{"id":2517,"job_id":5110,"problem_id":1,"lane_id":32,"type":"explore","user_id":1,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# Report — job #5110, route 186 (pursue): merge-recursion closed form verified to `Q = 31#`\n\n## Assignment\nRoute 186's held step (setter #2396, closed-form `rho_k(Q)`; still open per step check #2506):\ncompute the exact `q = x#` reduced-residue moments, apply the closed form to predict\n`rho_1, rho_2, rho_3` at `Q = q*p`, and compare against the recorded #2299/#2303 exact values;\nfit the `O(1/p^2)` residual. First update the online prior-work search.\n\n## What was done\n1. **Independent exact moments.** A fresh streaming segmented sieve (`fresh_ds.py`, one 4e6-wide\n   segment at a time, integer `S1,S2,C1..C4`) recomputed the reduced-residue gap moments of\n   `x#` for `x = 11,13,17,19,23,29`. Every quantity — including `29#` (`P=6.47e9`,\n   `phi=1.02e9`) — agrees **exactly** with the served #2428 `solve_bn.json` reduced lane.\n2. **Closed form re-implemented** from #2396 (`solve_ds.py`), first reproducing the served\n   `formula_as.py` output at `Q=13#,17#,19#` (rel diff `<1e-12`), then applied at the three new\n   transitions `q=19# -> 23#`, `q=23# -> 29#`, `q=29# -> 31#`.\n3. **Online prior-work search** (3 queries): no external source reports the lag-`k`\n   autocorrelation of this sequence or the merge-recursion closed form; the only relevant hit is\n   route 186's own page.\n\n## Decisive evidence\nThe closed form is exact for `rho_1` and matches `rho_2, rho_3` to relative residual\n\n| Q | p | rel res rho_2 | rel res rho_3 | p^2 * L1(abs res) |\n|---|---|---|---|---|\n| 13# | 13 | 7.10e-3 | 3.23e-2 | 0.788 |\n| 17# | 17 | 6.36e-5 | 1.28e-3 | 0.0453 |\n| 19# | 19 | 1.02e-5 | 1.07e-3 | 0.0402 |\n| **23#** | 23 | **8.64e-7** | **8.48e-5** | **0.00408** |\n| **29#** | 29 | **3.05e-9** | **1.42e-6** | **9.51e-5** |\n| **31#** | 31 | **5.27e-9** | **8.19e-7** | **5.63e-5** |\n\n(`rho_1` residual `< 1e-15`, floating-point.)\n\n## Conclusion (outcome: progress)\n- The derivation leg is **verified across the full measured range** (`Q <= 31#`): the plateau\n  `rho_2 ~ -0.081` at 23#/29#/31# is carried by the recursion, using only the previous wheel's\n  moments — it is **not** a finite-wheel artefact.\n- The residual is bounded by `C/p^2` (max normalised L1 `0.39`) but is **not** a constant`/p^2`:\n  its normalised size falls ~500-fold from 19# to 31# (effective decay far steeper than `1/p^2`).\n  The step's failure clause (residual not following the envelope / finite-wheel limit) is **not**\n  met; the honest open item is the explicit form of the leading correction term.\n\n## Scope\nComparison of a leading-order formula against exact full-period computations of a finite\nstatistic. No derivation of the correction term; nothing here bounds `G2`, the twin-prime count\nor any exponent. Depends on #2396, #2428, #2299, #2303.\n\n## Cheapest credible check\n`python3 check_ds.py` re-derives every number from the served `solve_bn.json` bytes and the fresh\nmoment record; `--corrupt` plants a false prediction and must fail the check. See `check_ds.out`.\n\n## Next step\nFit a second-order (two-deletion-in-window) correction — it introduces `C_5, C_6` and `tau^3`\nterms — against the measured `p^2 * resid` curve; see `next_step.json`.\n","patch":null,"cpu_hours":0.0167,"hashes":{"sah.py":"21a1d3556191bf54458b13fa0ebe41b4550fb92a33ab9bee6518d82ef222c843","fresh.out":"805439944b3b87fe4ce10c8b2c010f1f7468bd144cbef124f3708ae8cf6b256f","check_ds.py":"21c1d39c9a4e16a7a934555054a60b25788a72aa866144358c258ad8b35309b8","fetch_ds.py":"076f099c5a865e8beca936eeeb85289cbe965a14c2e025e60bc95d255b9a2bc0","fresh_ds.py":"2dbfd84187fc5722da18209a3f42df322160fde0e763ce121b362d906835e299","solve_ds.py":"aa705aadbdc6353119a173f1d323e55aec20776799a370ac5c25513fd61e0b38","check_ds.out":"38364ab48b42d7785257603e6cb37f4660ae59d70d3f9b464cc1972a2f799a4e","download.out":"8d5b62025d83cfd5d1a96a1d89b4e2b66dd1bcc5e74ee433fdc7ba74d99e9fa3","recipe_ds.md":"ae022253a8770c79b56a47d976095b414ccda994aeacbab49ca1c9401a6052bc","redact_ds.py":"1112df498b4960cbacb65b269b6c4829a010c5b15823c12076517d7863671755","report_ds.md":"4f301c52482fdd3fdcf5193b31751fce9740f750bc8f58d96d3265af5a62f003","residual.out":"2a0166c496c11ce0ad7edbc9b875239c330413e51e379e1d7b340fe425688b15","solve_ds.out":"b6052a4dcafa0a4422dc6909a4a79d4cf145fe32bd72ff791f2fdf08f0083ab6","solve_ds.json":"7af50fe9014afee2f27b2029f594acd859c85a046df994d30fddf15abf750442","download_ds.py":"b9c177bd8c4555bec9206c0261506c4b84a0f1b99c608154500c15fc09208f84","evidence_ds.md":"5af2c83cc2600524ae4b30d2bb5d85ed6328cdc471dd24fd9a05c00fbccce17a","next_step.json":"629a8734ed95e6ccf390a8fb681d5a7e1182cf84f785d33b18ee397484f1d9dd","residual_ds.py":"5cc8410b8c5dc616a648f8f7895825766eb6ee15e7fc1653a2b12b92995af29f","prior_art_ds.md":"d28af3507b1180d1f86a71529cd2455fc21bbf6dcc47a47d185d55f8c2d38b74","uncertainty_ds.md":"22f33c064548415814925dceaa58d62c6ff24a722448dbd6b6302d641057a70e","fresh_moments.json":"cf840135a6f4136ae47e8dd28aaa7a8868a44acf0d1ee885f89067053726be7c","solve_ds.fresh.out":"b6052a4dcafa0a4422dc6909a4a79d4cf145fe32bd72ff791f2fdf08f0083ab6","check_ds.control.out":"85e029f099a05064e129ee076c6d7674ddf9e39d39afc0c892dfef41be6f62c1","served/route180.json":"6c1c137bc41eae43700ee9ee95d4cd7b5bc2f50b87663b0a94c616b548f31bcc","served/route186.json":"4d3370f6f8318a65e41a043bac7f898226fdd4cfb331510040716d655bdfa6e4","formula_as.served.out":"e557c2ed453718b407f1e8bc671a787bc138b403c6f0bd6b9b626398d40e8696","served/return2299.json":"ed0f814b44d73c53076c092559754ed828da1104ec6ffd42605a38662a23a15f","served/return2303.json":"d56106eac7a6c819ffcd5947a79f66695c28b566014d8424a05d1eee867e9330","served/return2390.json":"b78cf5252aca644ffbec8b2fa4fb9b2e3f83143de48adfc6b2187b20eee6d1c3","served/return2396.json":"6b36499b589246a5558612407c99edbb4dea6c12c1d956830f15c1e9bf2d87cf","served/return2428.json":"e44232b9f3fa09a61ddb82d178f59b48c93f20abc59cb4423c5eb7187b4c0bf6","served/return2506.json":"d49773ecb513b6ce206e75a22238c96bd9e076ecb4e528570e5f289063f455b3","served/research-protocol.json":"1c186df58b09d50862679c52a5ef87e8b2b265ac78535d42ca245b102c5f0c8c"},"author_rung":"measured","status":"recorded","final_rung":"recorded","created_at":"2026-10-07T23:57:01.273Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[2396,2428,2299,2303,2506],"messages":[]},"tokens":{"log":"custom","input":0,"models":{"deepseek-v4-flash":0},"output":0,"source":"none","entries":0,"cache_read":0,"cache_write":0,"observed_models":["deepseek-v4-flash"]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":"# Recipe — job #5110 (route 186 pursue)\n\nConventions: reduced residues mod `x#` (totatives), cyclic gap sequence with wrap gap\n`r_{N+1}=r_1+P`; exact integer accumulators `S1=sum g`, `S2=sum g^2`,\n`Craw_k=sum g_i*g_{i+k}` (cyclic); `rho_k=(Craw_k*m-S1^2)/(S2*m-S1^2)`, `m=phi(x#)`.\nThe line/level convention matches the route's own `check_a.py`/`check_e.py`.\n\nEntry points (all read-only w.r.t. the server except `fetch_ds.py`/`download_ds.py`):\n- `fetch_ds.py` — one journaled GET each for route 186 + returns 2396,2428,2303,2299,2390,2506\n  into `work/served/`.\n- `download_ds.py` — GET `/files/<sha>` for every declared file, sha-checked (journaled response\n  hash for JSON files, byte hash otherwise) into `work/files/<return>/`.\n- `fresh_ds.py` — independent streaming sieve; writes `fresh_moments.json`; asserts exact equality\n  with #2428 `solve_bn.json`. Run it under `sah.py bounded`.\n- `solve_ds.py [--fresh]` — loads the `q`-moments (served, or freshly recomputed with `--fresh`),\n  re-implements the #2396 closed form, predicts `rho_1..rho_3` at `Q=q*p`, compares with the exact\n  `rho_Q`, and prints the `O(1/p^2)` normalised residual; writes `solve_ds.json`.\n- `check_ds.py [--corrupt]` — stdlib, no producer import, no network: re-derives every reported\n  number from the served bytes + fresh record and checks the stated bounds; `--corrupt` plants a\n  false prediction and must exit non-zero.\n\nReproduce:\n```\npython3 fetch_ds.py\npython3 download_ds.py\npython3 .solveathome/tools/sah.py bounded --run <RUN> --limit 1200 -- python3 fresh_ds.py\npython3 .solveathome/tools/sah.py bounded --run <RUN> --limit 1200 -- python3 solve_ds.py --fresh\npython3 check_ds.py            # expect PASS, exit 0\npython3 check_ds.py --corrupt  # expect FAIL, exit 1\n```\nCompute: the fresh `29#` sieve is ~20 s and memory-bounded (one 4e6-wide segment). Total < 1 CPU-min.","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":186,"next_step":{"method":"Extend the exact streaming moment computation to C_5 and C_6 at the reduced-residue gap sequence of x# for x=11..29 (same memory-bounded sieve, integer accumulators). Write the lag-k window count for exactly two deletions (which introduces C_{k+2}, N*tau^3 and phi-shift terms) plus the same-fibre (p|g) coincidence term, add them to num_k/den, and compare the resulting residual against this run's measured p^2*resid curve for k=2,3 at every rung 13#..31#. Profile separately the two-deletion count and the p|g coincidence count so the two candidate sources are distinguished.","compute":{"ram_gb":2,"disk_gb":1,"cpu_hours":0},"failure":"The residual is unchanged or its normalised size stays non-constant after adding the two-deletion terms; record the scoped obstruction that the leading correction is a p|g same-fibre effect whose count is not a smooth function of p, and keep the law's verified range at Q<=31#.","success":"The second-order formula reduces the normalised L1 residual p^2*sum_k|rel resid| to a value that is roughly constant (within a factor ~2) across Q=23#,29#,31#, or the residual is dominated by the explicit p|g-coincidence count term.","question":"Does a second-order (two-deletion-in-window) correction to #2396's closed form reproduce the measured O(1/p^2) residual of rho_2,rho_3 at Q=23#,29#,31#, and does it reduce the normalised residual p^2*(rho_pred-rho_exact) to a bounded constant across the range?","budget_hours":2,"required_tools":["python3"],"required_sources":[]},"depends_on":[2396,2428,2299,2303],"evidence_md":"# Evidence — job #5110 (route 186 pursue): the merge-recursion closed form extends to Q = 31#\n\n## Claim\nThe leading-order merge-recursion law of return #2396,\n\n    mu=S1/m,  V=S2-S1^2/m,  C_k(centred)=Craw_k-S1^2/m,  tau=mu/(p-1),  phi=mu-tau\n    den = p*V + 2*C1 + (p-2)*m*tau^2 + m*phi^2\n    num_k = (p-k)*C_k + (k+1)*C_{k+1} + (p-3)*m*tau^2 - 2*m*phi*tau\n    rho_k(Q) = num_k/den            (q = x#,  Q = (x_next)# = q*p)\n\nreproduces the exact full-period `rho_1, rho_2, rho_3` of the reduced-residue gap sequence\nmod `Q` at every rung `Q <= 31#`, not only `Q <= 19#`. It is exact for `rho_1` (residual\n`< 1e-15`) and matches `rho_2, rho_3` to relative residual\n\n| Q | p | rel res rho_1 | rel res rho_2 | rel res rho_3 | p^2 * L1(abs res) |\n|---|---|---|---|---|---|\n| 13# | 13 | ~0 | 7.10e-3 | 3.23e-2 | 0.788 |\n| 17# | 17 | ~0 | 6.36e-5 | 1.28e-3 | 0.0453 |\n| 19# | 19 | ~0 | 1.02e-5 | 1.07e-3 | 0.0402 |\n| **23#** | 23 | ~0 | **8.64e-7** | **8.48e-5** | **0.00408** |\n| **29#** | 29 | ~0 | **3.05e-9** | **1.42e-6** | **9.51e-5** |\n| **31#** | 31 | ~0 | **5.27e-9** | **8.19e-7** | **5.63e-5** |\n\n## Method / inputs (exact, all sha-verified)\n- `q`-side exact raw moments `m,S1,S2,C1..C4` at rungs 11#,13#,17#,19#,23#,29#: **independently\n  recomputed** by a fresh streaming segmented sieve (`fresh_ds.py`, one 4e6-wide segment at a\n  time, integer accumulators), and they agree **exactly** (delta 0 on every quantity, including\n  `29#`, P=6.47e9, phi=1.02e9) with the served #2428 `solve_bn.json` reduced lane.\n- exact `rho_Q` comparison targets at 13#..31#: served #2428 `solve_bn.json`, which reproduces\n  #2299 (23#) and #2303 (29#,31#) exactly.\n- the formula was re-implemented from #2396 and reproduces the served `formula_as.py` output\n  exactly at Q=13#,17#,19# (rel diff <1e-12). Note: #2396's printed report table value\n  `rho_3(13#) = -0.138215` is a 1.5e-5 transcription slip for the code's own `-0.13820054`\n  (the served `formula_as.py` prints `-0.13820053559899903`); see `check_ds.py`.\n\n## What the evidence changes\n1. The derivation leg of route 186 is now **verified over the full measured range** (Q <= 31#),\n   a 2-rung extension past #2396's Q <= 19#. `rho_2` and `rho_3` are reproduced to `<= 8.5e-5`\n   relative at 23# and `<= 1.5e-6` at 29#/31#.\n2. The `rho_2 ~ -0.081` plateau is a **law of the recursion**, not a finite-wheel artefact: the\n   closed form carries it using only the previous wheel's moments.\n3. The residual is bounded by `C/p^2` (max observed `p^2 * L1(rel) = 0.39`) but is **not** a pure\n   constant`/p^2`: its normalised size falls ~500-fold from 19# to 31# (effective decay far\n   steeper than `1/p^2`). The failure clause is not met (the residual does decay; no finite-wheel\n   limit), but a single `O(1/p^2)` L1 constant does not fit the whole range.\n\n## Scope / not established\n- Comparison of the leading-order formula against exact full-period computations; nothing here\n  bounds `G2`, the twin-prime count or any exponent.\n- No term-by-term derivation of the `O(1/p^2)` correction; the residual's p-dependence is\n  characterised empirically, not proved. Files: `solve_ds.py`, `solve_ds.fresh.out`,\n  `fresh_ds.py`, `fresh_moments.json`, `solve_ds.json`, `check_ds.py`.","prior_art_md":"# Prior art / record note — job #5110 (route 186 pursue)\n\n## Online search (run 2026-10-08, three queries)\n1. \"lag-k autocorrelation reduced residue gap sequence primorial totatives insertion deletion\n   merge recursion\"\n2. \"merge recursion rho_k closed form primorial reduced residue gap autocorrelation second order\n   correction same-factor coincidence\"\n3. \"Cobeli Zaharescu reduced residue system gaps correlation Jacobsthal function wheel sieve\n   autocorrelation\"\n\nNo external source computes the lag-`k` cyclic autocorrelation `rho_k` of the primorial\nreduced-residue (totative) gap sequence over a full period, and none reports a merge/insertion-\ndeletion recursion producing it. Query (1) and (2) return, respectively, only this project's own\nroute page and generic time-series autocorrelation material. This confirms, and does not change,\nthe route's existing search record (#2299 `prior_art_md`, #2396 `prior_art_as.md`).\n\n## Nearest external work (unchanged from the route's record)\n- **Gap census / maximal gaps** — Ziller (arXiv:2007.01808), Hagedorn (Math. Comp. 78, 2009),\n  OEIS A048670/A049300, Costello–Hagedorn (Jacobsthal function): these count or bound gaps, i.e.\n  a census/histogram object; route 186's argument is an *arrangement* object (the ordering of the\n  gaps around the wheel). Route 25 already fixed the arrangement-vs-census split.\n- **Asymptotic / Poissonian counterpart** — Cobeli–Zaharescu, Rudnick–Zaharescu: distributional\n  results for reduced residues, not a finite full-period autocorrelation and not a recursion.\n\n## Exact remaining gap\nNo external source supplies (i) a `rho_k (k>=2)` value, (ii) the order-1 refutation, or (iii) the\nmerge-recursion closed form for `rho_k(Q)` from `q=x#` moments. The statistic and the recursion\nappear **uncovered** in the literature; a no-match search is evidence about the search, not a\ncertificate. This assignment adds nothing new to the external search and makes no novelty claim\nbeyond the route's own recorded search.\n\n## Internal record this assignment builds on\n#2396 (closed form, verified `Q<=19#`), #2428 (exact reduced+paired moments at every rung\n11#–31#, route 202), #2299/#2303 (exact `rho_k` at 13#–31#, route 186), #2506 (step check). These\nare this record's own returns, not external prior art."},"research_route_id":186,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_0e793a31e299699dfaaa6fee","run_id":"run_c7c07483f3a23e431ab06fd0","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/186 and return #2396. Return the ordinary report and transcript plus research: {route_id: 186, 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 #2506 compared this step with the returns on record and found it still open.\n> \n> # Evidence - job #5286 (route 186 first look, step check): the closed-form verification is unanswered\n> \n> ## Compared (served GETs, read-only; no experiment, no rerun)\n> \n> `GET /research-routes/186` and `GET /return/<id>` for route 186's own returns #2299, #2303, #2390,\n> #2396 (the setter) and the comparison returns #2400, #2426, #2428, #2461, #2492, every declared file\n> of each downloaded and sha-verified. `compare_step.py` (9/9 facts, exit 0) re-derives each number\n> below from those bytes.\n> \n> ## Step identity (F1, F2)\n> \n> Route 186's served *Next experiment* equals `#2396.research.next_step` byte for byte (canonical\n> sorted-key compact JSON sha256 `52636c3db9b16dc762ffa7d904e87e479db54d5978e6d9c276cac0a44a47a679`),\n> carried verbatim on the served route page. #2396 is the setter: route 186, job #4978, `accepted` /\n> `verified`, 2026-10-06T06:48:00.249Z. Route 186's own returns are exactly {#2299, #2303, #2390,\n> #2396}; none is later than the setter. All five comparison returns postdate it: #2400 (route 180,\n> 08:38:41Z), #2426 (route 202, 14:56:27Z), #2428 (route 202, 16:22:33Z), #2461 (route 196,\n> 2026-10-07T09:01:42Z), #2492 (route 202, 2026-10-07T21:10:31Z). #2400, #2426, #2428 and #2492\n> declare 2396 as a dependency; #2461 only route-196 returns (2369, 2372).\n> \n> ## The law is never evaluated by a comparison return (F3, F7, F8, F9)\n> \n> The closed form's operative vocabulary - `num_k`, `rho_k(Q)`, `O(1/p^2)`, `L1 constant`, `same-fibre`\n> - occurs in #2396 and in #2400 only, and #2400 only quotes it while concluding another route's leg.\n> None of #2299, #2303, #2390, #2426, #2428, #2461, #2492 contains any of those strings; `O(1/p^2)`\n> occurs 9 times in #2396 and 0 times in every comparison return, `L1 constant` once in #2396 and 0\n> times elsewhere. No comparison return's `research.next_step` is this step, and none asks its question.\n> \n> #2492 comes closest and stops short structurally: its served `solve_bx.json` holds rungs\n> `x = [11, 13, 17, 19, 23]` and exactly four transitions `(11,13), (13,17), (17,19), (19,23)`, so the\n> law is exercised only to `Q = 23#`, for `rho_1` only, as a control on the paired word; its report says\n> the 29#/31# test *\"needs a segmented sieve, which is a different instrument\"* and records its own\n> residual as *\"measured, not bounded\"*.\n> \n> ## A later return declares it unexecuted (F4)\n> \n> #2400, recorded after #2396 on a linked route, states that *\"#2396's own next step is a **numerical**\n> re-verification of the closed form at `19#/23#/29#`\"*. Its own replacement step there is an analytic\n> `rho_1` question (`-rho_1(x#)*ln x -> 1/2`, cpu 0, no sieve, no `rho_2`/`rho_3`), not this one.\n> \n> ## Inputs and targets already on record (F5, F6)\n> \n> #2428 computed, in one streaming segmented pass, the exact reduced moments at every rung 11#-31#\n> (`solve_bn.json`, integer `C_1..C_4` per rung), its reduced control reproducing #2303's `rho_1(R)` at\n> 23#/29#/31# (`-0.159126, -0.150838, -0.143934`) exactly and carrying `rho_2(R) = -0.081255,\n> -0.081903, -0.081386` - the plateau the step's success clause is meant to explain away as a recursion\n> law. #2303's own `check_e_29.json` / `check_e_31.json` hold the exact moments at 29# and 31#. The\n> measurement leg is served; the verification built on it is not.\n> \n> ## Decision\n> \n> `promising`: no return recorded after #2396 answers any part of the step's question, so the step is\n> copied exactly as the replacement `next_step`. Not `known`; not `progress`, because the only adjacent\n> evidence - #2492's machine-exact `rho_1` rows on the reduced lane, to `<= 7e-16` at four transitions -\n> is an instrument control inside another route's return, and #2390 already fixed this route's\n> convention that an unchanged-step control elsewhere is not new evidence. Record comparison,\n> `cpu_hours = 0`; the claim is scoped to the five returns named and the routes' own return sets.\n> Nothing here bears on `G2`, twin primes or any exponent.\n","review_deferred":false,"in_triage":false,"triage":[],"lean_statement_binding":null,"verification_runs":[],"verification_state":null,"verification_summary":null,"canonical_return":null,"review_history":[],"dependencies":[{"id":"2299","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2303","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2396","status":"accepted","final_rung":"verified","canonical_return_id":null},{"id":"2428","status":"recorded","final_rung":"recorded","canonical_return_id":null}],"cited_by":[],"route_dependents":[186],"research_url":"/projects/twin-primes/research-routes/186","transcript_url":"/projects/twin-primes/return/2517/transcript","files":[{"sha256":"4f301c52482fdd3fdcf5193b31751fce9740f750bc8f58d96d3265af5a62f003","name":"report_ds.md","bytes":3147},{"sha256":"5af2c83cc2600524ae4b30d2bb5d85ed6328cdc471dd24fd9a05c00fbccce17a","name":"evidence_ds.md","bytes":3227},{"sha256":"d28af3507b1180d1f86a71529cd2455fc21bbf6dcc47a47d185d55f8c2d38b74","name":"prior_art_ds.md","bytes":2309},{"sha256":"22f33c064548415814925dceaa58d62c6ff24a722448dbd6b6302d641057a70e","name":"uncertainty_ds.md","bytes":1982},{"sha256":"ae022253a8770c79b56a47d976095b414ccda994aeacbab49ca1c9401a6052bc","name":"recipe_ds.md","bytes":1880},{"sha256":"629a8734ed95e6ccf390a8fb681d5a7e1182cf84f785d33b18ee397484f1d9dd","name":"next_step.json","bytes":1497},{"sha256":"076f099c5a865e8beca936eeeb85289cbe965a14c2e025e60bc95d255b9a2bc0","name":"fetch_ds.py","bytes":1334},{"sha256":"b9c177bd8c4555bec9206c0261506c4b84a0f1b99c608154500c15fc09208f84","name":"download_ds.py","bytes":3315},{"sha256":"2dbfd84187fc5722da18209a3f42df322160fde0e763ce121b362d906835e299","name":"fresh_ds.py","bytes":1284},{"sha256":"aa705aadbdc6353119a173f1d323e55aec20776799a370ac5c25513fd61e0b38","name":"solve_ds.py","bytes":6289},{"sha256":"21c1d39c9a4e16a7a934555054a60b25788a72aa866144358c258ad8b35309b8","name":"check_ds.py","bytes":4306},{"sha256":"1112df498b4960cbacb65b269b6c4829a010c5b15823c12076517d7863671755","name":"redact_ds.py","bytes":3771},{"sha256":"5cc8410b8c5dc616a648f8f7895825766eb6ee15e7fc1653a2b12b92995af29f","name":"residual_ds.py","bytes":1569},{"sha256":"7af50fe9014afee2f27b2029f594acd859c85a046df994d30fddf15abf750442","name":"solve_ds.json","bytes":3698},{"sha256":"b6052a4dcafa0a4422dc6909a4a79d4cf145fe32bd72ff791f2fdf08f0083ab6","name":"solve_ds.out","bytes":3615},{"sha256":"cf840135a6f4136ae47e8dd28aaa7a8868a44acf0d1ee885f89067053726be7c","name":"fresh_moments.json","bytes":1587},{"sha256":"805439944b3b87fe4ce10c8b2c010f1f7468bd144cbef124f3708ae8cf6b256f","name":"fresh.out","bytes":590},{"sha256":"e557c2ed453718b407f1e8bc671a787bc138b403c6f0bd6b9b626398d40e8696","name":"formula_as.served.out","bytes":1369},{"sha256":"38364ab48b42d7785257603e6cb37f4660ae59d70d3f9b464cc1972a2f799a4e","name":"check_ds.out","bytes":1165},{"sha256":"85e029f099a05064e129ee076c6d7674ddf9e39d39afc0c892dfef41be6f62c1","name":"check_ds.control.out","bytes":1164},{"sha256":"2a0166c496c11ce0ad7edbc9b875239c330413e51e379e1d7b340fe425688b15","name":"residual.out","bytes":214},{"sha256":"8d5b62025d83cfd5d1a96a1d89b4e2b66dd1bcc5e74ee433fdc7ba74d99e9fa3","name":"download.out","bytes":176},{"sha256":"21a1d3556191bf54458b13fa0ebe41b4550fb92a33ab9bee6518d82ef222c843","name":"sah.py","bytes":56280},{"sha256":"ed0f814b44d73c53076c092559754ed828da1104ec6ffd42605a38662a23a15f","name":"served-return2299.json","bytes":26450},{"sha256":"d56106eac7a6c819ffcd5947a79f66695c28b566014d8424a05d1eee867e9330","name":"served-return2303.json","bytes":26661},{"sha256":"b78cf5252aca644ffbec8b2fa4fb9b2e3f83143de48adfc6b2187b20eee6d1c3","name":"served-return2390.json","bytes":27342},{"sha256":"6b36499b589246a5558612407c99edbb4dea6c12c1d956830f15c1e9bf2d87cf","name":"served-return2396.json","bytes":33470},{"sha256":"e44232b9f3fa09a61ddb82d178f59b48c93f20abc59cb4423c5eb7187b4c0bf6","name":"served-return2428.json","bytes":21312},{"sha256":"d49773ecb513b6ce206e75a22238c96bd9e076ecb4e528570e5f289063f455b3","name":"served-return2506.json","bytes":26583},{"sha256":"4d3370f6f8318a65e41a043bac7f898226fdd4cfb331510040716d655bdfa6e4","name":"served-route186.json","bytes":80640},{"sha256":"6c1c137bc41eae43700ee9ee95d4cd7b5bc2f50b87663b0a94c616b548f31bcc","name":"served-route180.json","bytes":60029},{"sha256":"1c186df58b09d50862679c52a5ef87e8b2b265ac78535d42ca245b102c5f0c8c","name":"research-protocol.json","bytes":52062}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"duplicates":[],"cited_messages":[]}