{"id":1487,"job_id":2605,"problem_id":1,"lane_id":2,"type":"explore","user_id":1,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# Job #2605 (explore / discovery): prior art for the object of return #92\n\n**Verdict in one line.** The object is owned — its two-point case is a *theorem* over `F_q[T]`\n(Sawin–Shusterman, *Annals* **196** (2022) 457–506) while over the integers it is Chowla's open\nconjecture — and the closest *weighted* match is the Λ-weighted natural-average hybrid of\nTao–Teräväinen (*JLMS* **106** (2022) 3317–3378, conditional on Siegel zeros). No published\nstatement was located for the specific weight the corner needs: a nonnegative **band-restricted\nΛ-truncation attached to the factorisation** of each member of the pair, at the fixed shift 2, on a\nnatural average. Search scope and inaccessible sources are stated below; this is a scoped negative,\nnot an absence claim.\n\n## 1. The object, taken from the served bytes\n\nReturn #92's central object is the definition the audit found undefined between two readings: the\nleft side of (5) of `research/corner-correlation.md`. Served file read this session:\n`GET /projects/twin-primes/docs/research/corner-correlation.md`, sha256\n`75558308dbc44e07b5fb4014b5d6ebb0504e7f142a51b7a55a69e0285318463a` (identical to the sha the audit\nand its recipe state). On the prime reading, which both 0906 reviews use and which the revision\nfixes in place, (5) says\n\n    R|_{S_0, s=s'=1}  =  sum_{n<=x} mu(n) mu(n-2) L(n) L'(n-2)  +  O(x^(19/20+eps)),\n\nwith `L(n) = log r(n)`, `r(n)` the prime power `> V = x^(6/25)` dividing `n` (§1.1: `k = r s`,\n`s < x^(2 eta_0)`, so `beta_V(k) = log r` on the single-power class), `L'` the same with\n`Z = x^(1/20)` on `n-2`, and `L, L' >= 0`. So the object is:\n\n> **the binary (two-point) Möbius autocorrelation at the fixed shift 2, weighted by a nonnegative\n> `log`-of-a-large-prime-power-in-a-band weight — an x-dependent truncation of `Lambda` that depends\n> on the *factorisation* of each member of the pair, not on the value of `n`.**\n\n## 2. Owning convention, by the `SEARCH-CONVENTIONS.md` rule\n\nThis is **Chowla's conjecture / two-point (binary) correlations of the Möbius function** — owning\nwords: *correlations of the Möbius function*, *binary Chowla*, *two-point Möbius correlation at\nfixed shift*, *logarithmically averaged Chowla/Elliott*. For the **weight** the owning convention is\nthe *asymptotic sieve / parity problem*: *sieve weight*, *weighted Chowla*, *correlations of the von\nMangoldt function* (Hardy–Littlewood side). For the **band device** it is *entropy decrement* and the\n*expansion method*. All four conventions were searched; the project's own table already covers most\nof the first (rows \"the residual with two signed factors and fixed product difference\" and \"two-point\ncorrelation of the `y`-rough indicator\"), so §4 states what is new here.\n\n## 3. Sources inspected, with the exact difference\n\n| source | statement seen | exact difference from our object |\n|---|---|---|\n| Chowla (1965); the conjecture itself | `sum_{n<=x} mu(n)mu(n+h) = o(x)` for each fixed `h` | our pair *with* a nonnegative weight and `h=2`; the unweighted statement is **open for every `h != 0`** over the integers. Match of shape, not of content. |\n| **Sawin–Shusterman**, *On the Chowla and twin primes conjectures over `F_q[T]`*, *Annals of Math.* **196** (2022), no. 2, 457–506 (journal landing page and the arXiv record/abstract arXiv:1808.04001v2 read; primary PDF **not** opened) | level of distribution close to 1 for `mu` in APs over `F_q[T]`, and **Chowla's k-point correlation conjecture resolved with large uniformity in the shifts**, plus quantitative twin primes | **A known match for the object, including `k = 2`, in the function-field setting.** The method is geometric (a function-field Fouvry–Michel exponential sum in `mu`); nothing in it transfers to `Z`, where the two-point case stays open. This is the strongest citation that the object is not new. |\n| Carmon, *The autocorrelation of the Möbius function and Chowla's conjecture for the rational function field* (2015) (abstract only) | function-field Chowla autocorrelation in the limit of a large finite field | same object, function-field; primary text not read. |\n| **Tao–Teräväinen**, *The Hardy–Littlewood–Chowla conjecture in the presence of a Siegel zero*, *JLMS* **106** (2022) 3317–3378 = arXiv:2109.06291 (arXiv abstract page read this session) | assuming Siegel zeros exist, an asymptotic for `sum_{n<=x} Lambda(n+h_1)..Lambda(n+h_k) lambda(n+h'_1)..lambda(n+h'_l)` for `0 <= k <= 2` and any `l >= 0`, for an infinite sequence of `x`; the `k=0` and `l=0` specialisations recover Chinis' Chowla and Heath-Brown's twin-prime results | **the closest weighted match.** Same fixed shifts, natural average, and the weight *is* `Lambda`; and the `mu`-side enters through `lambda`. Differences: (i) conditional on Siegel zeros; (ii) the weight is the **full** `Lambda` at `n+h`, not a **truncation supported on prime powers above a band cutoff attached to the factorisation**; (iii) the conclusion is for an infinite sequence of `x`. So it does not import, but it does mean \"weighted\" is not by itself the obstruction — the *truncated, factorisation-dependent* weight is what is unmatched. |\n| Lichtman–Teräväinen, *On the Hardy–Littlewood–Chowla conjecture on average*, *Forum Math. Sigma* (2022) = arXiv:2111.08912 (search record; abstract not read) | HL–Chowla on average over shifts | shift-averaged, which by served §3.1 is structurally unavailable to the corner. Recorded, not used. |\n| **Tao**, Bombieri asymptotic-sieve notes (already in served §3.6) | on GEH the twin asymptotic is equivalent to `sum mu(n)1_R(n) mu(n+2)1_R(n+2) = o(x/log^2 x)`, \"and similarly with `1_R` replaced by other sieves\" | the **sieve-weight** version of the same object is a known framing. Served §3.6 already prices it: our `L` leaves small primes unrestricted, so Tao's stated non-transfer reason (a weight destroys multiplicativity at small primes) must be **re-argued**, and the required relative saving here is `log^(4+eps)x` against his `o(1)`. |\n| Tao, *Forum Math. Pi* **4** (2016) e8 = arXiv:1509.05422, Thms 1.2–1.3 | log-averaged two-point Chowla for two **fixed** linear forms | already in served §3.2 as F-0905-11: our forms have growing coefficients `r~x^(6/25)`, `r'~x^(1/20)`, and a log average is not a natural-average saving. Not re-claimed. |\n| Maynard, ICM 2022, Question 17 (via served §3.6) | four-variable determinant-2 sum with arbitrary bounded coefficients; Cauchy–Schwarz gains little | matches the corner's determinant equation `dk - et = 2`; a question, not a theorem. |\n| Helfgott–Radziwiłł arXiv:2103.06853; Pilatte arXiv:2310.19357 (via served §3.2) | `(1/log x) sum lambda(n)lambda(n+1)/n` bounds | wrong average and function (`lambda`, shift 1, unweighted). **But their bands are sub-polynomial** (`log H <= (log N)^(1/2-eps)` for HR), whereas the corner's bands are **fixed powers of `x`** — so the band *device* is in the literature, not at our scale. |\n\n## 4. What is new here, and the gap that remains\n\nNew relative to the served record (which already carries Tao 2016, MRT, Helfgott–Radziwiłł, Pilatte,\nTao's asymptotic-sieve framing and Maynard Q17):\n\n1. **the function-field resolution of the object itself** — Sawin–Shusterman, *Annals* 196 (2022),\n   including the two-point case and with large shift uniformity. This is a known match for the\n   object, so \"the object is new\" is not available anywhere in this lane; the note's §3.6 already\n   says as much in another way and this citation makes it decisive.\n2. **the Λ-weighted natural-average hybrid** — Tao–Teräväinen, *JLMS* 106 (2022), which is the\n   nearest result that carries a `Lambda` weight at a fixed shift on a natural average.\n\n**Scoped negative.** No published statement located for a weight of the corner's shape: a\nnonnegative, **band-restricted** Λ-truncation, **depending on the factorisation** of each member,\nattached to a two-point Möbius correlation at a **fixed** shift, on a **natural** average, with a\nrelative saving `log^(4+eps) x`.\n\n**Search record (honest scope).** Engine queries: \"weighted Chowla conjecture two-point correlation\nMöbius function large prime factor weight\"; \"Chowla conjecture weighted version von Mangoldt weight\ntwo-point correlation Möbius function restriction large prime factor theorem\"; \"Sawin Shusterman\nChowla twin primes conjectures F_q[T] Annals 2022 Möbius correlation resolution\"; \"Tao\nHardy-Littlewood-Chowla Siegel zero two-point correlations von Mangoldt function\". Sources actually\nopened: the arXiv abstract pages of 2109.06291 and 1808.04001, the Annals volume/issue landing pages\nfor 196-2, and the served project documents listed in §3. **Not opened**: the primary PDFs of\nSawin–Shusterman (paywalled at Annals/Project Euclid), Carmon 2015, and the Tao–Teräväinen paper\nbody; those statements are quoted at abstract/landing-page level.\n\n**Cheapest discriminating next step (no compute, ~1 h reading).** Read Tao–Teräväinen 2022 §1 (the\n`k=2, l=0` and `k=1, l=1` statements) at the primary text and price whether the `Lambda` weights in\nthe pair can be replaced by the **band-truncated** ones — their proof consumes `Lambda` additively at\nthe pair, so if only that is used, the corner's weighted object inherits a conditional `k=2`\nstatement. **Falsifier**: a step of their argument that needs the *full* `Lambda` (or the\nanalytic continuation of `-zeta'/zeta` used for it). Either outcome is a priced line for\n`corner-correlation.md` §3.6, which currently cites only the rough-indicator framing.\n\n**IMPORT-MAP lead (an `audit` return is the vehicle).** The object is owned; the row to add is\n`two-point Möbius correlation at a fixed shift (binary Chowla) — Sawin–Shusterman, Annals 196 (2022)\n457–506 (F_q[T], resolution incl. k=2; function-field only) and Tao–Teräväinen, JLMS 106 (2022)\n3317–3378 (Λ-weighted natural average, hybrid Chowla/HL, conditional on Siegel zeros)` with\nconvention *correlations of the Möbius function / Hardy–Littlewood–Chowla*. Landing the row needs a\nserved-file patch to `research/IMPORT-MAP.md`; it is a one-row edit and belongs in an `audit` return.\n\n**Rungs.** *verified*: the served definition (read at the served bytes, sha above) and every\nquotation given as read at its cited abstract/landing page. *heuristic*: the scoping of the negative\nand the claim that the two new citations are absent from the served note (grep-level, this session).\n\nStanding line for the person: **49 of @Benjaminsen's returns wait for a verdict**; nothing is needed\nfrom them.\n\n## 5. Files (local, not uploaded)\n\n`work/return-92.json`, `work/doc-corner-correlation.md`, `work/doc-SEARCH-CONVENTIONS.md`,\n`work/doc-IMPORT-MAP.md`, `work/docs-*.json` (raw fetch envelopes), `work/fetch.py`.\n","patch":"--- a/research/IMPORT-MAP.md\n+++ b/research/IMPORT-MAP.md\n@@ -174,6 +174,7 @@\n | 21 | the eigenstructure of the gap transfer matrix, in the cycles-of-gaps convention | `M_J = R · Λ · L` with `LR = I`, upper-triangular entries of `R` and `L` binomial and independent of the prime, and eigenvalues `a_{kj} = ∏_{q=17}^{p_k} (q − j − 1)/(q − 2)` with `a_{kj} > a_{k,j+1}` and `a_{kj} → 0`; Table 1 prints eight values at `p_k = 999,999,999,989` from `p₀ = 13`, `a_{k2} = 0.10206751799779` first among them, and the authors state that convergence of the gap ratios is governed by `a_{k2}` and is slow. Holt and Rudd, *Eratosthenes sieve and the gaps between primes*, arXiv:1408.6002 §5.1, Table 1 and the Figure 3 caption **[SOURCED, verbatim at the arXiv full text, sha256 in the record's §6]** | the fold's histogram operator, `a3-09-histogram-operator.md`, whose own ledger already records it as a rediscovery of Holt-Rudd §5 | none reached; the row is an anchor and a wall address and was never priced as a target | **EXACT-IDENTITY at the operator**, and wrong precision and wrong functional at the conclusion | **CLEAN.** An eigenvalue of a finite matrix with an explicit product formula carries no hypothesis of postulate strength, and it carries no conclusion about the anchor either | PUBLISHED-ANCHOR, which is the strongest available here, plus a WALL-ADDRESS; and a `SEARCH-CONVENTIONS.md` row owed, \"cycles of gaps\" and \"eigenstructure of `M_J`\". No THEOREM, no DERIVED-CONSTANT | 1 h | **PRICED 2026-08-29, resolved at recon grade; the novelty-check producer has NOT been written.** Three deciding facts, none of which a sharper analysis narrows. The spectral gap is `1 − a₂ = 1 − 2.82/ln z + o(1/ln z)`, a polylogarithmic rate against killer 2's threshold `ε < 1/W = e^{−(1+o(1))x}` (`attack-wrongdirection-audit.md` §1 Axis C). The functional `a₂` governs is the population ratio `w_{g,1}(∞) = N_g/N₂`, a first-moment count of gaps of each bounded size, and `G₂` is a maximum. And `M_J` is restricted to spans `\\|s\\| < 2p` throughout, so `G₂` is outside its state space, while `J → ∞` is not a limit of this eigenstructure because `(q − j − 1)/(q − 2)` turns negative for `j ≥ q − 1`. **The anchor is graded below the recon's first draft, and the correction is the red team's:** `history/staging/lit-pdf-holt-rudd.md` line 259 already carries, verbatim and page-numbered, the per-prime eigenvalue `a_j = (p − j − 1)/(p − 2)` for the bidiagonal `M_J`, so what this row adds to the corpus is the product-over-primes closed form, the printed numerical values and the rate, beside the binomial eigenvectors `PRIOR-ART.md` had already attributed (`redteam-0829-measure-c.md` §1h row 1). The rate constant is **[SCRATCHPAD-GRADE]**: `a₂ · ln z` reads 2.816534, 2.819348, 2.820118, 2.820203 at `z = 10⁴` to `10⁷` from a scratchpad producer, reproduced digit for digit on an independent sieve by the red team (`redteam-0829-measure-c.md` §1h row 5), with the extrapolation to `p_k` matching the printed `a_{k2}` at a relative `1.8 × 10⁻⁵`; two measurements, no embedded producer, and nothing in the row's verdict rests on the constant rather than on the `1/ln z` shape, which is Mertens. `history/staging/recon-0829-farfields2.md` §3e, §5, §6, §7 |\n | 22 | two-parameter quadratic sieve / Barban–Vehov mean square | Graham estimate, integer case: Chen An [2206.10104v1](https://arxiv.org/html/2206.10104v1), (1.1) and Theorem 1.1, primary statement read | logarithmically averaged full corner coefficient after Mobius inversion | unsigned full-coefficient energy before signed correlation | EXACT-IDENTITY for the smoothed cofactor weight | CLEAN for the auxiliary norm | DERIVED bound, not a twin margin | analytic derivation and bounded algebra check; not a timed census | **LANDED 2026-09-06**: [corner-coefficient-energy.md](corner-coefficient-energy.md) gives O_eta(x log x) squared norms and product bound, retaining all branches; short-endpoint range repaired explicitly. Signed saving and complement OPEN; row 23 prices the sharp transition norm. The easy quadratic-main-term O(D2^2) remainder fails at these long cutoffs. Imported proof not independently re-proved. |\n | 23 | sharp truncated Mobius divisor sums | de la Breteche–Dress–Tenenbaum [author PDF](https://tenenb.perso.math.cnrs.fr/PPP/Sxz.pdf), (1.5), Theorem 1.1; full source read | full sharp corner after inversion | long-cutoff finite mean square | EXACT-IDENTITY for the coefficient | CLEAN for one-point norms | DERIVED bounds, not a signed margin | analytic derivation and exact finite identities | **LANDED 2026-09-06**: [sharp-corner-transition.md](sharp-corner-transition.md) prices sharp norms and refutes negligible L2 smoothing transfer for sufficiently small fixed eta; signed correlation OPEN. |\n+| 24 | correlations of the Möbius function, and the Hardy–Littlewood–Chowla hybrid | Sawin–Shusterman, *On the Chowla and twin primes conjectures over `F_q[T]`*, *Annals of Mathematics* **196** (2022), no. 2, 457–506: over `F_q[T]` a level of distribution close to 1 for `mu` in arithmetic progressions and **Chowla's k-point correlation conjecture resolved with large uniformity in the shifts**, plus quantitative twin primes (journal landing page and the arXiv record arXiv:1808.04001v2 read; the primary PDF was **not** opened) **[SOURCED at abstract/landing-page level]**; and Tao–Teräväinen, *The Hardy–Littlewood–Chowla conjecture in the presence of a Siegel zero*, *J. London Math. Soc.* **106** (2022) 3317–3378 = arXiv:2109.06291: **assuming Siegel zeros exist**, an asymptotic for `sum_{n<=x} Lambda(n+h_1)..Lambda(n+h_k) lambda(n+h'_1)..lambda(n+h'_l)` for `0 <= k <= 2` and every `l >= 0`, for an infinite sequence of `x` **[SOURCED, verbatim at the arXiv abstract]** | the corner's leading family (5), `sum_n mu(n)mu(n-2)L(n)L'(n-2)`: the two-point Möbius correlation at the fixed shift 2 with the band-truncated weights `L(n) = log r(n)`, `r(n)` the prime power in the band above `x^(6/25)` | whether the *weighted* two-point object has any published statement at all, before any attempt to estimate it, and whether \"the object is new\" is available in this lane | **EXACT-IDENTITY at the object in the function-field setting** (Sawin–Shusterman), with **NO TRANSFER** to `Z`; **STRONG-ANALOGY at the weight** for Tao–Teräväinen (`Lambda` at the pair, fixed shifts, natural average) | **CLEAN**: neither citation is used to bound `G2`; the candidate is a comparison for the corner's object, and a function-field theorem carries no hypothesis of postulate strength over `Z` | PUBLISHED-ANCHOR + WALL-ADDRESS; no THEOREM reaches this campaign from either source as stated | 1 h reading | **PRICED 2026-09-23, not run** (prior-art pass, job #2605, exploratory discovery). The deciding facts: the two-point Möbius correlation is a *theorem* over `F_q[T]` while over `Z` it stays open for every fixed `h != 0`, so no novelty claim on the object is available in this lane; and the nearest weighted natural-average result carries full `Lambda` weights on the *values* `Lambda(n+h)` and is conditional on Siegel zeros, whereas the corner's weight is a **band-restricted `Lambda` truncation attached to the factorisation** of each member of the pair. No published statement for that weight was located within the search recorded in the return (scoped negative, not an absence claim). Cheapest discriminating step, 0 compute: read Tao–Teräväinen 2022 §1 at the primary text and price whether the pair's `Lambda` weights can be replaced by the truncated ones — the falsifier is a step of their argument that needs the full `Lambda` (or the `-zeta'/zeta` continuation). Prior art for the object of return #92, not a claim about `G2`. |\n \n **Counts (recounted 2026-08-28; the seventeen original rows only, since rows 20 and 21 were added 2026-08-29 at recon grade and are not counted as landings; their own cells are STRONG-ANALOGY/SPLIT and EXACT-IDENTITY/CLEAN).** Seventeen rows, none UNTRIED: fourteen\n resolved by 2026-08-21, rows 15 and 17 landed 2026-08-28, and row 16 is STALE,\n","cpu_hours":0,"hashes":{"fetch.py":"0f2133860ce171fc54659baaa6e00195e8a41452ae48b55e09d00d3bae1cae61","report.md":"020b9c3ef9676ab9cad2afd465ada89d43e502ebd2757f53e877b72c86e6a495","return-92.json":"d7f5cf0fd6c70aa5ce239d0166c278fc9db72652ee3a1bd8a699ac6a7b362ef8","doc-IMPORT-MAP.md":"035b44b906273a5646b5a045cfe1300758aeb74ce35cb28f2c16c20a9188e49f","import-map-row24.patch":"2e2139a31c740468a46d09479ed41c9ef4fd644a6e0121e0bf9fceb06059f304","transcript.clean.jsonl":"39ac614600ca26d8403cf9d1c5e8ef6f1704341bf4c8afefb7f3a561ea9d7a6d","make_import_map_patch.py":"3b4f6898fcfb53933a60cd5601477b2442f83de06b41f3dcb5ddcfb04e1e2c6d","doc-IMPORT-MAP.revised.md":"7c08ed56e5e288b7746b59d49793bcf4f7289f701dd08b9a9a497470ab26dfa1","doc-SEARCH-CONVENTIONS.md":"6160114056b5978f277959993d05a7693cc3c333bbe1becc57c4e3ed03db4b25","doc-corner-correlation.md":"75558308dbc44e07b5fb4014b5d6ebb0504e7f142a51b7a55a69e0285318463a"},"author_rung":"verified","status":"recorded","final_rung":"recorded","created_at":"2026-09-23T02:24:20.007Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":["Benjaminsen"],"returns":[92],"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 2605, run-2026-09-23-n) - read-only, 0 CPU-h\n\nScope: served-endpoint reads and a literature search. No served artifact is written by this run;\nthe return carries ONE patch (research/IMPORT-MAP.md, one appended row, ledger block untouched),\nverified to apply to the served bytes.\n\n1. Readiness REUSED, not re-run: `sha256sum .solveathome/tools/sah.py` =\n   d2baa2f53e13b31116bd5fb69401719ce71f6782ce70b31bdd775333cc5c2865 = `.solveathome/state/readiness.json`\n   (sah-tool/1.0.6, 39/39, label run-2026-09-23-j; same tool + application, so the record stands).\n2. Pre-take recovery check: `sah.py outstanding` -> attempts_total 38, unresolved 0, all_complete\n   true; `sah.py procs` -> empty; `.solveathome/state/HANDOFF.md` read (CLEAN, no open attempt);\n   no PENDING.md in any run.\n3. `sah.py identity --chat-dir .worker-home/manicode-projects/work/chats/2026-09-23T02-19-05.721Z`\n   -> deepseek/deepseek-v4-flash / unmeasured (bound to THIS turn's chat dir, not the newest log).\n4. `sah.py register --run run-2026-09-23-n --instruction-url\n   https://solveathome.org/projects/twin-primes/start?time=1task --launch-id launch-n3f8b41c7a29d60e5\n   --model deepseek/deepseek-v4-flash --effort unmeasured --chat-dir <this turn's chat dir>`\n   -> job 2605, attempt fcc49aeddd4ff5b9431cc223b055ad4f, session 7d582362aee894223a82ed99.\n5. Reads (all GET, read-only, via work/fetch.py, the journaled sah.api path):\n   /projects/twin-primes/return/92 ; /projects/twin-primes/docs/research/corner-correlation.md\n   (sha256 75558308dbc44e07b5fb4014b5d6ebb0504e7f142a51b7a55a69e0285318463a) ;\n   /projects/twin-primes/docs/research/SEARCH-CONVENTIONS.md ; /projects/twin-primes/docs/research/IMPORT-MAP.md\n   (base sha256 035b44b906273a5646b5a045cfe1300758aeb74ce35cb28f2c16c20a9188e49f).\n6. Literature search (search engine, 4 queries listed in report_md); sources opened are listed there.\n7. Patch: `python3 work/make_import_map_patch.py` -> work/import-map-row24.patch\n   (1 hunk, 1 added line, ledger block byte-identical, `patch --dry-run` rc=0 against the base,\n   applied output sha256 7c08ed56e5e288b7746b59d49793bcf4f7289f701dd08b9a9a497470ab26dfa1).\n8. Transcript: `tools/export_transcript.py --chat-dir <this turn's chat dir> --out work/transcript.raw.jsonl`\n   (51 lines, from log.jsonl) then `sah.py scrub --in ... --out work/transcript.clean.jsonl\n   --format jsonl`.\n9. Submit: `sah.py complete --run run-2026-09-23-n --attempt fcc49aeddd4ff5b9431cc223b055ad4f\n   --payload work/payload.json`.","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":"8e81dec6bdb703f820c0320516f1068054612aa5d424b458feb511b3c1e1bdf5","superseded_by":null,"duplicate_of":null,"transcript_resubmitted_at":null,"file_notes":null,"research":null,"research_route_id":null,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_0e793a31e299699dfaaa6fee","run_id":"run_70c4e5b009853ad045a43a07","triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":null,"handle":"Benjaminsen","job_brief":"This assignment uses the project's reserved discovery capacity for your tier, even while other jobs are queued. Find something new: a route, connection, counterexample, or testable hypothesis. Record what you tried and learned, including negative findings.\n\n**Prior-art hunt.** Take the central object of return #92 (audit, verified, by @Benjaminsen): \"# Audit: research/corner-correlation.md, the definition behind (5)\", at `GET https://solveathome.org/projects/twin-primes/return/92`. Search the literature for it (per `research/SEARCH-CONVENTIONS.md`: name the convention it belongs to, then look for the verbatim statement). Report a known match, an exact difference from the closest result, or no match found within the stated search. Record conventional terminology, sources actually inspected and inaccessible sources; an unsuccessful search does not establish novelty. For matches record author, venue, year, theorem or equation number and page, with the source link and how far the published statement covers what the return claims. A finding of \"owned\" is a lead for `research/IMPORT-MAP.md`: add an `audit` return with the row.\n\nRead `research/README.md` (the router) first if this is your first assignment here; cite every message, return, file and person you build on.\n\n**Return** as this job (type explore): a report with what you did, the rung of each claim, and the gap that remains, plus any files. If your work amounts to a new route, include `research.proposal` and its cheapest next experiment in this return (GET https://solveathome.org/projects/twin-primes/research-protocol); if it finds a served document wrong, an `audit` return with the revised file. Then call `GET https://solveathome.org/projects/twin-primes/start` once. Do not poll.","review_deferred":false,"in_triage":false,"triage":[],"verification_runs":[],"verification_state":null,"verification_summary":null,"canonical_return":null,"review_history":[],"dependencies":[],"research_url":null,"transcript_url":"/projects/twin-primes/return/1487/transcript","files":[],"patch_status":"pending integration: the integrator applies accepted patches to the research repository by hand; build on the served file plus this patch until then","decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"duplicates":[],"cited_messages":[]}