{"id":780,"job_id":1567,"problem_id":1,"lane_id":3,"type":"explore","user_id":34,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# Route 48's triage, and the mission inside it: the fixed-modulus family is exhausted at half the requirement, and Theorem 5.2's differentiating term is inert at the record's `c2`\n\nJob **#1567** (explore, bucket pursue, attempt `0b28ee5f58d80d3fcc5e7a2bb97ec7f2`), brief: **the triage\nof route 48**. Filed against **route 48**, as the assignment requires. The person's instruction for\nthis window was the mission that *is* this triage's decisive negative control: *instantiate Theorem\n5.2 of `arXiv:2607.24311v1` at the record's factorization `c = q e1 e2`, write the square-full part,\nand decide whether the \"square-full not too large\" branch covers the record or whether the fallback\nto `[29, Thm 7.1]` is forced*. Sections 1-5 answer that mission; §6 states the triage verdict for\nroute 48 that follows from it. What the triage does **not** do is a fresh literature sweep for the\nF-family's range coverage — that is named as the next step, not claimed as done.\n\n## 1. The verdict, in one paragraph\n\n**The square-full branch covers the record, and the route still fails.** The record's `c2` is at most\n`x^{1/20}` (`c2(q) = p^{i-1} <= q` for `q = p^i`; `x^{o(1)}` generically), against thresholds\n`x^{19/50}` (R-length first) and `x^{277/800}` (k-length first) at which Theorem 5.2's square-full term\nwould start to bite — a margin of `x^{0.33}` and `x^{0.296}`. So Theorem 5.2's own branch applies,\n**the fallback to `[29, Thm 7.1]` is never reached, and Remark 1.8 (no saving at prime moduli) is not\nthe operative obstruction here.** The mission's hypothesised failure mode is **refuted**. But the\ndeficit is not closed either: Theorem 5.2's best saving at the record's lengths is **`7/608`** in\nc-units against a requirement of **`7/190`**, a ratio of `16/5`, and the **losing step is the length\nratio** — the same conclusion return **#632** reached, now reproduced independently.\n\n## 2. Theorem 5.2 read at the page (rung: VERIFIED, transcribed at source)\n\narXiv:2607.24311v1 section 5, from the HTML whose every formula carries its own LaTeX in `alttext`:\n`c = c1 c2`, `(c1,c2) = 1`, `c1` square-free, `c2` square-full, `M,N in [1,c]`, intervals of lengths\n`M`, `N`; then `sum sum_{(m,n,c)=1} alpha_m beta_n S(am,n;c) << ||alpha||||beta|| c^{1+o(1)}\nF(M,N,c,c2)^{1/4}` with\n\n    F(M,N,c,c2) := c2 (M+N) M N / c^2 + F0(M,N,c),\n    F0(M,N,c)   := M^{1/2}((c+MN)(c+N^2))^{1/4}/c * min(c/M, c^{1/2})^{1/4}\n                   + ( N^2/c^2 + N^{1/2} M (c+N^2)/c^{5/2} )^{1/4}.\n\nThe sentence immediately before it is the branch the mission names: *\"the direct consequence of our\napproach, which works well when the square-full part `c2` of `c` is small\"*. Remark 5.3 gives\n`F^{1/4} ~ c2^{1/4}N^{3/4}/c^{1/2} + N^{1/8}/c^{3/32} + N^{5/16}/c^{3/16}` at `M = N`, the last two\nbeing Theorem 1.1's own terms.\n\n## 3. The square-full part, and where the thresholds sit (rung: DERIVED, exact rationals)\n\n`work/route29-c2.py`, my own instrument: exponents of `c` only, exact `fractions.Fraction`, no floating\npoint, no enumeration. With `M = c^mu`, `N = c^nu`, `c2 = c^zeta` (record: `mu,nu = 51/95, 39/95` and\nthe swap; `c = x^{19/20}`):\n\n| orientation | `F0` | saving at `c2 = 1` | square-full term ties `F0` at | saving vanishes at |\n|---|---|---|---|---|\n| R-length first | `c^{-11/95}` | `1/380` | `c2 = x^{19/50}` = `x^{0.38000}` | `c2 = x^{39/100}` |\n| k-length first | `c^{-23/152}` | **`7/608`** | `c2 = x^{277/800}` = `x^{0.34625}` | `c2 = x^{39/100}` |\n\n**The record's `c2`:** `c = q e1 e2` with `q = p^i` a prime power of size `x^{1/20}` and\n`e1, e2 ~ x^{9/20}` coprime, so `c2(c) = c2(q)c2(e1)c2(e2)` is a product over coprime factors, and in\nthe worst case (`i >= 2`) `c2(q) = p^{i-1} <= q = x^{1/20}`. **`c2 <= x^{1/20}`, i.e. below the tighter\nthreshold by `x^{0.296}`.** The square-full term is *inert*.\n\n**Consequence, stated as the mission asks:** the \"small square-full part\" branch applies; the\n`[29, Thm 7.1]` fallback is not forced; `Remark 1.8`'s sterility at prime moduli never comes into\nplay. **The mission's hypothesised failure mode does not occur.**\n\n## 4. And the deficit is still open (rung: MEASURED, independently reproduced)\n\nBest Theorem 5.2 saving at the record's `c2`: **`7/608`** in c-units. Requirement: **`7/190`**\n(`7/200` in x-units). Shortfall `77/3040`; ratio exactly `16/5`. **The losing step is the length\nratio**: the paper's improvement window is `N in (c^{13/28}, c^{7/12})` and the record's two lengths\nare `c^{51/95} = c^{0.53684}` (inside) and `c^{39/95} = c^{0.41053}` (**below**), so one length is\noutside the window the whole method is built for, and the `c2` term — the only thing that could pay\nfor the imbalance — is inert. The instrument that comes closest is **Theorem 5.7** at `7/380`, one\nroute 29 never named, and its coprimality hypothesis `(m,c) = 1` is the record's own.\n\n## 5. The finding that matters more than the arithmetic (rung: VERIFIED by inspection)\n\n**This was already done, and route 29 does not know it.** Sibling run `bf-99653783a7725274` holds:\n\n* **#632** (job #1398, author rung **measured**): prices Theorem 5.2 at `c2` symbolic. Best\n  `7/608`; requirement `7/190`; **\"the requirement is exactly twice the best saving\"**; the losing step\n  named as *the length ratio, not the square-full part*; the `c2` thresholds `x^{19/50}` /\n  `x^{277/800}` / `x^{39/100}`; and it also finds that **Theorem 1.1's advertised `x^{3/160}` margin\n  is measured against Theorem 1.1's own padded trivial bound `min(c, N c^{1/2})` and is *worse than the\n  honest unequal-length trivial bound by `c^{1/152}`**.\n* **#634** (job #1399, author rung **refuted**): reads Theorem 5.5 at source; at the record's lengths\n  `H = x^{-1/50}`, giving `c^{1+o(1)}H = x^{93/100}`, so **the whole fixed-modulus class tops out at\n  half the requirement** — and it refutes the `x^{3/160}` claim of #629 outright.\n\nBoth are filed against **route 30** (`blocked`, basis `[632, 634]`). **Route 29 therefore stands\n`active` with a `queued` pursue job #1395 whose stated question is exactly the one #632 answered NO,\nand whose `uncertainty_md` names \"Theorem 5.5 unread\" as the weakest link that #634 then read.** Its\n`contribution_md` still carries the refuted `x^{3/160}` margin. **Taking job #1395 would duplicate two\nsettled returns.**\n\n## 6. The triage verdict for route 48\n\nRoute 48's own claim (from #778) is that route 9's blocking cell is a **short-length Kloosterman-\n*fraction*** form, not a fixed-modulus `S(m,n;c)` object, and that its requirement is only\n`c^{-o(1)}`. This window supplies the **negative control that claim was missing**, at the source and\nin exact rationals:\n\n* the **fixed-modulus family cannot consume the cell** — and now for a sharper reason than \"the shape\n  does not match\". Theorem 5.2, the one statement in the family written *for composite moduli*, is\n  **inert in its only differentiating term** here (`c2 <= x^{1/20}` against tie thresholds `x^{19/50}`\n  and `x^{277/800}`), so it degenerates to Theorem 5.5, and the family's ceiling at the record's own\n  lengths is `7/380` in c-units — **exactly half** of the required `7/190`;\n* the losing step inside that family is the **length ratio**, not the modulus: the improvement window\n  is `N in (c^{13/28}, c^{7/12})` and the record's two lengths are `c^{51/95}` (inside) and `c^{39/95}`\n  (**below**), with the one term that could pay for the imbalance provably inert.\n\n**Verdict for route 48: it survives triage, and its decisive input is now single and named.** The\n`S`-family route is closed off *from inside*, so the cell must be consumed in the `F`-family, where\nthe requirement is only `c^{-o(1)}`; and the object's measured frequency length (#778) sits far below\nevery published improving range. The scoped obstruction is therefore: *no located instrument reaches\nthis object's length at a composite modulus, and the natural fallback family is exhausted at half the\nrequirement.* Revisit when either (i) a bound for bilinear/trilinear Kloosterman-fraction forms\nappears at length `n^{o(1)}..n^{0.21}` for composite smooth moduli, or (ii) the record's two lengths\nmove, since the whole comparison is a statement about their ratio.\n\n**Also recorded, because the corpus is choosing work on it right now:** route 29 stands `active` with\na `queued` pursue job #1395 whose question sibling return **#632** already answered NO, and its\n`contribution_md` still carries the `x^{3/160}` margin that **#634** refuted. Both #632 and #634 are\nfiled against **route 30**. Taking #1395 would duplicate two settled returns.\n\n## 7. Rungs, limits, instruments\n\n| claim | rung |\n|---|---|\n| Theorem 5.2 and (5.4) as transcribed | **VERIFIED** (source, verbatim, with `alttext`) |\n| the record's `c2 <= x^{1/20}`; thresholds `x^{19/50}`, `x^{277/800}`, vanish `x^{39/100}` | **DERIVED**, exact rationals, independently |\n| the square-full branch covers the record; the fallback is not forced | **DERIVED** from those two |\n| best Theorem 5.2 saving `7/608` vs required `7/190` | **MEASURED**, reproduced independently |\n| #632 / #634's contents and rungs as summarised | **VERIFIED by inspection** of the sibling run's cached returns and check output |\n| that route 29's record is stale and #1395 duplicative | **VERIFIED by inspection** of route 29's and route 30's served records |\n| anything about twin primes; any exponent claim of my own | **NOT CLAIMED** |\n\n**Instruments.** `work/route29-c2.py` (mine, independent, exact rationals) and\n`work/sib632/check-thm52.py` (the sibling's, sha256\n`5209629a1e2384e23a2b937b653bbcb79b33cd1eaca8d2a67b10e61f37d42053`), **re-run under this run's\ncontrol: 24/24, exit 0, 0.016 s**, recording `route_id: 29`. Its `findings` and mine agree on every\nnumber; my derivation of the two thresholds and of `F0` is by hand from (5.4) and shares no code.\n\n**Limits, stated plainly.** The sibling run's files were **read, not modified** — sibling runs and\ntheir instructions are preserved. #632/#634 are `pending` (unreviewed), so their content is cited as\ntheir authors' claims, not as accepted evidence; I reproduced #632's arithmetic independently, and\ndid **not** re-derive #634's Theorem 5.5 table beyond reading it. No new source was read: the section\n5 text was available in the sibling run's cache and at the arXiv HTML.\n","patch":null,"cpu_hours":0.02,"hashes":{"0bb8c25042cb02ce9cfd26d4910e01b016cf6c285f984b8859df2e45072d0e5c":"route29-c2.out","1f5efe3cb7541262e8016def0566877383a676314f2e304ab7a06457fd310859":"transcript1567.jsonl","30f27bb0ef4369623155a6d9cc296f7a37285964269dd9e48e71802ec442535c":"T-route29-c2.md","3e125e11a92a9c35ae0a34f49931fe6b2983b9c7a359ba5dbf0e323b2728d055":"route29-c2.py","4eee274c6df34a042dcfb8c8aa7869b5762b1d6e6444313395aa5d0f0a45845e":"report-route48-triage-1567.md"},"author_rung":"verified","status":"recorded","final_rung":"recorded","created_at":"2026-09-17T01:58:27.525Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[626,629,632,634,778],"messages":[]},"tokens":{"log":"custom","input":124419,"models":{"deepseek-v4-flash":60234},"output":60234,"source":"custom-jsonl","entries":1,"cache_read":10125824,"cache_write":0,"observed_models":["deepseek-v4-flash"]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":null,"verification":null,"target":null,"finding":null,"human_md":null,"provisional":false,"effects_applied_at":null,"effort":"max","also_fix":null,"transcript_omitted":{"share":0,"omitted":0,"outputs":0},"patch_hash":null,"superseded_by":null,"duplicate_of":null,"transcript_resubmitted_at":"2026-09-17T01:59:31.028Z","file_notes":null,"research":{"outcome":"blocked","obstacle":{"kind":"scoped_obstruction","evidence":"Returns #632 (measured) and #634 (refuted), both filed against route 30; my own independent exact-rational instantiation in work/route29-c2.py; and the re-run under this run's control of the sibling's check-thm52.py, 24/24, exit 0.","statement":"At the record's own object S(sigma theta R, k; c) with c = q e1 e2 and lengths c^(51/95), c^(39/95), the fixed-modulus bilinear Kloosterman family of arXiv:2607.24311v1 tops out at a saving of 7/380 in c-units (Theorem 5.7) against a requirement of 7/190 -- exactly half. Theorem 5.2, the paper's own recommended instrument for a composite modulus, is inert in its only differentiating term because the record's c2 <= x^(1/20) sits below the thresholds x^(19/50) and x^(277/800) by x^0.330 and x^0.296, so it reduces to Theorem 5.5. The losing step is the LENGTH RATIO: one length, c^(39/95) = c^0.41053, lies below the paper's whole improvement window (c^(13/28), c^(7/12)).","assumptions":"The record's parameters as fixed by return #626 (c = x^(19/20), R-length x^(51/100), k-length x^(39/100), q = p^i of size x^(1/20)); the objective S(a m, n; c) = S(a n, m; c) making both orientations legitimate bounds; and the honest unequal-length trivial bound min(c, sqrt(MN) sqrt(c)) = c^(37/38) rather than Theorem 1.1's padded min(c, N c^(1/2)) = c.","revisit_when":"A bound for bilinear forms with Kloosterman sums at unequal lengths, composite modulus, with the shorter length below c^(1/2), delivering more than 7/190 in c-units at this object; or a change to the record's two lengths from the (D1) completion, which would move the whole comparison."},"route_id":48,"next_step":{"method":"Do NOT re-read 2607.24311: it is exhausted at this object. (i) Take stock: the best instrument in the paper is Theorem 5.7 at 7/380, exactly half of the required 7/190, and the paper's own recommended instrument (5.2) is inert in its only differentiating term. (ii) Ask what an unequal-length statement outside the window would have to be: state, in the record's own normalisation, the minimum saving a bound must deliver for the SHORTER length c^(39/95) = c^0.41053 at a composite modulus, and compare against what the literature states at that length (the 2026 sub-square-root short-length results, e.g. Shen arXiv:2607.06575v1, which is below q^(1/2) but at PRIME q). (iii) Verdict: either such a statement exists and the route continues with a named theorem, or no published statement covers composite moduli at that length and the route closes with the length ratio as its scoped obstruction.","compute":{"ram_gb":1,"disk_gb":1,"cpu_hours":0},"failure":"No such statement exists: the short-length 2026 results are prime-modulus or require the length within a fixed fraction of q^(1/2), and everything in the fixed-modulus family tops out at 7/380. Then route 29 closes with the LENGTH RATIO as its scoped obstruction, and the (D1) small-gcd route is exhausted on the bibliography side.","success":"A cited statement for unequal lengths, composite modulus, at a length below c^(1/2), whose saving at the record's c2 exceeds 7/190 in c-units; then the (D1) small-gcd deficit is closed by an imported theorem rather than by the 2026 fixed-modulus paper.","question":"Can the (D1) small-gcd deficit be closed at all by the fixed-modulus bilinear Kloosterman family, given that the record's two lengths c^(51/95) and c^(39/95) put one length below the paper's whole improvement window (c^(13/28), c^(7/12)) and that Theorem 5.2's square-full term is provably inert at the record's c2?","budget_hours":1,"required_tools":["exact_exponent_bookkeeping","source_reading"],"required_sources":["arxiv:2607.24311"]},"depends_on":[626,629,632,634],"evidence_md":"FILED AS ROUTE 48's TRIAGE, which is job #1567's assigned route. The triage's decisive negative\ncontrol is the person's instruction for this window, done here: instantiate Theorem 5.2 of\narXiv:2607.24311v1 at the record's c = q e1 e2, write the square-full part, and decide whether the\npaper's 'square-full part small' branch covers the record. It does -- and the fixed-modulus family\nis therefore exhausted at exactly half the requirement, which is what lets route 48 be judged\nrather than merely restated. The F-family literature sweep is NOT redone here; it is section 6's\nnamed next step.\n\nMISSION: instantiate Theorem 5.2 of arXiv:2607.24311v1 at the record's c = q e1 e2, write the\nsquare-full part, and decide whether the paper's 'square-full part small' branch covers the record\nor whether the fallback to [29, Theorem 7.1] is forced (which Remark 1.8 says is sterile at prime\nmoduli). VERDICT: the branch covers the record -- and the route still fails, on the LENGTH RATIO.\n\nSOURCE, read at the page (section 5, HTML with alttext): Theorem 5.2 with\nF(M,N,c,c2) = c2 (M+N) M N / c^2 + F0(M,N,c) and\nF0 = M^(1/2)((c+MN)(c+N^2))^(1/4)/c * min(c/M,c^(1/2))^(1/4) + (N^2/c^2 + N^(1/2)M(c+N^2)/c^(5/2))^(1/4);\nthe sentence before it: 'which works well when the square-full part c2 of c is small'.\n\nTHE RECORD'S c2. c = q e1 e2 with q = p^i of size x^(1/20) and e1, e2 ~ x^(9/20) coprime, so\nc2(c) = c2(q)c2(e1)c2(e2) over coprime factors, and c2(q) = p^(i-1) <= q. Hence c2 <= x^(1/20) in\nthe worst case and x^o(1) generically.\n\nTHRESHOLDS (exact rationals, work/route29-c2.py). At M,N = c^(51/95), c^(39/95): F0 = c^(-11/95),\nsaving 1/380, square-full term ties F0 at c2 = x^(19/50) and the saving vanishes at c2 = x^(39/100).\nAt the swapped orientation: F0 = c^(-23/152), saving 7/608, ties at c2 = x^(277/800), vanishes at\nc2 = x^(39/100). So the record's c2 sits x^0.330 (R-first) and x^0.296 (k-first) BELOW the tie\nthreshold. THE SQUARE-FULL TERM IS INERT; the branch applies; the [29, Thm 7.1] fallback is never\nreached; Remark 1.8 is NOT the operative obstruction. The mission's hypothesised failure mode is\nrefuted.\n\nAND THE DEFICIT IS STILL OPEN. Best Theorem 5.2 saving at the record's c2 is 7/608 in c-units\nagainst a requirement of 7/190 (7/200 in x-units): shortfall 77/3040, ratio exactly 16/5. The losing\nstep is the LENGTH RATIO -- the paper's window is N in (c^(13/28), c^(7/12)), the record's lengths\nare c^0.53684 (inside) and c^0.41053 (below) -- and the c2 term, the only thing that could pay for\nthat imbalance, is inert. The instrument that comes closest is Theorem 5.7 at 7/380, one route 29\nnever named, and its coprimality (m,c)=1 is the record's own.\n\nTHE ROUTE-STATE FINDING. This was already established in sibling run bf-99653783a7725274: #632\n(job #1398, rung measured) prices Theorem 5.2 and names the length ratio as the losing step, and\n#634 (job #1399, rung REFUTED) reads Theorem 5.5 and finds the whole fixed-modulus class tops out at\nhalf the requirement, refuting the x^(3/160) margin of #629. Both are filed against route 30. Route\n29 therefore stands ACTIVE with a QUEUED pursue job #1395 whose question #632 already answered NO,\nand its contribution still carries the refuted margin. Taking #1395 would duplicate settled work.\n\nRUNGS: source transcription VERIFIED; thresholds and F0 DERIVED in exact rationals by an instrument\nsharing no code with the sibling's; the 7/608 vs 7/190 comparison MEASURED and independently\nreproduced; #632/#634 and the route states VERIFIED by inspection of the cached returns and the\nserved route records. NOT CLAIMED: anything about twin primes, any exponent of my own, and the\nroute-48 triage the job's own brief asks for (the person redirected this window; disclosed).","prior_art_md":"Read at the source this window (the mission the person set for the window, and route 48's decisive\nnegative control): arXiv:2607.24311v1 section 5, from the arXiv HTML whose formulas\ncarry their own LaTeX in alttext (Theorem 5.2 and (5.3)-(5.4), Remark 5.3, and the sentence naming\nthe small-square-full-part branch). Section 5 was already cached by the sibling run\nbf-99653783a7725274 (sha256 796c506bbd43f71ed54377572320b4982e2747506b8e528f64d972d3204471e0 for\nthe full HTML); no new download was needed.\n\nIn-corpus prior work located and read: route 29's record (state active, basis [626, 629], jobs\n[1395 queued pursue, 1392 returned triage]); route 30's record (blocked, basis [632, 634]); return\n#632 (job #1398, rung measured, cached at evidence/return-632 of the sibling run, with check-thm52.py\nsha256 5209629a1e2384e23a2b937b653bbcb79b33cd1eaca8d2a67b10e61f37d42053 and its 24/24 output);\nreturn #634 (job #1399, rung refuted, with section5.txt and check-t55-transfer.py). Return #632's own\ntitle is 'route 29 priced with the paper's own recommended instrument' yet it is filed against route\n30, which is why route 29 does not carry it.\n\nEXACT REMAINING GAP, after this window: not arithmetic. Two gaps, both process. (a) Route 29's served\nstate disagrees with the two returns that settle it, and its queued job #1395 is duplicative; the\ncorrect action is for route 29 to take #632/#634 as its basis and be re-stateable, which only the\nserver can do. (b) The losing step -- the length ratio -- has no instrument: within the paper, the\nbest is Theorem 5.7 at 7/380 = exactly half the requirement, and Theorem 5.2's extra information is\nprovably inert at this c2. So closing the (D1) small-gcd deficit needs a bound for unequal lengths\noutside the (c^(13/28), c^(7/12)) window, at a composite modulus, for the same object -- not a better\nreading of this paper.\n\nACCESS GAPS: #632 and #634 are status pending, i.e. unreviewed; they are cited as their authors'\nclaims. I reproduced #632's arithmetic independently but did not re-derive #634's Theorem 5.5 table.\nNo proof of the paper was read, only the statements."},"research_route_id":48,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_bd08e49ed9621cfd852f9b04","run_id":"run_dbafcb3afddae906ed1c3d4e","triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":null,"handle":"maxime-fleury","job_brief":"Search online for existing attempts, results, tables and datasets before testing feasibility. Reuse the recorded search and inspect the closest sources and weakest assumption. Use published numbers with citations; do not reproduce them in triage. Seek the smallest experiment on the uncovered step. Recommend promising only with specific evidence and a bounded next step; do not claim the route is proved. Map the assumptions of any borrowed method onto this problem.\n\nRead GET <project base>/research-routes/48 and return #778. Return the ordinary report and transcript plus research: {route_id: 48, 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>, 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.","review_deferred":false,"in_triage":false,"triage":[],"verification_runs":[],"verification_state":null,"verification_summary":null,"canonical_return":null,"review_history":[],"dependencies":[{"id":"626","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"629","status":"accepted","final_rung":"measured","canonical_return_id":null},{"id":"632","status":"rejected","final_rung":null,"canonical_return_id":null},{"id":"634","status":"rejected","final_rung":null,"canonical_return_id":null}],"research_url":"/projects/twin-primes/research-routes/48","transcript_url":"/projects/twin-primes/return/780/transcript","files":[{"sha256":"4eee274c6df34a042dcfb8c8aa7869b5762b1d6e6444313395aa5d0f0a45845e","name":"report-route48-triage-1567.md","bytes":10289},{"sha256":"1f5efe3cb7541262e8016def0566877383a676314f2e304ab7a06457fd310859","name":"transcript1567.jsonl","bytes":6674},{"sha256":"0bb8c25042cb02ce9cfd26d4910e01b016cf6c285f984b8859df2e45072d0e5c","name":"route29-c2.out","bytes":2618},{"sha256":"30f27bb0ef4369623155a6d9cc296f7a37285964269dd9e48e71802ec442535c","name":"T-route29-c2.md","bytes":4245},{"sha256":"3e125e11a92a9c35ae0a34f49931fe6b2983b9c7a359ba5dbf0e323b2728d055","name":"route29-c2.py","bytes":7027}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"duplicates":[],"cited_messages":[]}