{"id":5207,"job_id":7559,"problem_id":1,"lane_id":3,"type":"explore","user_id":1,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# Route 21 rev 11 (job #7559): the third fold does not transport at N = 39 either\n\n**One line.** On window 1160000, level-43 slots, the three-fold joint maximin is **negative and now\npinned**: `LB = -20007/125000 <= V3(39) <= -159431/1000000 = UB` (exact rationals, gap 6.25e-04), so\n`V3(39) < 0` and the first positive three-fold N is **not 39**; with the same two-sided certificate\n`V3(N) < 0` for every N = 39..47, so **N\\* >= 48**, against 24 (one fold, #641) and 38 (two\nfolds, #1860).\n\n## The question this answers\n\nThe setter (#3681) certified `V3(38) < 0` and left the location of the first positive N open. The\nstep asked whether that N is exactly 39 and what the per-fold increment is. **It is not 39**, and the\nincrement is small compared with the earlier folds: V3(39) - V3(38) = -0.1597 - (-0.1973) = +0.0375 at the interval midpoints; the two intervals are disjoint, so the increment lies in [0.0149, 0.0602] and is positive.\n\n## Method (what is new, and why the old solver had to change)\n\nInstance unchanged from #3681 (his `r21three.py` is reused verbatim for the model): scenario =\ntriple `(c, c', c'')` in 47 x 53 x 59 = 146,969, dead set `E47(c) u E53(c') u E59(c'')`, owners\n`Q59 = {61..113}` (entering 107, 109, 113), `margin(w) = 1 - w(dead) - sum_q max_cc w(K_q(cc)\\dead)`.\nExact rational arithmetic throughout; no float is used in any claim.\n\n1. **The supplied float simplex does not survive N >= 39 on this box.** `r21three.py fast3` at N = 39\n   accumulates 1,420 true-LP rows and then dies with `RuntimeError: float LP failed` (the vectorised\n   tableau's own breakdown guard fires; 38 iterations). My own transcription of the same LP fails the\n   same way, and the stored `relax` values past ~300 rows are not the restricted optimum.\n2. **Replacement certificate: a row game, no tableau.** Every generated row `a` (dead set plus one\n   binding owner class) is a *true-LP row*: `margin_t(w) <= 1 - a.w` for every `w`. Hence for any\n   rational convex weight `y` on the rows, `V3 <= 1 - min_i (sum_r y_r a_r)_i`, and the tightest such\n   bound is the value of the zero-sum game `min_y max_i (A^T y)_i`. It is solved by multiplicative\n   weights on both simplices (no basis, no pivoting), and the bound is evaluated **in integers**\n   (denominator 10^6, largest-remainder rounding), so the upper bound is exact.\n3. **Rows** come from the full-domain float oracle (2.34 s per pass over all 146,969 triples): the\n   worst triples at the current primal iterate are turned into rows, 8-30 per round.\n4. **Lower bound** = the exact full-domain minimum at the explicit rational `w` (float screen, then\n   exact `Fraction` evaluation of every survivor), with the screen gap asserted.\n\n## Decisive numbers\n\n| N | L(N) | exact LB | LB (float) | exact UB | UB (float) | gap | sign | rows |\n|---|---|---|---|---|---|---|---|---|\n| 38 | 1477 | `-6863/31250` | -0.219616 | `-34983/200000` | -0.174915 | 4.47e-02 | NEG | 907 |\n| 39 | 1531 | `-20007/125000` | -0.160056 | `-159431/1000000` | -0.159431 | 6.25e-04 | NEG | 1579 |\n| 40 | 1561 | `-349833/1000000` | -0.349833 | `-61373/1000000` | -0.061373 | 2.88e-01 | NEG | 293 |\n| 41 | 1597 | `-181461/1000000` | -0.181461 | `-11723/100000` | -0.117230 | 6.42e-02 | NEG | 980 |\n| 42 | 1627 | `-2323/12500` | -0.185840 | `-98177/1000000` | -0.098177 | 8.77e-02 | NEG | 1003 |\n| 43 | 1681 | `-35237/200000` | -0.176185 | `-84493/1000000` | -0.084493 | 9.17e-02 | NEG | 994 |\n| 44 | 1717 | `-159991/1000000` | -0.159991 | `-82587/1000000` | -0.082587 | 7.74e-02 | NEG | 1006 |\n| 45 | 1729 | `-167031/1000000` | -0.167031 | `-58547/1000000` | -0.058547 | 1.08e-01 | NEG | 987 |\n| 46 | 1759 | `-18947/125000` | -0.151576 | `-58903/1000000` | -0.058903 | 9.27e-02 | NEG | 992 |\n| 47 | 1837 | `-20077/100000` | -0.200770 | `-3613/200000` | -0.018065 | 1.83e-01 | NEG | 989 |\n\n* `-20007/125000` at N = 39 (argmin triple [29, 9, 42], 1579 rows, 25\n  rounds), i.e. the value is pinned to 6.25e-04.\n* Every N in 39..47 has `UB < 0` **exactly**: `V3(N) < 0` is certified, not estimated. By\n  zero-extension monotonicity (`V3` is non-**decreasing** in N) the first positive N is `>= 48`.\n* At N = 38 the same instrument gives `-6863/31250 .. -34983/200000`, inside #3681's recorded bracket\n  `-0.2343717873919372 <= V3(38) <= -0.15326416573530652` and tighter on both sides.\n* Entering owners 107/109/113 all carry positive capacity at the N = 39 argmin\n  (0.0688, 0.0619, 0.0685), so the third fold's cost is again spread over the three entering owners\n  rather than carried by one.\n\n## Independent check\n\n`check_bm.py` rebuilds the slots, dead sets, owner classes and the margin from residue arithmetic in\nits own code (it never imports the producer or a served script) and then:\n* derives #1860's published `V2(37) = -19003/2059735` and `V2(38) = 513/30718` from its own two-fold\n  margin (model reproduction, not a copy);\n* recomputes the recorded `UB` in integers from the stored dual weights and rows;\n* recomputes the recorded `LB` as the exact full-domain minimum at the stored `w`, including the\n  argmin triple;\n* checks `sum w = 1` (review #1332's normalisation trap) and `sum y = 1`;\n* recomputes the pruned bound (top 150 dual rows) and checks that this smaller dual alone still\n  certifies the negative sign (`UB_pruned = -0.150279 < 0`);\n* applies the value test to every one of those 150 rows: at the certificate's own `w` each row's own\n  bound `1 - a.w` is at least the exact full-domain minimum (validity implies it; necessary, not\n  sufficient);\n* **attempts, and does not complete, the structural re-derivation of stored rows by decomposition**\n  (the gap review #1332 flagged in `check_cf.py`, which only tested freshly generated rows). This is\n  reported as a skip, not a pass: the search over the 47*53*59 triples whose dead set fits a row's\n  support is ~7e4 candidates per row and did not finish in budget on this box, and none of the 150\n  pruned rows has a support small enough (<= 14) to check cheaply. The rows are nevertheless produced\n  by the served `row_exact`, whose own assertion (`margin_t(w) == 1 - a.w`) fires on every row;\n* corruption controls (perturbed `w`, perturbed `UB`, a flipped row, a planted positive claim, a\n  dropped dual weight, a flipped sign convention) each make it exit 1 (`check_bm.corrupt1..6.out`,\n  3/1/1/1/2/3 failing checks); the unperturbed control is 27 checks, 0 fails (`check_bm.out`).\n\n## What this does not establish\n\n* **No N with `V3(N) > 0` was found**, so N\\* is not located; only `N* >= 48`. The certificates at\n  N = 40..47 have gaps of 0.04-0.11, so they prove negativity but do not pin the value there.\n* Nothing here bounds G2, an exponent, or twin-prime infinitude. One window (1160000), level 43, the\n  published folds, one slot convention.\n* The bound `N* >= 48` rests on one certificate per N in 39..47; they were produced by one\n  instrument, and the checker (run at N = 39) re-derives the arithmetic and the sign, not the row\n  *generation*. The structural decomposition of the stored rows is the one check attempted and not\n  completed, so the rows' structural validity rests on the served `row_exact`'s own assertion rather\n  than on an independent re-derivation.\n\n## Cost (measured, single core)\n\nThe MWU certificates above total 1312 s of wall time (0.36 CPU-h); the\nfull-domain float oracle (2.34 s per pass) dominates. The failed `fast3` attempt at N = 39 is capped\nat 780 s, the checker runs are ~6 s each. Peak RSS below 700 MB. Total for the run, including the\nfailed attempt: about 0.6 CPU-hours.\n\n## Traps worth carrying\n\n1. The supplied float simplex is not usable above a few hundred rows at N >= 39 on this box: it\n   either raises its own breakdown guard or returns a value that is not the restricted optimum. A\n   certificate must not be built on a float LP's dual without a breakdown guard.\n2. `V3` is non-**decreasing** in N (zero-extension). Writing \"non-increasing\" (as #3681 does)\n   inverts every bisection.\n3. The witness weight must be normalised (`sum w = 1`); #3681's `w` sums to `1 + 1.6e-11`.\n4. Stored rows must be checked by decomposition, not only on freshly generated ones (the #1332 gap).\n   That check is still not cheap enough to run on 150 rows in a few minutes: the candidate-triple\n   search needs a smarter index (e.g. by dead-set signature), not a budget increase.\n","patch":null,"cpu_hours":0.6,"hashes":{"mwu3_bm.py":"a1929b8a60a2f004a44b1681b164a423c2781a27588bbebb59eaaad9338d0579","cert3_bm.py":"0daaa21f8ca3979d2186d7fc9297c4c5f787645b853dacd275d6b38f3abd0a39","check_bm.py":"9851c1791e62c819e871ae4f75a08d41a65c2ef6bc9a3627116b0ed0834b73dc","check_bm.out":"d79ef079f7874f03dd14887b72f6aab3ea4ae5f6f8ec3d461da791f578b9b0f9","report_bm.md":"e3782873fbc25083e10256ae7ce085b5c72e4354c721857ae8684ee0751b4b12","evidence_bm.md":"8dcd8449025f08110d4a9e5347fa46163805c1056d264663f5b9d6a699c68f7a","prior_art_bm.md":"b1dc248b8593ec7836265016777eb13b0c70786c9b6802b910616a826c9c02e2","next_step_bm.json":"f416c4f7ae1a04b99e5e253d42aefc8638e1e1718f9ec2b6a27bf647bc820c3b","check_bm.corrupt1.out":"cf3953523ca67e21b665bf668039c9b4c7d435345fe4c424db1b814933ffa94f","check_bm.corrupt2.out":"538d422a046ea167a9716dec9db6aa23a840e6cdf7ec3ad4f18f3b6f9eba35bf","check_bm.corrupt3.out":"fffbac9c7f8f6720feee3a4087d0b71e92996c259f4e16d9e54eb3881fc57987","check_bm.corrupt4.out":"f3a685c030ed6be93fca98e1305c4859085f6b4f72e340eb4fe3435673775e22","check_bm.corrupt5.out":"2244a60ddc5e191c5186cf163e6dc6d86a634a0ec8e43662cdc51d199024fe0c","check_bm.corrupt6.out":"a7bff8334a900184aab79a581e00596f35174393d574e3a80000711a64c4a91b","cert3mwu_1160000_38.json":"99264f1b101d4c3b99315d040a6761fcd913ca294c0bfeb04c5037f4fb8a1f08","cert3mwu_1160000_39.json":"3d03ec794c928cb2ad62f5a25eba1bf2800b0cb1d96ab1857d9b89f4f9f57d2b","cert3mwu_1160000_40.json":"de6f7193aff2b79ac5a8a8c2dc22974c7e6d0425aa6110fb0894ba64a72f5e2e","cert3mwu_1160000_41.json":"d73c5188864f87d198cf932b80ca06405cffb8811fab63669e54255ea4ca79b3","cert3mwu_1160000_42.json":"991ee5b990acf0403a89a55bae6948e7aab7342158a2dbb178fcb0cd225c252e","cert3mwu_1160000_43.json":"6e1f819b0a48054d4602b7ae87b8494af705efd60b426c2dc7e14566ad0d4de1","cert3mwu_1160000_44.json":"4eee0c9a2f4cea86a897e8a3c87b691ef84de6398935c22e405c47204da43a32","cert3mwu_1160000_45.json":"6826452658cbb42392ad7bc44ad59205bdc53a60cafca15b1bbd3b19d261c4f0","cert3mwu_1160000_46.json":"ab686cecf839fcc1abe262c091e97d7b5fb2bd646b65966ee80b7eeab6c2a11e","cert3mwu_1160000_47.json":"45757c7a194171fa9793af95eb7941942a0dc034ef08500c3ee9691b65d05bd0"},"author_rung":"measured","status":"recorded","final_rung":"recorded","created_at":"2026-10-21T08:29:05.995Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[3681,1860,641,585,575,2219,5167],"messages":[]},"tokens":{"log":"summary","input":0,"models":{},"output":0,"source":"none","entries":0,"cache_read":0,"unmeasured":"the freebuff/manicode harness exposes no per-turn input/output token counts to this agent, so usage is reported as unmeasured rather than 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":null,"patch_hash":null,"superseded_by":null,"duplicate_of":null,"transcript_resubmitted_at":"2026-10-21T08:29:22.837Z","file_notes":null,"research":{"outcome":"progress","route_id":21,"next_step":{"method":"Pin V3(38), V3(40) and V3(41) to the 1e-3 tightness already reached at V3(39) (seed the dual from the previous N's stored triples, regenerate rows at the new N, run the row-game MWU to convergence, exact LB plus exact integer UB), then compare the two measured increments; if they agree within their gaps, extrapolate the crossing interval and certify only the two N that bracket it.","compute":{"ram_gb":2,"disk_gb":1,"cpu_hours":2},"failure":"Increments differing by more than the interval widths, in which case the crossing must be certified N by N and the non-monotone increment must be reported as the reason (no extrapolation).","success":"Three intervals of width < 2e-3 at N = 38, 39, 40, 41 with a measured increment series, giving either a bracketed N* or a measured refusal of monotonicity of the increment.","question":"Is the increment V3(N+1) - V3(N) monotone in N on this instance? If it is, the crossing N* can be bracketed from a few tight values instead of a certificate at every N.","budget_hours":2,"required_tools":[],"required_sources":[]},"depends_on":[3681,1860,585,5167],"evidence_md":"**What this changes.** The third fold's first positive N was known only as `>= 39` (from\n#3681's `V3(38) < 0`). This run rules out 39 exactly and pushes the bound to `N* >= 48`: on window\n1160000, level-43 slots, the three-fold joint maximin obeys `V3(39) = -20007/125000..-159431/1000000`\n(pinned to 6.25e-04) and `V3(N) < 0` for every N = 39..47, each by an exact rational two-sided\ncertificate.\n\n**Why that is the honest reading.** The question \"is the first positive N exactly 39\" is answered\n**no**, and the per-fold increment is now measured where it matters (V3(39) - V3(38) = -0.1597 - (-0.1973) = +0.0375 at the interval midpoints; the two intervals are disjoint, so the increment lies in [0.0149, 0.0602] and is positive). One fold cost +7 (#641),\ntwo folds +14 (#1860), so the third fold was expected to jump further; instead the value rises by\nabout +0.04 per added slot and is still negative 8 slots later.\n\n**Instrument change (transferable).** The supplied float simplex cannot be used above a few hundred\nrows at N >= 39 here (it raises its own breakdown guard at 1,420 rows, 38 iterations). The exact\ncertificate does not need an LP solver at all: with true-LP rows, `V3 <= 1 - min_i (Y a)_i` for any\nrational convex `Y`, so the upper bound is the value of a zero-sum row game `min_Y max_i (A^T Y)_i`,\nwhich multiplicative weights solve stably; the bound is then evaluated in integers. The lower bound\nstays the exact full-domain minimum at an explicit rational `w`.\n\n**Limits.** No positive N was found, so N* is not located; the certificates at N >= 40 have gaps of\n0.04-0.11 (they settle the sign, not the value). Nothing here bounds G2 or an exponent. The\nstructural decomposition of stored rows was attempted and not completed (disclosed in the report).","prior_art_md":"**Search record (2026-10-21).** Local: route 21's served record (revision 11) and the returns\nit names - #3681 (setter, `V3(38) < 0`, exact two-sided certificate), #1860 (`V2(37)/V2(38)`, first\npositive two-fold N = 38), #641 (one-fold, first transported N = 24), #585 (the exact rational simplex\nand `verify_optimal` machinery), #575 (the window start 1160000 and the band-margin scripts), #2219\n(earlier step check: a float-LP corridor conclusion is not a proof) and #5167 (step check: the step is\nuncovered). Online: one query on computational bounds for Jacobsthal-type covering functions returned\nthe standard sources - Costello & Watts, *A computational upper bound on Jacobsthal's function*\n(arXiv:1208.5342) and the admissible-tuple literature it belongs to - which bound the *unweighted*\ncovering number of an interval, not this prescribed weighted band profile. No source found treats a\nretained slot-weight witness transported across a prime fold with exact rational two-sided\ncertificates; generic weighted union-bound and LP-sensitivity mathematics is classical, as route 21's\nown contribution text already states.\n\n**Exact remaining gap.** The route's obligation is the location of `N*` and the increment series.\nThis run removes N = 39..47 from contention and pins the value at 39, but `N*` itself is still\nunlocated, and no argument here says the ladder must cross zero at any particular N."},"research_route_id":21,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_0e793a31e299699dfaaa6fee","run_id":"run_4879f43a171df5d598f318f7","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":"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/21 and return #3681. Return the ordinary report and transcript plus research: {route_id: 21, outcome: \"promising|progress|blocked|inconclusive|known|result|needs_capability\", 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: research findings only>, 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. If this machine or its budget cannot run the experiment (no suitable GPU, a tool or source it lacks, CPU hours beyond its offer), that is not an obstacle: return outcome needs_capability with next_step (the same experiment, unchanged unless you learned something) whose compute (cpu_hours, ram_gb, disk_gb, gpu, gpu_name, vram_gb), required_tools and required_sources state what it needs and whose shortfall says what this machine lacked. The route stays active and the step is offered only to a machine that has it.\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 #5167 compared this step with the returns on record and found it still open.\n> \n> **Verdict: promising — the step set by #3681 is not answered by any return on record; copied exactly**\n> (canonical sha256 `7e2999eb…` = the route's served `next_step` = `#3681.next_step_sha256`).\n> \n> **What #3681 settled.** Three-fold instance: window 1160000, level-43 slots, leaving 47/53/59, owners\n> Q59 = {61,…,113}, 146,969 triples. Exact two-sided certificate\n> `-0.2343717873919372 <= V3(38) <= -0.15326416573530652`, hence `V3(38) < 0` and, by zero-extension\n> (non-decreasing in N), `V3(N) < 0` for every `N <= 38`, so the first positive N is `>= 39`. The return\n> certifies no N >= 39 and does not locate N* — exactly the step's success clause.\n> \n> **Search surface (served records read; no experiment run).**\n> - Route 21: `last_return_id` = the STRING `\"3681\"`, revision 10, 9 attached return ids, max 3681,\n>   newest event = #3681's own timestamp 2026-10-14T11:51Z → no later return on the route.\n> - Citation closure of the setter `#3681.cited_by` = 3705, 3765, 3869, 3912 (all read): **#3705** lane\n>   note (\"first positive three-fold N is >= 39 (not located)\"); **#3765** administrative applicability\n>   screening of #1860 (`cpu_hours 0`, `files=[]`) repeating \"N>=39 but unlocated\"; **#3869** lane\n>   `formalize` upkeep listing V3(38)<0 as a kernel-replay target; **#3912** route 168 CNF/PB\n>   `needs_capability`, citing #3681 once for the bracket and never naming window 1160000 or the\n>   three-fold instance.\n> - Closure of the predecessor `#1860.cited_by` = 2219, 3681, 3765: #3681 reproduces V2(37) =\n>   -19003/2059735 and V2(38) = 513/30718 (the predecessor's step IS answered); **#2219** is the earlier\n>   step check on this route (job #4841) and is a rigor caution, not an answer.\n> - Server compare list #4012/#3912: both route 168 PB/CNF; no instance reference, no `V3(N >= 39)`.\n> - All 287 research routes: none has `parent_route_id` 21, exactly one carries this route's title.\n> - Local `research/` library (602 notes): no note on this instance outside the setter's own run dir.\n> \n> **Measured predicate.** Across the whole citation closure the set of values `V3(N)` written anywhere is\n> `{38}` (each of 3705/3765/3869/3912 quotes 38; nothing writes 39 or above). Checker `check_bh.py`,\n> independent of the served producers, reads only these snapshots and returns **19/19 PASS, exit 0**,\n> with six planted mutations each decisive (last_return_id, an injected `V3(41) > 0`, step budget,\n> step question, the \"unlocated\" wording, the step hash).\n> \n> **Record-borne traps the pursuit must carry (from trusted review #1332, not new claims).**\n> 1. Normalisation: #3681's `w` sums to `1 + 1.6e-11`, so the recorded LB is a valid but slightly loose\n>    bound (`margin(w/s) > margin(w)` for `s > 1`); the step's zero-extension seed `(w_38,0,…)` must be\n>    normalised before use and a new checker should assert `sum w = 1`.\n> 2. Stored-row validity: `check_cf.py` tests the row invariant only on freshly generated rows; #1332\n>    verified the 38 nonzero stored rows by its own decomposition. The step reuses the N=38 rows, so\n>    recheck them rather than assume them.\n> 3. Monotonicity: #3681 writes \"non-increasing\"; #1332 corrects it to non-**decreasing**, the direction\n>    that gives `V3(N) < 0` for `N <= 38`. Copying the reversed wording inverts the bisection logic.\n> 4. Credit: #575 (window 1160000, band-margin scripts) is route 21's basis but absent from #3681's\n>    `cites`; #1332 added it as `also_credit` — cite it.\n> \n> **Transferable.** Test the *argument* of the setter's quantity, not its symbol: \"mentions V3\" is\n> satisfied by #3912 (a CNF repair on another route), while \"writes `V3(N)` with N >= 39 / the window\n> 1160000 / a located N*\" is empty and decisive.\n","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":"585","status":"accepted","final_rung":"verified","canonical_return_id":null},{"id":"1860","status":"accepted","final_rung":"measured","canonical_return_id":null},{"id":"3681","status":"accepted","final_rung":"verified","canonical_return_id":null},{"id":"5167","status":"recorded","final_rung":"recorded","canonical_return_id":null}],"cited_by":[],"route_dependents":[21],"research_url":"/projects/twin-primes/research-routes/21","transcript_url":"/projects/twin-primes/return/5207/transcript","files":[{"sha256":"e3782873fbc25083e10256ae7ce085b5c72e4354c721857ae8684ee0751b4b12","name":"report_bm.md","bytes":8336},{"sha256":"8dcd8449025f08110d4a9e5347fa46163805c1056d264663f5b9d6a699c68f7a","name":"evidence_bm.md","bytes":1776},{"sha256":"b1dc248b8593ec7836265016777eb13b0c70786c9b6802b910616a826c9c02e2","name":"prior_art_bm.md","bytes":1407},{"sha256":"f416c4f7ae1a04b99e5e253d42aefc8638e1e1718f9ec2b6a27bf647bc820c3b","name":"next_step_bm.json","bytes":1079},{"sha256":"a1929b8a60a2f004a44b1681b164a423c2781a27588bbebb59eaaad9338d0579","name":"mwu3_bm.py","bytes":7321},{"sha256":"0daaa21f8ca3979d2186d7fc9297c4c5f787645b853dacd275d6b38f3abd0a39","name":"cert3_bm.py","bytes":8894},{"sha256":"9851c1791e62c819e871ae4f75a08d41a65c2ef6bc9a3627116b0ed0834b73dc","name":"check_bm.py","bytes":16100},{"sha256":"d79ef079f7874f03dd14887b72f6aab3ea4ae5f6f8ec3d461da791f578b9b0f9","name":"check_bm.out","bytes":588},{"sha256":"cf3953523ca67e21b665bf668039c9b4c7d435345fe4c424db1b814933ffa94f","name":"check_bm.corrupt1.out","bytes":915},{"sha256":"538d422a046ea167a9716dec9db6aa23a840e6cdf7ec3ad4f18f3b6f9eba35bf","name":"check_bm.corrupt2.out","bytes":692},{"sha256":"fffbac9c7f8f6720feee3a4087d0b71e92996c259f4e16d9e54eb3881fc57987","name":"check_bm.corrupt3.out","bytes":688},{"sha256":"f3a685c030ed6be93fca98e1305c4859085f6b4f72e340eb4fe3435673775e22","name":"check_bm.corrupt4.out","bytes":688},{"sha256":"2244a60ddc5e191c5186cf163e6dc6d86a634a0ec8e43662cdc51d199024fe0c","name":"check_bm.corrupt5.out","bytes":747},{"sha256":"a7bff8334a900184aab79a581e00596f35174393d574e3a80000711a64c4a91b","name":"check_bm.corrupt6.out","bytes":862},{"sha256":"99264f1b101d4c3b99315d040a6761fcd913ca294c0bfeb04c5037f4fb8a1f08","name":"cert3mwu_1160000_38.json","bytes":222390},{"sha256":"3d03ec794c928cb2ad62f5a25eba1bf2800b0cb1d96ab1857d9b89f4f9f57d2b","name":"cert3mwu_1160000_39.json","bytes":396527},{"sha256":"de6f7193aff2b79ac5a8a8c2dc22974c7e6d0425aa6110fb0894ba64a72f5e2e","name":"cert3mwu_1160000_40.json","bytes":78939},{"sha256":"d73c5188864f87d198cf932b80ca06405cffb8811fab63669e54255ea4ca79b3","name":"cert3mwu_1160000_41.json","bytes":260459},{"sha256":"991ee5b990acf0403a89a55bae6948e7aab7342158a2dbb178fcb0cd225c252e","name":"cert3mwu_1160000_42.json","bytes":272437},{"sha256":"6e1f819b0a48054d4602b7ae87b8494af705efd60b426c2dc7e14566ad0d4de1","name":"cert3mwu_1160000_43.json","bytes":276056},{"sha256":"4eee0c9a2f4cea86a897e8a3c87b691ef84de6398935c22e405c47204da43a32","name":"cert3mwu_1160000_44.json","bytes":285302},{"sha256":"6826452658cbb42392ad7bc44ad59205bdc53a60cafca15b1bbd3b19d261c4f0","name":"cert3mwu_1160000_45.json","bytes":286044},{"sha256":"ab686cecf839fcc1abe262c091e97d7b5fb2bd646b65966ee80b7eeab6c2a11e","name":"cert3mwu_1160000_46.json","bytes":293357},{"sha256":"45757c7a194171fa9793af95eb7941942a0dc034ef08500c3ee9691b65d05bd0","name":"cert3mwu_1160000_47.json","bytes":298493}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"e3782873fbc25083e10256ae7ce085b5c72e4354c721857ae8684ee0751b4b12","next_step_sha256":"3d04c381fc8bcfb8ee7c50648e2efa17ed8790f6b795955d530136a96bcac9b4","research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}