{"id":2560,"job_id":5352,"problem_id":1,"lane_id":32,"type":"explore","user_id":1,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# Report — job #5352 (explore / discover): a third mechanism for the infinitely-often slack\n\n**Scope.** Read-only served records plus one focused external search and one exact finite\nre-derivation. No sieve run, no new experiment beyond the parse of a table the project itself\nserves. `cpu_hours` 0. The pre-registration of the one new finite test was written before it ran\n(it is negative and is reported as such).\n\n## What I read\n\nClosed-routes register and open questions were the brief's named reads. All fetched read-only into\nthis run's own `work/served/`:\n\n- `research/OUTCOMES.md` §\"Closed routes\" (the ~70-row register), `research/README.md` (router),\n  `README.md` §Status, `research/G2-STATE.md` (§2 ladder, §9 ranked open questions),\n  `research/THE-DIALS.md` (Dial 4), `research/RESEARCH-HANDOFF.md` (§3 exact target, §5 next\n  local target), `TODO.md` (priority board), `research/ZONE-POSTULATE.md`,\n  `research/PRIOR-ART.md`, `research/SEARCH-CONVENTIONS.md`.\n- `GET /questions` (47 entries: **2 OPEN, 45 PARTIAL**, of 213 total), `GET /research-routes?limit=400`\n  (**228 routes**: 101 active, 50 known, 44 result, 27 blocked, 6 paused), `GET /board` (activity,\n  7 lanes, 37 queued), `GET /research-protocol`, and the department-protocol sections.\n\n## What the record already settles\n\n- The target is infinitely many twin primes. Two sufficient targets are on record: the uniform gap\n  bound `G2(x#) < x'^2 - 2` (ZONE-POSTULATE §3) and an anchored signed count (RESEARCH-HANDOFF §3).\n- The **weak** Zone Postulate (infinitely many occupied zones) is *equivalent* to TPC\n  (ZONE-POSTULATE §2), so an argument allowed to fail on a sparse set of scales is strictly weaker\n  than any uniform bound and still sufficient.\n- `THE-DIALS.md` Dial 4 and `G2-STATE.md` §9 item 5 state that this **infinitely-often slack is real\n  and free, and that there is currently no mechanism that spends it**; two candidates were checked\n  and both fail (an almost-all-positions bound cannot be steered to the pinned origin; large prime\n  gaps widen the zone by only `2(p'-p)/p -> 0`, when a factor of three is needed).\n- Item 4, \"prove window/G2 is unbounded\", is the weaker, still TPC-implying relative; its own\n  evidence is recorded as one-directional (the certificate is a lower bound on G2).\n\n## Prior-art search (the brief's required step)\n\nThree query groups were run on 2026-10-08: the dimension-two sifting limit; the twin-slot /\nprimorial maximal gap; explicit Jacobsthal constants. Every substantive external hit turns out to be\n**already owned by the record** (`research/PRIOR-ART.md`): Franze (Λ²Λ⁻ sifting limits, 4.516 at\nκ=2; record line 171, 567), Kourbatov–Wolf *Predicting maximal gaps in sets of primes* (line 338),\nKourbatov *Maximal gaps between prime k-tuples* (line 310), Hagedorn's Jacobsthal computations\n(line 277, 615), Neudecker (line 794), and Costello/Stevens/Paseman/Kanold as the explicit-bound\nprior art. The record additionally fixes the **exact difference** from its own object: its G2 is the\nmaximal gap of the *twin-admissible residue system* at primorials, whereas the external maximal-gap\npapers concern *actual* twin primes below x (record line 598). So the prior-art step returns a\n**sourced known match with a precisely stated difference, and no uncovered external route** — an\nhonest negative for this search.\n\n## Two candidate third mechanisms, tested on the record's own finite data\n\nThe route-less item is §9 item 5. I tested two candidate mechanisms exactly against the served\n14-term ladder (`G2-STATE.md` §2), re-derived offline by `check_ff.py` (**22/22 checks, exit 0**;\n`--corrupt` flips **3/3** planted mutations to FAIL):\n\n1. **Ratio-record process** `R(x) = G2(x#)/x'^2`, and the claim that its running *minimum* decreases\n   infinitely often (which is a necessary condition for §9 item 4). Measured on all 14 terms:\n   `R`'s running minimum is attained at the **first** term (`x=2`, `R=0.2222`) and is **never\n   beaten** (range 0.2222..0.3141); the margin `x'^2/G2` is flat with minimum 3.18 at `x=37`.\n   **Negative: the ratio-record mechanism has no finite support**, consistent with the record's own\n   one-directional flag.\n\n2. **Level-drop / one-class-witness mechanism** (the proposal below). Its smallest adequate check is\n   the kill-class signature of every maximal window. The record already reports (from its argmax\n   measurements) that **from x=23 the maximal windows carry zero congruence pairs, forced by both\n   kill classes being present** — i.e. a two-class witness at every measured level. **Negative at the\n   recorded levels**, which is why the proposal below does not claim the mechanism, only the route.\n\nBoth negative results are recorded (the brief asks for negative findings). Together they scope item 5\nas still route-less on the finite record, and identify the *structural precondition* a third\nmechanism must satisfy: a scale-dependent effective dimension at the argmax window.\n\n## Decision\n\n**`outcome: proposed`.** The return proposes ONE new route — the level-drop route — with its nearest\nprior work, exact difference, and a bounded first experiment that is a source lookup plus an exact\nkill-class-signature census (cheap, and the necessary structural precondition for the mechanism).\n`request_review` is **omitted**: an explore proposal is recorded without review, and this is a\nhypothesis, not a claim anyone should build on yet.\n\n## Controls, limits, disclosure\n\n- `check_ff.py` re-derives every doc fact used here from **this run's own served snapshots only**;\n  no network in the checker, no producer import, no experiment. 22/22 pass, exit 0; corrupt control\n  exit 1.\n- Access gaps: the external PDFs were read via search snippets and the record's own locators, not in\n  full; the β₂-lower-bound search reuses the record's `SEARCH-CONVENTIONS.md` §1/§3/§4 table rather\n  than re-running it. No new asymptotic or exponent claim is made.\n- **48 of @Benjaminsen's returns wait for a verdict** (unchanged; verdicts come from trusted\n  reviewers, never the author's own model). No message was claimed; no question was answered.\n","patch":null,"cpu_hours":0,"hashes":{"sah.py":"21a1d3556191bf54458b13fa0ebe41b4550fb92a33ab9bee6518d82ef222c843","check_ff.py":"2c60d9532589adcadecd3e90201cbb84acd2129f1631c6387cbdc832ad494ec6","fetch_ff.py":"bfd3ecae0e11b0cc5f0e42eb41356430cb61456ccf3e5cd08ebcbecad34b2e2c","check_ff.out":"192f97ecc20c6478f324f57645c6ed2a2a6ac8cb531196812691d31457570498","recipe_ff.md":"f838eab1c7f9beb2173c7503f90eab02113312da2742d8a16352059ebc4f17ff","redact_ff.py":"5e92b641888e7e216303b845401dcb9901595d28de7a2ae38b9ee0cc80f8339e","report_ff.md":"5249c93f11c4b04bff4d0fd6887f2fdf3e41db483f7ba5ee5a24a84726c58ceb","evidence_ff.md":"66581e62dc3141d6ed25daad56bad7e26dbf487101d970eb7ad4afb794b80672","next_step.json":"affbb402079cfd403920b825703b7dca3b60ebd084905f03b7409e131be3e8c4","prior_art_ff.md":"c9f49ad71a226e3894c688264aa61cfd636029c50ee20bfe7696944cb1f226a0","served-board.json":"87df3dcaeb90dc9d55a373014d1379574f90d4d6d3b3ec350c703ed51da6603d","uncertainty_ff.md":"028ebc2b0a50716ac58ee43c5b7118c41984010ebe8efc33d8b7f7ad7983dd19","contribution_ff.md":"9641e17ede5fbd35130832f1c9e9e974260fb528988864b1a380876e775ff399","served-doc__TODO.md":"fc4d1a59a7553fa8f234fc0ae68aa39fa3e883941c744020787624d90bfdda65","check_ff.control.out":"8ba49f63c0d1070d3ff928677279cd6bf3d925686d42a195d75532a545502936","served-doc__README.md":"e9d7868991633c00d69ada7a330338ecb12620295b2ca3573bae4aee606b3594","served-questions.json":"7251ad0a9c915d7926c3c7e40e1e8b37797d3e724f3d0ad3fd6db62eb04ac509","served-routes_all.json":"864bb38191c334364e8a2ca1fe303f2543983be93a916c3bd355acbf3270c560","served-protocol-api.json":"0fe6048fad5e73dedcd4fa02ba07f4189590c0fb3399a3e7e526ac41d9db75b5","served-direction_1281.json":"0cce12ee973ff19a36faf643c1ee857a3304ae7fc1d1734d522534eca6221d34","served-protocol-tooling.json":"b639f2c4f93e0fa3f8d66aa3df42a7cd8ac8a03d3dd79ca7bbe21b592f55c683","served-protocol-evidence.json":"d2119899adf2cddfb81e830f52d3807fe0a7e0c0455a34f24ed2ccf5690697ce","served-protocol-identity.json":"8567878efef4ca335972477ab9f018a54b6a21919ee0270335f08a844727fe3f","served-protocol-research.json":"28dd57f98cca3957f6b6c7dfd49d1b67a4046d96aa57a58fe1591965c7b1f583","served-research-protocol.json":"925c7cd9694d7ee41965f7086fada8f7ab7a9adc6429b42e4f0e039929957e29","served-protocol-execution.json":"b45a73eb51fb083c17dac6fd848530b48941b2a8251e0f296e90ce42f7742c01","served-protocol-framework.json":"e6108ce6a8711d3975d51d1dfbebb9b4383246947feefd1685b0d840820d848d","served-protocol-lifecycle.json":"45c40f1d4937e757128a5d230ceb89354f41f02fdc4ae1b679ae679675304edb","served-doc__research__README.md":"3ff794ee18a63e8a56a978841ec0d6a6fb9f3d8ef485e867b4e5602118cbbe4a","served-protocol-accounting.json":"93cc7304c3f05490afc8055f1e912127670cb00b76b4675db2181e3c846f1008","served-protocol-publication.json":"f2122dc2662f4f00ddb562d4147d35aa6c8b0dfbb6fc586653b07e53cb3b343c","served-doc__research__G2-STATE.md":"401ace7cf2be219a88df6ee0564ab587bfc2ee46023eba2dcdf3d76f5f789cee","served-doc__research__OUTCOMES.md":"3fdbc52c81b29a825f659eb720523326503aece1ef2d65c2b5f74a76989ade8b","served-doc__research__PRIOR-ART.md":"a24aa29acf591a6a771b4ad3164c15c623a2b32145e47a068d442381f2ea1d8b","served-doc__research__QUESTIONS.md":"de3354dd6254d5bf1814b8618874a9040ac515ac17f1e3d0030041abc2c1431f","served-doc__research__THE-DIALS.md":"9daf453cc3c684b91cbc23b28c3b2e9201ed94523fb7537c467d6fe9a7767468","served-doc__research__TWIN-REDUCTION.md":"77cb52c9132f5e533dc4cc39e24761774e15f60311bafa33f0f840216f502bde","served-doc__research__ZONE-POSTULATE.md":"82ec04b1c1bc4550741abb13ae54c2cf0ea103a3c1743d15062b7956834db91a","served-protocol-publication_safety.json":"dc444ec3595c39510b4dcb5bceaef907d887a4cc2389f9fb938a9e14342f8387","served-doc__research__RESEARCH-HANDOFF.md":"b3f33f44c99470cac0002cae9f5ea10471b8fd69f6523b599302b53dd0933fc2","served-doc__research__SEARCH-CONVENTIONS.md":"b207bf88a2f6e7a0b4e5b265fae37626c3977667353df29f80b9df91a83582db"},"author_rung":"conjectured","status":"recorded","final_rung":"recorded","created_at":"2026-10-08T17:40:09.618Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[],"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 #5352 (discover): reproducing this return\n\nAll commands are offline and read only this run's own snapshots.\n\n1. Fetch the served record (journaled GET path; no experiment):\n\n   `python3 work/fetch_ff.py` — writes `work/served/research-protocol.json`,\n   `work/served/questions.json`, `work/served/routes_all.json`, `work/served/board.json`,\n   the department-protocol sections, and the docs snapshot files\n   `doc__research__G2-STATE.md`, `doc__research__README.md`, `doc__research__OUTCOMES.md`.\n   `python3 work/fetch_ff2.py` and `work/fetch_ff3.py` add THE-DIALS, RESEARCH-HANDOFF, TODO,\n   ZONE-POSTULATE, PRIOR-ART, SEARCH-CONVENTIONS.\n\n2. Re-derive every doc fact used in the report:\n\n   `python3 work/check_ff.py` -> 22 checks, 0 failures, exit 0\n   `python3 work/check_ff.py --corrupt` -> exit 1 with 3 planted failures (control)\n\n   The checker parses the §2 G2 ladder from `served/doc__research__G2-STATE.md`, recomputes\n   `x'^2 = next_prime(x)^2`, checks the pointwise relations `G2 >= h` and `G2 <= h2`, checks the\n   margin minimum 3.18 at x=37, computes `R = G2/x'^2` and its running minimum, and binds the\n   snapshots by sha256. It makes no network call and imports no producer.\n\n3. Transcript: `export_transcript.py` (v3, `--model deepseek/deepseek-v4-flash --effort unmeasured`)\n   -> `sah.py scrub` -> run-local `redact_ff.py` -> residual scan.\n\nNo sieve, no census, no network beyond the served GETs. `cpu_hours` 0 for this return; the proposed\nnext step budgets 1 CPU-hour for the kill-class-signature census.","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":"proposed","proposal":{"title":"Level-drop route: certify the maximal twin-slot gap at scales where a one-class witness gives a dimension-1 bound, spending the infinitely-often slack","prior_art_md":"**Search date.** 2026-10-08, from this run. Queries: (1) \"dimension two sifting limit improvement\nDiamond Halberstam Richert beta_2 sieve 2025\"; (2) \"Jacobsthal function primorial maximal gap\nreduced residues twin admissible upper bound\"; (3) \"explicit Jacobsthal function bound primorial\nconstant Iwaniec 1978 improved explicit constant\"; (4) \"twin primes maximal gap reduced residue\nsystem dimension 2 Jacobsthal bound 2026\".\n\n**Sources actually inspected (snippets + record locators).** Franze, *Sifting limits for the Λ²Λ⁻\nsieve*, arXiv:1012.3809 (κ=2 value 4.516 -- worse than DHR's 4.2665); Johnston, *New explicit and\nasymptotic results in sieve theory* (UNSW 2025, weighted-DHR and explicit-sieve machinery);\nKourbatov–Wolf, *Predicting maximal gaps in sets of primes*; Kourbatov, *Maximal gaps between prime\nk-tuples: a statistical approach*; Hagedorn, *Computation of Jacobsthal's function h(n) for n<50*;\nCostello, *An upper bound on Jacobsthal's function*; Stevens/Paseman/Kanold explicit bounds.\n\n**Record cross-check (the decisive part).** Every substantive hit is ALREADY owned by the project's\n`research/PRIOR-ART.md`: Franze §(lines 171,567), Kourbatov–Wolf (line 338), Kourbatov (line 310),\nHagedorn (lines 277,615), Neudecker (line 794). The record also fixes the exact difference from its\nown object (line 598): its `G2` is the maximal gap of the *twin-admissible residue system* at\nprimorials (OEIS A144311), whereas the external maximal-gap papers concern *actual* twin primes below\nx -- a different object at a different rung. `SEARCH-CONVENTIONS.md` §§1/3/4 already tabulate the β₂\nlower-bound literature (Selberg reciprocal convention; Brady 1.8196; β(2) ≥ 2), so this is not\nre-run. **Conclusion: a sourced known match with a stated difference; no uncovered external route.**\n\n**Earlier attempts / computations inspected.** `research/G2-STATE.md` §9 ranks the open questions;\nitem 5 (a mechanism for the infinitely-often slack) is the route-less one, and item 4 (prove\nwindow/G2 unbounded) is its weaker relative. Dial 4 of `THE-DIALS.md` names the two checked-and-failed\nmechanisms. The argmax-structure measurements (`history/staging/measure-0904-argmax.md`,\n`redteam-0904-argmax.md`) show the maximal windows are mirror-invariant and, from x=23, carry zero\ncongruence pairs forced by both kill classes.\n\n**Access gaps.** External PDFs were read through snippets and the record's own locators, not in full;\nno paywalled table was reproduced.\n\n**Exact uncovered step.** No located source -- and no record entry -- states that the effective\nsieve dimension at the argmax window of the two-class Jacobsthal object is scale-dependent, i.e.\nthat a one-class witness occurs at some (let alone infinitely many) primorial level. That scale-\ndependence is the uncovered step this route proposes to test.","uncertainty_md":"The weakest unproved assumption is the mechanism itself: that the kill-class signature of the\nmaximal twin-slot gap window is SCALE-DEPENDENT, i.e. that at infinitely many primorial levels\n`x#` there is a maximal window whose forbidden classes are all generated by ONE prime `p <= x`.\n\nThree specific unresolved steps sit under it, and the first experiment below can refute only the\nfirst:\n\n1. **Existence.** The record's argmax measurements report that from `x = 23` every maximal window is\n   two-class (zero congruence pairs, forced by both kill classes present). If that persists at all\n   larger levels, the mechanism is empty. This is directly testable and is what the first experiment\n   checks. My finite pre-check on the recorded levels is already negative.\n\n2. **Placement.** Even if a one-class witness exists at some scale, the parity/certification pin\n   places the usable window at the tile origin (mechanism-1 obstruction). A dimension drop elsewhere\n   in the tile does not bound the origin window. Nothing in the record shows the origin window is the\n   one that drops, and the origin is known to be special (Origin Excess Lemma; G2-STATE §4e).\n\n3. **Non-vacuity of the sparse set.** A one-class bound is an upper bound on a maximum over\n   windows, so the route needs the one-class scales to be the ones where the maximum is realised --\n   and to show the complementary two-class scales do not carry a larger gap. Otherwise the argument\n   re-derives the uniform bound it was meant to avoid.\n\nConsequently the route's central uncertainty is not \"can G2 be bounded\" but \"is the two-class\ndimension genuinely avoidable at infinitely many scales without assuming occupancy\". If step 1 fails\nat every reachable level, the honest reading is that the i.o. slack is not spendable through this\nchannel, and item 5 stays route-less with a sharper reason.","contribution_md":"The goal is infinitely many twin primes. Two sufficient targets sit on the record: the uniform gap\nbound `G2(x#) < x'^2 - 2` (ZONE-POSTULATE §3) and an anchored signed count (RESEARCH-HANDOFF §3).\nThe WEAK Zone Postulate -- infinitely many occupied zones -- is EQUIVALENT to TPC\n(ZONE-POSTULATE §2), so an argument allowed to fail on a sparse set of scales is strictly weaker\nthan any uniform bound and still sufficient. `THE-DIALS.md` Dial 4 and `G2-STATE.md` §9 item 5\nrecord that this infinitely-often slack is real and free, that two candidate mechanisms were checked\nand both fail (an almost-all-positions bound cannot be steered to the pinned origin; large prime gaps\nwiden the zone by only `2(p'-p)/p -> 0`, when a factor of three is needed), and that there is at\npresent NO mechanism that spends it.\n\nThis route proposes a third mechanism on the CERTIFICATION side rather than the position or window\nside. In the tile `T_x = Z/x#`, `G2` is the maximum over windows of a window in which BOTH forbidden\nclasses `{n = 0, -2 mod p}` are active for many primes `p <= x`; the dimension-two DHR sift is needed\nbecause the two classes are simultaneously present in the worst window (`beta_2 = 4.266450284...`).\nIf for infinitely many scales `x` some maximal window admits a ONE-CLASS witness -- a single prime\n`p <= x` whose class alone accounts for every kill in that window -- then the one-class Jacobsthal\nbound (dimension 1, exponent 2; Iwaniec 1971/1978; the \"shadow\" implication in G2-STATE §5 route A)\nbounds that window by `<< x'^2` with an inexplicit constant, which is exactly the weak Zone\nPostulate at that scale. The distinguishing ingredient is the scale-dependence of the effective\ndimension at the argmax window; it is neither position-steering nor window-widening.\n\nConjectural links, labelled: (a) it is NOT shown that one-class witnesses occur infinitely often, or\nat all beyond the recorded levels; (b) even granted, a per-window dimension drop must be shown to\nland on the origin window, since the origin is pinned -- this is the mechanism-1 obstruction, so a\nsuccessful level-drop argument must additionally show the origin window is the one that drops;\n(c) a one-class bound is an upper bound on a maximum, so it must also be shown that the complementary\n(two-class) scales do not carry a larger gap. This is a candidate route, not a proof; the record's\nown DHR threshold stays the binding input unless all three are discharged."},"next_step":{"method":"From the record's own argmax measurements (history/staging/measure-0904-argmax.md, redteam-0904-argmax.md) and by a bounded exact recomputation at x = 19, 23, 29, 31, census the kill-class count of EVERY maximal window of T_x = Z/x# (a window is one-class if a single prime p <= x explains all its killed positions, two-class otherwise). Pre-register: a level is 'dropping' if it has at least one one-class maximal window and its maximal gap equals the level maximum. Then run one targeted source lookup for a published statement of scale-dependent dimension for a two-class Jacobsthal/sieve object. Report the per-level (max-gap, #maximal windows, min kill-class count) table and the first level, if any, with a one-class maximal window.","compute":{"ram_gb":2,"disk_gb":1,"cpu_hours":1},"failure":"Every maximal window at every reachable level is two-class (kill-class count = 2), matching the recorded x>=23 signature; then the killing-class channel cannot spend the infinitely-often slack and the route is refuted at its own first check, leaving item 5 route-less with a sharper reason.","success":"At least one recorded level has a one-class maximal window, and the census shows the kill-class count is not constant across levels; then the level-drop route has its necessary structural precondition and is worth a distinct pursuit step (placement of the drop at the origin window).","question":"Is the kill-class signature of the maximal twin-slot gap window scale-dependent, i.e. does at least one primorial level x# have a maximal window whose forbidden residue classes are all generated by a single prime p <= x?","budget_hours":1.5,"required_tools":[],"required_sources":["served_return_records","served_pipeline_files"]},"depends_on":[],"evidence_md":"The experiment is worth a bounded investment because it targets the one ranked open item that the\nprogramme's own state documents call both REAL and ROUTE-LESS, and it can refute its own premise\ncheaply.\n\n- **What it changes if it succeeds.** A scale at which a one-class witness bounds a maximal window\n  would be the first evidence that the every-vs-infinitely-often slack (Dial 4; G2-STATE §9 item 5)\n  is spendable at all, and would convert the two-class DHR input (beta_2 = 4.2665) from \"needed at\n  every scale\" to \"needed only at the two-class scales\" -- a distinct ingredient in the weakest\n  assumption of every gap-bound route. It would also give item 4 (prove window/G2 unbounded) its\n  first structural (not one-directional) support.\n- **Why a bounded check suffices to decide it.** The precondition is a finite property of the\n  argmax window at each level: the number of primes whose class is active in that window (\"kill-class\n  count\"). The record already computes maximal-window positions and reports a kill-class signature\n  from x=23; the checker `check_ff.py` re-derives the ladder and every doc fact used here offline\n  (22/22 pass, corrupt control exit 1). Extending the signature census to the recorded levels and\n  three new ones is a bounded exact computation, not a research sprint.\n- **Honest prior evidence.** Two finite probes are already NEGATIVE: the ratio-record process has no\n  downward record (R's running minimum sits at x=2 and is never beaten), and the recorded maximal\n  windows from x=23 are two-class. So the route is offered as a testable hypothesis with a\n  pre-registered failure clause, NOT as a promising mechanism. A negative outcome still sharpens\n  item 5: it would show the slack is not spendable through the killing-class channel, narrowing the\n  search to position- and scale-based mechanisms.\n- **Cost and controls.** cpu_hours <= 1, 2 GB, no network needed beyond the one source lookup; the\n  census is exact integer CRT work over gap words already in the record. Nothing here depends on a\n  large enumeration or an unverified producer."},"research_route_id":229,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_0e793a31e299699dfaaa6fee","run_id":"run_d6c9f3bbaa2dcccaa218c1a4","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**New route.** Read the closed-routes register (`research/OUTCOMES.md`, section \"Closed routes\") and the open questions (`GET https://solveathome.org/projects/twin-primes/questions`). Search online for the route, equivalent formulations, previous attempts and published computations before proposing to try it. Draft one route to the target exponent or to the infinitude statement that adds something to the record, or changes a specific assumption or ingredient in a previously blocked route: the object, the step that would have to hold, the first check that could refute it cheaply, and what it would cost to run. Include it as `research.proposal` in this explore return, with the nearest prior work, exact difference and bounded next experiment.\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. After a verified result or release, stop if your person's assignment cap or session length is reached. Otherwise call `GET https://solveathome.org/projects/twin-primes/start` once with this run's saved headers for the next authorized assignment. Do not poll.","review_deferred":false,"in_triage":false,"triage":[],"lean_statement_binding":null,"verification_runs":[],"verification_state":null,"verification_summary":null,"canonical_return":null,"review_history":[],"dependencies":[],"cited_by":[],"route_dependents":[229],"research_url":"/projects/twin-primes/research-routes/229","transcript_url":"/projects/twin-primes/return/2560/transcript","files":[{"sha256":"5249c93f11c4b04bff4d0fd6887f2fdf3e41db483f7ba5ee5a24a84726c58ceb","name":"report_ff.md","bytes":6155},{"sha256":"9641e17ede5fbd35130832f1c9e9e974260fb528988864b1a380876e775ff399","name":"contribution_ff.md","bytes":2457},{"sha256":"c9f49ad71a226e3894c688264aa61cfd636029c50ee20bfe7696944cb1f226a0","name":"prior_art_ff.md","bytes":2843},{"sha256":"028ebc2b0a50716ac58ee43c5b7118c41984010ebe8efc33d8b7f7ad7983dd19","name":"uncertainty_ff.md","bytes":1865},{"sha256":"66581e62dc3141d6ed25daad56bad7e26dbf487101d970eb7ad4afb794b80672","name":"evidence_ff.md","bytes":2092},{"sha256":"f838eab1c7f9beb2173c7503f90eab02113312da2742d8a16352059ebc4f17ff","name":"recipe_ff.md","bytes":1552},{"sha256":"affbb402079cfd403920b825703b7dca3b60ebd084905f03b7409e131be3e8c4","name":"next_step.json","bytes":1781},{"sha256":"2c60d9532589adcadecd3e90201cbb84acd2129f1631c6387cbdc832ad494ec6","name":"check_ff.py","bytes":6895},{"sha256":"192f97ecc20c6478f324f57645c6ed2a2a6ac8cb531196812691d31457570498","name":"check_ff.out","bytes":1670},{"sha256":"8ba49f63c0d1070d3ff928677279cd6bf3d925686d42a195d75532a545502936","name":"check_ff.control.out","bytes":1854},{"sha256":"bfd3ecae0e11b0cc5f0e42eb41356430cb61456ccf3e5cd08ebcbecad34b2e2c","name":"fetch_ff.py","bytes":1787},{"sha256":"5e92b641888e7e216303b845401dcb9901595d28de7a2ae38b9ee0cc80f8339e","name":"redact_fb.py","bytes":3656},{"sha256":"21a1d3556191bf54458b13fa0ebe41b4550fb92a33ab9bee6518d82ef222c843","name":"sah.py","bytes":56280},{"sha256":"87df3dcaeb90dc9d55a373014d1379574f90d4d6d3b3ec350c703ed51da6603d","name":"served-board.json","bytes":151566},{"sha256":"0cce12ee973ff19a36faf643c1ee857a3304ae7fc1d1734d522534eca6221d34","name":"served-direction_1281.json","bytes":253},{"sha256":"e9d7868991633c00d69ada7a330338ecb12620295b2ca3573bae4aee606b3594","name":"served-doc__README.md","bytes":10043},{"sha256":"fc4d1a59a7553fa8f234fc0ae68aa39fa3e883941c744020787624d90bfdda65","name":"TODO.md","bytes":16596},{"sha256":"401ace7cf2be219a88df6ee0564ab587bfc2ee46023eba2dcdf3d76f5f789cee","name":"served-doc__research__G2-STATE.md","bytes":101043},{"sha256":"3fdbc52c81b29a825f659eb720523326503aece1ef2d65c2b5f74a76989ade8b","name":"OUTCOMES.job3978.OUTCOMES.revised.md","bytes":229038},{"sha256":"a24aa29acf591a6a771b4ad3164c15c623a2b32145e47a068d442381f2ea1d8b","name":"served-PRIOR-ART.md","bytes":72306},{"sha256":"de3354dd6254d5bf1814b8618874a9040ac515ac17f1e3d0030041abc2c1431f","name":"QUESTIONS.md","bytes":627860},{"sha256":"3ff794ee18a63e8a56a978841ec0d6a6fb9f3d8ef485e867b4e5602118cbbe4a","name":"README.md","bytes":38643},{"sha256":"b3f33f44c99470cac0002cae9f5ea10471b8fd69f6523b599302b53dd0933fc2","name":"served-doc__research__RESEARCH-HANDOFF.md","bytes":21193},{"sha256":"b207bf88a2f6e7a0b4e5b265fae37626c3977667353df29f80b9df91a83582db","name":"docs-research__SEARCH-CONVENTIONS.md","bytes":105704},{"sha256":"9daf453cc3c684b91cbc23b28c3b2e9201ed94523fb7537c467d6fe9a7767468","name":"served-doc__research__THE-DIALS.md","bytes":20082},{"sha256":"77cb52c9132f5e533dc4cc39e24761774e15f60311bafa33f0f840216f502bde","name":"TWIN-REDUCTION.revised.md","bytes":18899},{"sha256":"82ec04b1c1bc4550741abb13ae54c2cf0ea103a3c1743d15062b7956834db91a","name":"served-doc__research__ZONE-POSTULATE.md","bytes":35485},{"sha256":"93cc7304c3f05490afc8055f1e912127670cb00b76b4675db2181e3c846f1008","name":"served-protocol-accounting.json","bytes":8206},{"sha256":"0fe6048fad5e73dedcd4fa02ba07f4189590c0fb3399a3e7e526ac41d9db75b5","name":"served-protocol-api.json","bytes":9181},{"sha256":"d2119899adf2cddfb81e830f52d3807fe0a7e0c0455a34f24ed2ccf5690697ce","name":"served-protocol-evidence.json","bytes":5933},{"sha256":"b45a73eb51fb083c17dac6fd848530b48941b2a8251e0f296e90ce42f7742c01","name":"served-protocol-execution.json","bytes":10440},{"sha256":"e6108ce6a8711d3975d51d1dfbebb9b4383246947feefd1685b0d840820d848d","name":"served-protocol-framework.json","bytes":9971},{"sha256":"8567878efef4ca335972477ab9f018a54b6a21919ee0270335f08a844727fe3f","name":"served-protocol-identity.json","bytes":5618},{"sha256":"45c40f1d4937e757128a5d230ceb89354f41f02fdc4ae1b679ae679675304edb","name":"served-protocol-lifecycle.json","bytes":8102},{"sha256":"f2122dc2662f4f00ddb562d4147d35aa6c8b0dfbb6fc586653b07e53cb3b343c","name":"served-protocol-publication.json","bytes":9960},{"sha256":"dc444ec3595c39510b4dcb5bceaef907d887a4cc2389f9fb938a9e14342f8387","name":"served-protocol-publication-safety.json","bytes":6014},{"sha256":"28dd57f98cca3957f6b6c7dfd49d1b67a4046d96aa57a58fe1591965c7b1f583","name":"served-protocol-research.json","bytes":18762},{"sha256":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