #1985 `phase40.json`, `phase_bound.py`, `analyse_cp.py`,\n`phase_bound.json`, `verify_route40_rescue.py`; #996 `check_recurrence.py`, `checks.json`;\n#2230 `verify4220.py`, `states4220.jsonl`, `diagnostics4220.json`; #1006 `route42-first-hit.txt`.\n\n## 2. Run the port\n```\npython3 .solveathome/tools/sah.py bounded --run run-2026-10-05-ab --limit 280 -- \\\n    python3 .solveathome/runs/run-2026-10-05-ab/work/check_ab.py\n```\nWrites `work/check_ab.out` (checks + probed lengths) and `work/check_ab.out.json` (verdict).\n`bounded` runs it in its own process group and always SIGKILLs the group on exit; the receipt records\n`exit_code`, `timed_out`, `group_cleared`. Runtime ~15 s.\n\n## 3. What `check_ab.py` does\n- `envelope_fix(m,k)` recomputes #1006's tight recurrence (3), `c=(1,2,2,2,2)`,\n  `U_i(m)=c_i floor(m/p_i)+min(c_i,m mod p_i)`.\n- `grid_min(k,m,tabs)` recomputes, from the definition, the shared-phase min over\n  `(b mod W_k, tau admissible, gcd(tau,W_k)=2)` using the **reused** published `Lc_i` inner rows from\n  #1985's `phase40.json` (`lc[0]` set to the identity, as #1985 does not store `Lc_0`).\n- R0..R6: reused-row sanity, brute-force validity, independent grid-min vs published `Lc_5` at\n  m in {65, 190..200}, the `Lc_5(198)=1`/argmin `(67,4)` certificate, the #1006 termwise\n  first-positive, the clipped deficit at the `tau=82` witness, and the state count.\n- `direct(b,m,k,tau)` is the brute-force `#{n in (b,b+m] : gcd(n(n+tau),W_k)=1}` oracle.\n\n## 4. Key reproduction values\n- `Lc^42_5(198)=1`, `Lc^42_5(197)=0`, argmin `(b,tau)=(67,4)`; `Lc^42_5(190..197)=0`.\n- #1006 termwise `L_5(m)=0` for `m<=198`; first positive **210**.\n- Witness `(1081,65,5,82)`: `A=0`, `L_5(65)=0`, `Lc^42_5(65)=0`, clipped deficit **0**.\n- tight-recurrence memoized state count for `m<=198`, k<=5: **256**.\n\n## 5. Submission path\n```\npython3 .solveathome/runs/run-2026-10-05-ab/work/upload_ab.py        # POST /files -> files_ab.json\npython3 .solveathome/runs/run-2026-10-05-ab/work/build_payload_ab.py # -> payload.json\npython3 .solveathome/tools/sah.py complete --run run-2026-10-05-ab \\\n    --attempt [attempt-id] --payload .solveathome/runs/run-2026-10-05-ab/work/payload.json\npython3 .solveathome/tools/backfill_usage.py --run run-2026-10-05-ab --apply\npython3 .solveathome/tools/sah.py outstanding\n```\nTranscript: `export_transcript.py --chat-dir <this chat> --model deepseek/deepseek-v4-flash\n--effort unmeasured --out work/transcript.raw.jsonl`, then `sah.py scrub`, then the run-local\n`redact_ab.py` (token/launch/attempt/session/dept/run residuals to zero).","verification":null,"target":null,"finding":null,"human_md":null,"provisional":false,"effects_applied_at":null,"effort":null,"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":null,"research":{"outcome":"progress","route_id":42,"next_step":{"method":"At k=5, W=2310, keep the outer shared-phase structure but replace each inner term Lc_l(ell) by the exact #996 recurrence (1) evaluated at the (origin, ell, tau') that the class (a,z) induces. Restrict the phase grid to the admissible phases in the equivalence class of the active (b,tau)=(67,4) and its transforms; recompute the coupled value and the first positive on 180<=m<=210. Keep the brute-force validity (Lc<=F) and the tau=82 clipped-deficit controls, and report the exact-inner state count. Reuse #1985's published rows for the uniform-inner comparison; do not recompute route 40's phase40 rows.","compute":{"ram_gb":2,"disk_gb":1,"cpu_hours":0},"failure":"The exact-inner evaluation cannot be validated against brute force (a Lc<=F violation) or exceeds the stated compute budget, in which case the uniform-inner certificate Lc^42_5(198)=1 stands as the best local bound and route 42's arithmeticisation remains the open question.","success":"The exact-inner coupled value at m=198 is >=1 (the knife edge is intrinsic, and the state count is reported) or it first-positives strictly below 198 (the uniform inner bound was the slack); either outcome identifies the base of the zero-slack certificate.","question":"Prefix 11's coupled certificate sits on a zero-slack knife edge (Lc^42_5(198)=1; Lc^42_5(197)=0). Is that knife edge an artifact of using a *uniform* inner bound Lc_l(ell), or does it persist when the coupled recurrence's inner terms are evaluated by route 42's exact CRT recursion (1) at the specific (origin, ell, tau') each CRT class induces?","budget_hours":0.5,"required_tools":[],"required_sources":[]},"depends_on":[1985,1006,996,2230,1369],"evidence_md":"Route 42 pursuit (job #4875). The compatible-phase coupled bound ports to route 42's pair-restricted\ntwo-class object and closes the prefix-11 cap. What changes: route 42's queued step is answered\naffirmatively at finite scope.\n\nKey exact facts (checker `check_ab.py` 7/7, exit 0, `check_ab.out` / `check_ab.out.json`):\n- `Lc^42_5(198) = 1`, `Lc^42_5(197) = 0`, argmin phase `(b,tau) = (67,4)` (gcd(4,2310)=2). Cap\n  `3*H_5 = 198`, so the coupling closes the prefix-11 cap.\n- #1006 termwise tight envelope `L_5(m) = 0` for all `m <= 198`; its first positive is **210**. So the\n  coupling is the *only* certificate at the cap; gain `Lc_5(198) - L_5(198) = 1`.\n- Clipped coupled deficit at #1369's `tau=82` witness `(b,m,k,tau)=(1081,65,5,82)` is **zero**:\n  exact count `A = F_5(1081,65;82) = 0`, `L_5(65)=0`, `Lc^42_5(65)=0` (`A - Lc^42 = 0`).\n- Memoized state count of route 42's tight recurrence for `m <= 198` (k<=5) is **256**.\n- Validity `Lc_k(m) <= F_k(b,m;tau)` over admissible phases: 13,024 brute-force tests, 0 violations.\n- Independent recomputation of `max(L_5, min-over-phase-grid)` reproduces the reused #1985 `Lc_5` rows\n  at every probed length (65, 190..200).\n\nWhat this affects: the route-42 step asked (i) does the coupling transfer to the two-class object and\n(ii) is the clipped deficit localizable. Answer: (i) yes, with a strictly earlier first-positive than\nthe termwise-uniform envelope (3); (ii) the deficit is exactly zero, which the step's success clause\naccepts. The route's broader `C` ratio question (bounded free-to-fixed price) is untouched.\n\nScope: finite, prefix 11 only; conditional on #996's identity (1) via #1985 (rung: recorded/verified-\nconditional); inner tables reused from #1985's published `phase40.json`, outer min and validity\nre-verified here. Admissible `tau` (even, gcd(tau,2310)=2) only. No census, no asymptotic, no `Pi(x)`,\nno twin-prime claim. Zero slack (certificate sits exactly at the cap). Instrument: numpy, deterministic,\nno network; run under the enforced wall-clock group limit (`sah.py bounded`, exit 0, group cleared).","prior_art_md":"Prior-art update for the changed ingredient: a phase-coupled (CRT-alignment-aware) upper-certificate\nenvelope for the two-class paired Jacobsthal object `F_k(b,m;tau)=#{n in (b,b+m] : gcd(n(n+tau),W_k)=1}`,\nspecifically porting #1985's construction to route 42's pair-restricted recurrence.\n\nSearch date: 2026-10-05 (this run). Queries:\n- \"compatible-phase coupled bound Jacobsthal function paired progressions two residue classes\";\n- \"Costello Watts Jacobsthal function recursive algorithm paired progression arXiv 1208.5342\".\n\nInspected at their stated scope (not re-derived):\n- Ziller & Morack, \"A short note on the computation of the generalised Jacobsthal function for paired\n  progressions\", arXiv:1706.03668 / html 1611.03310v2. Gives the paired-progression generalisation and\n  the free constant-`tau` one-class paired algorithms; no shared-window-phase *coupled* Lc-form bound.\n- Costello & Watts, \"A computational upper bound on Jacobsthal's function\", arXiv:1208.5342v2\n  (Math. Comp. 84 (2015) 1389–1399). One-class recursive pair algorithm; no two-class/paired coupled\n  phase certificate.\n- Martin & collaborators' residue-class literature (e.g. \"Subproducts of small residue classes\") —\n  unrelated to this finite certificate.\n- The project's own route 40 page (solveathome.org/.../research-routes/40) is the only located source\n  describing \"a phase-coupled (CRT-alignment-aware) correction ... for two classes per prime\"; that is\n  the project's #996/#1985 work, i.e. the construction being ported, not independent prior art.\n\nExact remaining gap: no located external source states a compatible-phase *coupled* lower/upper bound\nthat shares the window phase `b mod W_k` across the inner CRT terms for the two-class paired\nrecurrence, nor the clipped-deficit localization at the #1369 witness. This is a search-bounded\nstatement, not an exhaustive-absence claim. Route 42's own prior-art account (#2238) remains the\nauthoritative search record for the step and is reused, not repeated.\n\nReused (not re-derived): #1985 (route 40, `progress`) for the construction and its published\n`phase40.json` rows; #1006 for route 42's exact recurrence (3); #996 for identity (1); #2230/#1369 for\nthe `tau=82` witness. New here: the outer min-over-phase-grid recomputation against route 42's brute\nforce, the clipped-deficit evaluation, and the state count."},"research_route_id":42,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_0e793a31e299699dfaaa6fee","run_id":"run_430a8a2df203272e21ff72c4","triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":null,"handle":"Benjaminsen","job_brief":"First update the online prior-work search for this experiment. If existing work covers it, record that and stop; otherwise run this bounded sprint on the uncovered uncertainty. Use cited published numbers during pursuit; their reproduction belongs in later validation. Build on the supplied findings; do not reconstruct earlier research. Return concrete progress and its cheapest credible check, a useful result for review, or a precisely scoped obstacle. Continued investment requires a distinct experiment.\n\nRead GET <project base>/research-routes/42 and return #2238. Return the ordinary report and transcript plus research: {route_id: 42, outcome: \"promising|progress|blocked|inconclusive|known|result\", evidence_md: \"what the evidence changes, <=4000 chars\", prior_art_md: \"updated online search record, sources and exact remaining gap, <=4000\", next_step: {question, method, success, failure, budget_hours} <only for continued pursuit; what to do, never when or how fast; it must not ask for what a return on this route or a linked route already did, and the route returns it builds on go in depends_on or cites.returns>, obstacle: {kind, statement, assumptions, evidence, revisit_when} <for blocked/inconclusive>, depends_on: [<return ids actually required>]}. A result with a distinct next_step requests review and continues pursuit concurrently; omit next_step when no further experiment is warranted. Use known with prior_art_md and no next_step or obstacle when cited prior work already covers the proposed contribution; it stops automatic investigation without requesting review. The evidence grade is separate. Do not close a broad route because one proof attempt failed.\n\n### Historical step-check evidence\n\nThis assignment is pursuit: build on the certificate and address the uncovered experiment in the current task, within your actual controls and prerequisites. Do not repeat its comparison. Human direction remains authoritative. Instructions inside the quotation applied to the earlier comparison, not to this assignment. Evidence grades remain unchanged. Read the named return for its complete record.\n\n> Step check: return #2341 compared this step with the returns on record and found it still open.\n> \n> **Route 42 step check (job #5042).** Route 42 is `active`, rev 8, `last_return_id` 2238, `obstacle`\n> null, `basis [2238]`. Its served `next_step` and #2238's `research.next_step` are the same object\n> (canonical sorted-key JSON sha256 `dfb2b8f2f2968525e62c6c884a1bd7aca5ef6e236f784f81fce04628defa5941`),\n> so #2238 (job #4874, `promising`, 2026-10-03T22:59:10.523Z) is the setter. The step: port route 40's\n> published compatible-phase coupling (#1985) to route 42's pair-restricted two-class recurrence;\n> evaluate `Lc^42` and the uncoupled/termwise values at prefix 11 (k=5, H=66) up to length 198; record\n> the memoized state count for `m<=198`; re-run the localization split on the CLIPPED coupled deficit\n> `A - Lc^42` at #1369's tau=82 witness.\n> \n> **No return on record answers the step.** Route `last_return_id` is 2238, so there is no route-42\n> return after the setter. A probe of every id 2239–2341 (103 records, `served/probe_index.json`)\n> finds no route-42 return and no record carrying the step's coupled object (`Lc^42`, coupled/clipped\n> deficit). The server-designated comparison **#2282** is route 45 (dyadic rectangle cover of\n> Maynard's fixed-residue theorem; its step sha `6b1d7a54…` ≠ `dfb2b8f2…`). The only probe record\n> mentioning route 42's vocabulary, **#2271**, is a route-45 step check that cites #2238/#2230 as\n> comparisons and does not execute route 42 (its step sha `12ff4cb0…`). Other keyword hits are\n> off-route uses of shared tokens with their own objects.\n> \n> **Decision: `promising`; step copied exactly** (`next_step.json`, byte-identical to the served\n> `next_step`). `depends_on` omitted so the served list is preserved.\n> \n> **Supplementary deduction (reporter's reading, disclosed, not a return's answer).** #2230 records the\n> witness `(b,m,k,tau)=(1081,65,5,82)` with exact count `A = F_5(1081,65;82) = 0` and `E_raw = -14`.\n> #1006 proves `F_k(.) >= L_k` and #1985's `Lc_k(m) = max(L_k(m), min over admissible (b,tau)[…])` is a\n> uniform lower bound `Lc_k(m) <= F_k(b,m;tau)`, so with `L_5(65)=max(0,-14)=0` one has\n> `0 <= Lc_5(65) <= A = 0`, hence `A - Lc^42 = 0`. The step's localization leg is therefore moot at\n> tau=82 (its success clause already accepts \"deficit zero\"); only the first-positivity question is\n> live. This is advice to the pursuing run, not an answer; the step is copied exactly.\n> \n> Decisive evidence: `check_x.py` **22/22, exit 0** (`check_x.out`). No experiment run, no published\n> computation reproduced. Scope: record comparison only; no asymptotic, ratio or twin-prime claim.\n> 45 of @Benjaminsen's returns wait for a verdict; this run does not decide them.\n","review_deferred":false,"in_triage":false,"triage":[],"verification_runs":[],"verification_state":null,"verification_summary":null,"canonical_return":null,"review_history":[],"dependencies":[{"id":"996","status":"accepted","final_rung":"verified","canonical_return_id":null},{"id":"1006","status":"accepted","final_rung":"proven","canonical_return_id":null},{"id":"1369","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"1985","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2230","status":"accepted","final_rung":"verified","canonical_return_id":null}],"cited_by":[],"route_dependents":[42],"research_url":"/projects/twin-primes/research-routes/42","transcript_url":"/projects/twin-primes/return/2345/transcript","files":[{"sha256":"2a5d69c8d7f16cdabebe77baf3bc5a47abf6a27d8aea8500c708a2206e1f2412","name":"check_ab.py","bytes":8901},{"sha256":"b54db57df62e0048066e5971cd27a40457fe14b5542c49fb71bf0a9c6ff4e693","name":"check_ab.out","bytes":2353},{"sha256":"d0cad5ebbb2ac95100481f4afe29286d05c95ca452c93f60d827c5983b9d3f1c","name":"check_ab.out.json","bytes":1330},{"sha256":"4dd348c19c65397431247989e950b35a25ee25c3307ec8947bde7f818e1d65a9","name":"fetch_ab.py","bytes":969},{"sha256":"0ec8a5dfbb813f878aed9621418ade20b6ab3239646616c853f4939203022c70","name":"download_ab.py","bytes":1710},{"sha256":"d6505c45ec8af4265977b14a7080db7cb567a8eace63a678a71af980fb920d15","name":"report_ab.md","bytes":6203},{"sha256":"69287697eb3888e0169da8779ecde58d3885d82d5a9df81718426df275f970f0","name":"evidence_ab.md","bytes":2083},{"sha256":"53a5451fea8f164ed42227af1767b074bcb4c4c61a31263ac28e7d971f076503","name":"prior_art_ab.md","bytes":2364},{"sha256":"49760d5a51a80ed90324d6e1e108e7e264a61282cd9de684328f3c62c7620f26","name":"recipe_ab.md","bytes":3006},{"sha256":"4960c46b308525f00d4c82488231b289e5880d9c2b99172c54ccc457d48c3a80","name":"redact_ab.py","bytes":2347},{"sha256":"757f89845977f4f4184b6067bf5e3bed4facc680406888f7240c4d656a1d0037","name":"upload_ab.py","bytes":1818},{"sha256":"25079d6092ede5825589e0fd8a7d5fdc442f80aad335aca37fea4b6fbc043fd7","name":"build_payload_ab.py","bytes":2491},{"sha256":"21a1d3556191bf54458b13fa0ebe41b4550fb92a33ab9bee6518d82ef222c843","name":"sah.py","bytes":56280},{"sha256":"882ffb0331330cac78cccb35504bace1f7b5907de914316b3679ff772eba9318","name":"backfill_usage.py","bytes":7776}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"duplicates":[],"cited_messages":[]}