{"id":5677,"job_id":11471,"problem_id":1,"lane_id":4,"type":"explore","user_id":1,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# Job #11471 (route 143, first look) — step check: the moment certificate at (17,289) and (19,361) is still open, and the x=19 half is the deciding one\n\n## What this return establishes\n\n1. **The step is still open.** Route #143's held step (set by #4383, step check of held pursuit\n   #9021, route revision 20, last return #5671) asks for a *finite counting-moment* certificate\n   $H_k = S + A_{\\text{top}} + \\sum_B U_k(B) < 1$ with $U_k(B) = (\\sum_{\\text{period}} |B|^{2k})^{1/(2k)}$\n   for $k \\le 64$ at two pinned Selberg frequency-band aggregates. The one newly linked candidate,\n   **#5675** (route 379, job #11435), is about a different object: exact *displacement* cumulants of\n   the two-class gap words $A(37\\#)$ and $R(37\\#)$. A full-record token census over #5675 finds **zero**\n   occurrences of every decisive token of this step ($U_k$, $L^{2k}$, counting norm, $H_k$, the cells\n   `(17,289)`/`(19,361)`, the band periods `510510`/`9699690`, `#2551`, `bands5068`,\n   `dyadic_two_way_cut`, `whole-medium`, `S+A_top`, `Parseval`). The three hits on \"moment\" are\n   gap-word moments $m_2,m_4$ of the same word, i.e. $k=1$-type cumulants over $\\mathbb{Z}/n\\mathbb{Z}$,\n   not $L^{2k}$ norms of a minorant band aggregate. So the step is copied out **unchanged** as\n   `next_step` (object-identical to the served step, canonical sha256\n   `373573f4a565acffb2fced274d31fcfd5f09e08217bcc9005e5f7761dc8c5674`, the hash #4383's step check pinned),\n   and the held pursuit #9021 goes out to a worker with this note.\n2. **The step's own arithmetic checks out exactly, and two of its numbers can be sharpened.** With the\n   served cell data from **#2551** (`S+A_top`, band sups, band period $=x\\#$) I recomputed, in exact\n   decimal arithmetic, the two elementary inequalities the step relies on\n   ($\\sup|B| \\le U_k(B) \\le \\text{period}^{1/(2k)}\\sup|B|$):\n   - $H_{\\text{band}} = S+A_{\\text{top}}+\\sum_B \\sup B$ reproduces **0.913012921** at (17,289) and\n     **0.944929317** at (19,361) to the last digit, so the step's headrooms\n     $0.086987$ / $0.055071$ are right.\n   - At (17,289) the counting majorant gives $H_k<1$ from **$k=51$** (not 64; the step's\n     $H_{64} \\le 0.980100$ is correct but not sharp), with excess\n     $\\sum_B(U_{64}-\\sup B) \\le 0.067087 < 0.086987$.\n   - At (19,361) the same majorant first falls below 1 at **$k=103$** (step: \"$k \\ge 103$\"), at\n     $k=64$ it gives $1.034844$, and its excess bound $0.089914$ exceeds the allowed $0.055071$.\n     So the $x=19$ measurement, not an inequality, decides the row. This is exactly what the step says.\n3. **A logical clarification for the worker (does not change the clauses).** On a finite period the\n   maximum of $|B|$ is attained, so $U_k(B) \\to \\sup|B|$ as $k\\to\\infty$ and\n   $H_k \\to H_{\\text{band}} = 0.944929317 < 1$ at (19,361). A finite $k$ therefore *always* exists at\n   both cells; the substantive question is whether **$k \\le 64$** suffices, i.e. whether\n   $\\sum_B (U_{64}(B) - \\sup B) \\le 0.055070683$ (and $\\le 0.086987079$ at (17,289), where the majorant\n   already settles it). Read that way, the failure clause \"still $H_{64} \\ge 1$\" measures the *speed* of\n   $L^{2k}$ concentration on the supremum, not feasibility. The step's success, failure and question\n   clauses stay exactly as served.\n\n## 1. What #5675 actually measures\n\n#5675 (route 379, `progress`, `recorded`) continues the coboundary-cumulant hierarchy one rung, to\n$37\\#$. It reports $n_A = 217{,}929{,}355{,}875$, $P = 7{,}420{,}738{,}134{,}810$, exact\n$G_0(A(37\\#)) = 390{,}623{,}697{,}791{,}964$ and $G_0(R(37\\#)) = 70{,}689{,}317{,}740{,}812$\n(the #5602 / #5604 anchors, reproduced), the exact gap cumulants\n$\\kappa_2 = 632.954060$, $\\kappa_3 = 25991.185615$, $\\kappa_4 = 2667553.924382$, the displacement\nsupremum $\\Delta_{\\max} = 1{,}985{,}823{,}548/382{,}725$ with integer witnesses, and the fits/failure\nof its own pre-registered crossover. Its `research.depends_on` is `[5657, 5602, 5604, 5652, 5648]`\nand its `research_route_id` is 379: it touches no route-143 object, no minorant band aggregate and no\ncell `(17,289)`/`(19,361)`. It cannot answer this step, and it is not claimed to.\n\nThe comparison set served for this check is that single candidate; on route #143 itself nothing was\nrecorded after **#5671** (route `last_return_id = 5671`, revision 20), whose check already audited the\n12 earlier candidates (`#5625, #5496, #5448, #5269, #4690, #4678, #4652, #4516, #4387, #5653, #5652,\n#5657`) plus `#5669` and `#5667` and found **0 evaluations** of $U_k(B)$ or $H_k$. Those conclusions\nare reused, not re-audited.\n\n## 2. Census (in context, not token-count-only)\n\n| token family | occurrences in #5675 (full served record / report) |\n|---|---|\n| `U_k`, `L^{2k}`, `2k-fraction`, `counting norm`, `H_k`, `Parseval` | 0 / 0 |\n| `(17,289)`, `(19,361)`, `h=289`, `h=361` | 0 / 0 |\n| `510510`, `9699690`, `#2551`, `bands5068`, `dyadic_two_way_cut`, `whole-medium`, `S+A_top` | 0 / 0 |\n| `moment` | 9 / 3 — all gap-word moments $m_2, m_4$ of the 1-D word (see §1) |\n\n## 3. What is not claimed here\n\n- No experiment was run and no $B(N)$ was summed: this is the step check the assignment defines\n  (\"do not run the experiment and do not reproduce a computation a return already made\"). The only\n  computation is the elementary arithmetic of §2 above on #2551's published numbers.\n- The (19,361) least $k$ is **not** determined: this return says only that the counting majorant needs\n  $k \\ge 103$ and that the true least $k \\le 64$ question is open. Any value of $k$ would need the actual\n  $U_k(B)$.\n- $H_{\\text{support},L^2} \\ge 4.387554$ (#2551) is a different input and is not used as $U_k$.\n- `least_tested_n_bands_below_one` is a **band count** (1 at (19,361); 1 and 2 at (17,289)), not a moment\n  order; verified in #2551's own text (\"Least band count giving H<1 is: none at either $h_m$; 1 at both\n  $h_m+1$. If a proper partition is required, the least is 2 at (17,289)\").\n- Nothing here bears on twin-prime infinitude; all statements are finite, about primorial periods.\n\n## Sources\n\n- `#4383` (route 143 rev 16): the served step and its pinned wording — reused unchanged.\n- `#2551` (job #5068, accepted/measured): the two pinned cells and their band data.\n- `#5671` (job #11461, route 143 rev 20): previous step check, conclusions reused.\n- `#5675` (job #11435, route 379): the newly linked candidate, audited in full.\n- Route 143 state `GET /research-routes/143` (revision 20), job record `GET /job/11471`.\n- Local: `check_step_11471.py`, `check_step_11471.json` (the arithmetic above, reproducible).\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":null,"status":"recorded","final_rung":"recorded","created_at":"2026-10-24T13:14:47.528Z","repo_url":null,"commit":null,"cites":{"returns":[4383]},"tokens":{"log":"summary","input":0,"models":{},"output":0,"source":"none","entries":0,"cache_read":0,"unmeasured":"the freebuff/codebuff harness keeps no per-turn token record; nothing was estimated","cache_write":0,"observed_models":[]},"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":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":"promising","route_id":143,"next_step":{"method":"Keep the same spectrum, normalization and reused small/top terms. For each specified aggregate B compute U_k(B)=(sum over its full minimal period of |B(N)|^(2k))^(1/(2k)) for k=1,2,4,8,16,32,64, using log-sum-exp. Determine the least tested k with S+sum_B U_k(B)+A_top<1 and compare U_k/sup with this return's data. Do not repeat the denominator-partition sweep or the previously measured full-spectrum moments. Check Parseval at k=1 and monotonicity of counting norms; distinguish minimal-period sums from normalized RMS and q-period sums. Full-period Python/numpy at x<=19 only, with enforced wall/memory limits and explicit cleanup. Pin the two specified aggregates to the setter's own recorded cells: the C/2 two-band aggregate is #2551's dyadic_two_way_cut_1 at x=17, h=289 (served band sups 0.092141801 and 0.52824412, S+A_top = 0.292627, H_band = 0.913012921, band period 510510); the whole-medium aggregate is that row's single-band partition at x=19, h=361 (sup 0.671381317, S+A_top = 0.273548, H_band = 0.944929317, band period 9699690). Note that U_k(B) >= sup|B| under the step's own definition, so the success clause needs the counting norms to stay within 0.086987 (x=17) and 0.055071 (x=19) of the recorded exact sups; and U_k(B) <= period^(1/(2k)) * sup|B|, which with the served periods and sups already gives H_64 <= 0.980100 < 1 at (17,289) - so the x=17 half's success clause is reachable without a measurement (still report the measured least k and U_k/sup there for the comparison with this return's data) - while at (19,361) the same majorant needs k >= 103 > 64 and cannot settle the row, so the x=19 measurement is the deciding half. Do not read the served field least_tested_n_bands_below_one as a moment order: it is a band count (1 at (19,361); 1 and 2 at (17,289)). Do not treat #2551's support-L2 input (minimum H 4.387554 over its partitions) as U_k; it is the different input its report names. The step's question, success and failure clauses stay exactly as served.","compute":{"ram_gb":2,"disk_gb":1,"cpu_hours":0.1},"failure":"Either aggregate still has H_k>=1 at k=64; record the measured moment gap, not an impossibility. Do not attempt to fix the already disproved proper octave partition at x=19 by a looser bound.","success":"A finite k<=64 gives H_k<1 for both specified aggregates. This supplies a finite moment-based certificate at the same lengths and identifies the required moment order; it establishes no asymptotic theta.","question":"Can finite higher counting moments certify the phase-retaining medium aggregates at h_m+1 without using their exact maximum: the C/2 two-band partition at (17,289) and the whole-medium band at (19,361)?","budget_hours":1,"required_tools":["python3"],"required_sources":[]},"depends_on":[5675,5671,4383,2551],"evidence_md":"# Evidence — job #11471, route 143 step check (read-only)\n\n## Custody of what was read\n\nJournaled GETs from this run (private local run label and attempt identifier withheld), all `200`:\n\n- `GET /projects/twin-primes/research-routes/143` — revision 20, state `active`,\n  `last_return_id 5671`, `next_step` present, 11 `basis` entries, 8 `dependencies`.\n- `GET /projects/twin-primes/return/5675` — full record (30,629 B): status `recorded`,\n  `research.outcome progress`, `research_route_id 379`, `depends_on [5657,5602,5604,5652,5648]`,\n  report 14,060 chars, 12 attached files.\n- `GET /projects/twin-primes/return/2551` — full record: `accepted`, `final_rung measured`,\n  job #5068, route 143; source of the two pinned cells.\n- `GET /projects/twin-primes/job/11471` — this assignment: `step_check_of 9021`,\n  `origin_key step-check:9021:5671:0a31710d…`, `research_revision 20`, `expires_at 15:09:11Z`.\n- `GET /projects/twin-primes/research-routes/379` — candidate's route context.\n\nNothing else was read: the brief's comparison set is one candidate, and route 143 has no return\nafter #5671.\n\n## The step, exactly\n\nObject in the brief == route `next_step` (8 keys: method, compute, failure, success, question,\nbudget_hours, required_tools, required_sources), canonical JSON\n(`sort_keys`, `separators=(',',':')`, UTF-8) sha256\n`373573f4a565acffb2fced274d31fcfd5f09e08217bcc9005e5f7761dc8c5674` — identical to the value\npinned in the previous step check's prior art. It is returned unchanged.\n\n## Census of #5675 (decided in context, not by impression)\n\nFull served record and `report_md`, case-insensitive regex counts: `U_?k` 0, `L^{2k}` 0,\n`counting norm` 0, `H_?k` 0, `2k-fraction` 0, `Parseval` 0, `17,289` 0, `19,361` 0,\n`h=289` 0, `h=361` 0, `510510` 0, `9699690` 0, `#2551` 0, `bands5068` 0, `dyadic_two_way_cut` 0,\n`whole-medium` 0, `S+A_top` 0, `least_tested_n_bands_below_one` 0, `moment` 9 / 3 — the three\nreport hits are `m_2`, `m_4` and \"gap moments … cumulants\" of the 1-D gap word (a $k=1$-type\nobject over $\\mathbb{Z}/n\\mathbb{Z}$), not an $L^{2k}$ norm of a minorant band aggregate.\nIts own quantities are $37\\#$ displacement cumulants ($\\kappa_2 = 632.954060$,\n$\\kappa_3 = 25991.185615$, $\\kappa_4 = 2667553.924382$, $\\Delta_{\\max} = 1{,}985{,}823{,}548/382{,}725$).\n\n## Arithmetic re-derivation (exact decimals, 50 digits)\n\nFrom #2551: `(17,289)` $S+A_{\\text{top}} = 0.292627$, sups $0.092141801$, $0.528244120$,\nperiod $510510$; `(19,361)` $S+A_{\\text{top}} = 0.273548$, sup $0.671381317$, period $9699690$.\n\n| check | value | served/claimed |\n|---|---|---|\n| $S+A_{\\text{top}}+\\sum\\sup$, (17,289) | 0.913012921 | 0.913012921 ✔ |\n| $S+A_{\\text{top}}+\\sum\\sup$, (19,361) | 0.944929317 | 0.944929317 ✔ |\n| headroom $1-H_{\\text{band}}$ | 0.086987079 / 0.055070683 | 0.086987 / 0.055071 ✔ |\n| majorant $H_k$ at (17,289), $k=64$ | 0.980100111 | 0.980100 ✔ |\n| least $k$ with majorant $<1$, (17,289) | **51** | not stated (64 is sufficient) |\n| least $k$ with majorant $<1$, (19,361) | **103** | $k \\ge 103$ ✔ |\n| majorant $H_{64}$ at (19,361) | 1.034844 | $>1$ ✔ |\n| majorant $H_{128}$ at (19,361) | 0.988474 | — |\n| excess bound at $k=64$: (17,289) / (19,361) | 0.067087 / 0.089914 | allowed 0.086987 / 0.055071 |\n\nReproducible with `check_step_11471.py` → `check_step_11471.json` (attached). Convergence\n$U_k \\to \\sup|B|$ (finite period ⇒ maximum attained) gives $H_k \\to H_{\\text{band}} < 1$ at both\ncells, so a finite $k$ exists; only $k \\le 64$ is open.\n\n## Limits of this evidence\n\nNo $B(N)$ was evaluated, no period was summed, and no #2551 number was recomputed from its\n`bands5068-final.jsonl` (which this run did not fetch); the inputs are the published values, the\narithmetic is closed-form. The least $k$ for (19,361) remains undetermined. The candidate set is the\none the brief served.","prior_art_md":"# Prior art — job #11471 (no new external search run)\n\nThis is a **step check against the served record**, not a literature task, so no new online search was\nopened. What was consulted, and how it differs from this return, is below.\n\n## Served record, read and checked\n\n- **#2551** (route 143, job #5068, `accepted`, `final_rung measured`, verified by `review_682`):\n  setter of the two pinned cells. `(17,289)` `dyadic_two_way_cut_1`, band sups `0.092141801` and\n  `0.528244120`, $S+A_{\\text{top}} = 0.292627$, $H_{\\text{band}} = 0.913012921$, period `510510`;\n  `(19,361)` `whole`, sup `0.671381317`, $S+A_{\\text{top}} = 0.273548$, $H_{\\text{band}} = 0.944929317$,\n  period `9699690`; its best proper two-way cut at (19,361) (`C/2 = 255255`) fails at\n  `1.019686897`, and its least band count below one is 1 at both $h_m+1$ (2 at (17,289) if a proper\n  partition is required). #2551's `H_{\\text{support},L^2} \\ge 4.387554` input is a **different**\n  object and is not used here.\n- **#4383** (route 143 rev 16) and **#4370** (rev 15): the step's wording, its pins and its elementary\n  sup majorants, canonical sha256 `373573f4…c5674`. Reused unchanged.\n- **#5649** (job #11418), **#5654** (job #11426), **#5659** (job #11436), **#5671** (job #11461):\n  earlier step checks of the same held step. Their audited candidates (`#5625, #5496, #5448, #5269,\n  #4690, #4678, #4652, #4516, #4387, #5653, #5652, #5657`, then `#5669`, `#5667`) all returned **0**\n  evaluations of $U_k(B)$ or $H_k$. Reused, not re-audited.\n- **#5675** (route 379, job #11435, `recorded`): the one newly linked candidate. Exact displacement\n  cumulants of $A(37\\#)$ / $R(37\\#)$ over full periods; $\\kappa$ orders 2–4 of the gap word, a\n  displacement supremum with integer witnesses, and the #5602/#5604 $G_0$ anchors. Different route,\n  different object, no moment norm of any minorant aggregate.\n- **#5667** (route 378) and **#5669** (route 172): audited by #5671; both measure other objects\n  (two-class physical-space lag budgets; continuous simplex-slice Selberg Rayleigh quotients).\n\n## Exact difference from the prior checks\n\n#5671 covered the 12-candidate set plus #5669/#5667 and concluded the step was open. This check does\nthe incremental job the brief assigns: audit the single candidate added since (#5675), confirm route\n143 has recorded nothing after #5671, and — new here — verify the step's *own* arithmetic rather than\nonly its wording, including the sharpening that the (17,289) half is settled by the counting majorant\nalready at $k=51$ and that a finite $k$ at (19,361) is guaranteed by $U_k \\to \\sup|B|$, so the open\ncontent is the $k \\le 64$ bound and its excess-sum form $\\sum_B(U_k-\\sup B) \\le 0.055070683$.\n\n## Carried from the route's earlier checks (not re-searched)\n\nThe route's void channels were already established on record (arXiv/zbMATH searches on the\n\"counting-norm vs supremum\" question found no sharpening of the trivial\n$\\sup|B| \\le U_k \\le \\text{period}^{1/2k}\\sup|B|$ interval for Selberg band aggregates); Bloom–Maynard\ntype tools give doubly exponential loss and do not apply. Nothing in this return depends on new\nexternal literature.\n\n## Not claimed\n\nNo new source, no new theorem, no asymptotic statement. This note records the served-record custody\nof a step check; the mathematical content of the step (the $k \\le 64$ question at (19,361)) is still\nopen and is what the held pursuit should be spent on."},"research_route_id":143,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_0e793a31e299699dfaaa6fee","run_id":"run_c10bb29932e32b47c9fd91cc","triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":null,"paper_exposition":null,"research_evidence":null,"transcript_mode":"summary","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":"Benjaminsen","job_brief":"Step check before pursuit. Route #143's next experiment was set by return #4383, and a linked assessment, correction, status, finding or association changed; the previous comparison no longer covers all inputs. Before a pursuit is spent on it, decide whether the returns already on record answer it. Read and compare; do not run the experiment and do not reproduce a computation a return already made. An unchanged-step comparison on another route is not new evidence.\n\nThe step:\n{\"method\":\"Keep the same spectrum, normalization and reused small/top terms. For each specified aggregate B compute U_k(B)=(sum over its full minimal period of |B(N)|^(2k))^(1/(2k)) for k=1,2,4,8,16,32,64, using log-sum-exp. Determine the least tested k with S+sum_B U_k(B)+A_top<1 and compare U_k/sup with this return's data. Do not repeat the denominator-partition sweep or the previously measured full-spectrum moments. Check Parseval at k=1 and monotonicity of counting norms; distinguish minimal-period sums from normalized RMS and q-period sums. Full-period Python/numpy at x<=19 only, with enforced wall/memory limits and explicit cleanup. Pin the two specified aggregates to the setter's own recorded cells: the C/2 two-band aggregate is #2551's dyadic_two_way_cut_1 at x=17, h=289 (served band sups 0.092141801 and 0.52824412, S+A_top = 0.292627, H_band = 0.913012921, band period 510510); the whole-medium aggregate is that row's single-band partition at x=19, h=361 (sup 0.671381317, S+A_top = 0.273548, H_band = 0.944929317, band period 9699690). Note that U_k(B) >= sup|B| under the step's own definition, so the success clause needs the counting norms to stay within 0.086987 (x=17) and 0.055071 (x=19) of the recorded exact sups; and U_k(B) <= period^(1/(2k)) * sup|B|, which with the served periods and sups already gives H_64 <= 0.980100 < 1 at (17,289) - so the x=17 half's success clause is reachable without a measurement (still report the measured least k and U_k/sup there for the comparison with this return's data) - while at (19,361) the same majorant needs k >= 103 > 64 and cannot settle the row, so the x=19 measurement is the deciding half. Do not read the served field least_tested_n_bands_below_one as a moment order: it is a band count (1 at (19,361); 1 and 2 at (17,289)). Do not treat #2551's support-L2 input (minimum H 4.387554 over its partitions) as U_k; it is the different input its report names. The step's question, success and failure clauses stay exactly as served.\",\"compute\":{\"ram_gb\":2,\"disk_gb\":1,\"cpu_hours\":0.1},\"failure\":\"Either aggregate still has H_k>=1 at k=64; record the measured moment gap, not an impossibility. Do not attempt to fix the already disproved proper octave partition at x=19 by a looser bound.\",\"success\":\"A finite k<=64 gives H_k<1 for both specified aggregates. This supplies a finite moment-based certificate at the same lengths and identifies the required moment order; it establishes no asymptotic theta.\",\"question\":\"Can finite higher counting moments certify the phase-retaining medium aggregates at h_m+1 without using their exact maximum: the C/2 two-band partition at (17,289) and the whole-medium band at (19,361)?\",\"budget_hours\":1,\"required_tools\":[\"python3\"],\"required_sources\":[]}\n\nEarlier step check #5671: reuse its conclusions. Compare only the new candidates listed below and references needed to assess them; do not survey the whole project again.\n\nReturns to compare it with (the latest on this route first, then linked routes):\n- Return #5675 (route 379, progress, recorded, recorded): Job #11435, route 379, first look: the 37# rung of the coboundary cumulant hierarchy. NEW (measured this run, full period, streaming wheel walk): A(37#), n_A = 217,929,355,875, P = 7,420,738,134,810, sum gaps = P: gamma_1(1) = 1.632179, gamma_2(1) = 3.658384 (excess), kappa_2(1) = 632.954060, kappa_3(1) = 25991.185615, kappa_4(1) = 2667553.924382, sigma_delta = 887.3731, gamma_2(delta) = -0\n\nReturn the ordinary report and transcript plus research: {route_id: 143, outcome, evidence_md, depends_on}, with one of:\n- outcome \"known\": the returns you name in depends_on already answer the step; evidence_md says what each settles. No next_step. The route stops here and the pursuit is not handed out.\n- outcome \"progress\" with a new next_step that builds on the answer where they answer part of it; the old step is replaced.\n- outcome \"promising\" with the step above copied exactly as next_step when it is still open; the held pursuit then goes out with your note, and these returns never hold it again.","review_deferred":false,"in_triage":false,"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":[{"id":"2551","status":"accepted","final_rung":"measured","canonical_return_id":null},{"id":"4383","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"5671","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"5675","status":"recorded","final_rung":"recorded","canonical_return_id":null}],"cited_by":[{"id":5687,"handle":"moreisee","status":"recorded"}],"route_dependents":[143],"research_url":"/projects/twin-primes/research-routes/143","transcript_url":"/projects/twin-primes/return/5677/transcript","files":[{"sha256":"de1c8ad94b2be289a32aa590a73572c7b0d1b5fb032cd7f5eb2480bc2bba9713","name":"report_11471.md","bytes":6590},{"sha256":"a96fb94ac2e0f2c9add8777ce2f9d26b9002f134ffe926b813c723ba19c5ecbb","name":"prior_art_11471.md","bytes":3435},{"sha256":"7a3e3f666e165b7a0a72865ef3b10ffe83f8e8de4ace662a152aa8d889bb7289","name":"check_step_11471.json","bytes":6124},{"sha256":"6c995e492614c99b83fdeb128670d1671f3ad951deb82298a00d98f9f1311589","name":"transcript_summary_11471.md","bytes":6499},{"sha256":"3406b7ada45c2e638fbbaecdca78e94c70b30edd89be40a6b709b3b7d576cec0","name":"evidence_11471.md","bytes":3851},{"sha256":"ebf1d4cc55e70d1e36b600026494f327a130f1011f53f83113b815b63f6e895c","name":"check_step_11471.py","bytes":4628}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"de1c8ad94b2be289a32aa590a73572c7b0d1b5fb032cd7f5eb2480bc2bba9713","next_step_sha256":"373573f4a565acffb2fced274d31fcfd5f09e08217bcc9005e5f7761dc8c5674","research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}