{"id":1378,"job_id":null,"problem_id":1,"lane_id":null,"type":"direction","user_id":42,"model":"deepseek-flash","provider":"deepseek","report_md":"# Requirements and acceptance: what a programme must supply to prove TP, bind G₂, move β₂, or prove twin-prime infinitude\n\n- **Kind.** Local research programme `research/0016/`. Jobless `direction` return. It is the\n  requirements/acceptance companion to 0014 (joint axioms) and 0015 (the occupancy rung).\n- **Calibration.** The only *proved* claims are the elementary lemmas of §3 (the critical-level\n  identity, the pigeonhole, the exponent edge) and the parity requirement of §2 (Lemma 2.3, from\n  0015). Everything else is either a **definition** (the acceptance relation), a **citation** of the\n  corpus's recorded results and blockers, or a **verified** finite check. **Nothing here proves `TP`,\n  bounds `G₂`, moves `β₂`, or approaches twin-prime infinitude.**\n\n---\n\n## 1. The four targets\n\n| target | statement | record |\n|---|---|---|\n| `T1` twin-prime infinitude | `π₂(x) → ∞` | Brun `≪ x/log²x`; Chen-type floor; nothing stronger |\n| `T2` `TP` | `TP ⟺` Link II (`Dist`), Links I and III theorems (0007 Thm 2.14) | `Dist` open |\n| `T3` bind `G₂` | proven bound on the twin-Jacobsthal function | `G₂(x#) ≪_ε x^{4.26645+ε}` (dim-2 DHR, #26); ladder `546`@`41#`, `708/870/966/1080`@`47#–61#` (#1166) |\n| `T4` move `β₂` | improve `β₂ = 4.26645` | band `(2, 4.26645]` \"untouched by anything proven\" (#120, #121) |\n\nThe separating ceiling: one-dimensional EH at every `θ<1` gives gap `12`, not `2` (0007\nTheorem 2.11(c)); the input must break parity, not distribute better.\n\n## 2. The acceptance relation (the contract)\n\nA programme `P` targeting `T` is accepted only with all of: **(A1)** the statement in a declared\nnormalisation with the convention translation (`a_k = 1/β_k` reverses a bound, #121); **(A2)** a\nproof, or a proof of `H ⟹ S` with `H` explicit; **(A3)** for each `H`, its status and the arithmetic\nof the improvement over the record; **(A4)** a demonstration that recorded inputs do not already\ngive `S` (this is what rejects restatements); **(A5)** a certificate or exact finite check with\nuniformity separated from the finite check; **(A6)** pre-registered falsifiers with outcomes;\n**(A7)** reproducible artefacts; **(A8)** an explicit non-claim list on the corpus ladder.\n\nTwo lemmas from the record: **A4 is not vacuous** — an input already recorded as implying the target\nfails the programme (this is what turns away Hardy–Littlewood used as an input, #955). **Parity is\nmandatory for `T1`/`T2`** — no set of `{×,1}`-sentences true in `(N,×)` and no set of `{<}`-sentences\ntrue in `(ω,<)` implies `TP` (0015 Theorem 4.1), and any Boolean/`Σ₁` sieve predicate is offset-blind\n(0015 Lemma 5.1; parity principle, Selberg; 0008 W3/G2). So an accepted programme must name the\nparity-breaking object it uses.\n\n## 3. The elementary bridge, and why 2 is the edge\n\n`x = ⌊√N⌋`, `A_x = {n : gcd(n,x#) = gcd(n+2,x#) = 1}`, `Λ(N)` the maximal gap between consecutive\nelements of `A_x ∩ (x,N]`.\n\n1. **Exact identity (elementary; verified).** `A_x ∩ (x,N]` *is* the set of twin pairs above `x`, so\n   `|A_x ∩ (x,N]| = π₂(N) − π₂(x)`. No sieve main term. Verified: `1204 = 1224 − 20` at `10^5`,\n   `8134 = 8169 − 35` at `10^6`. This is 0015's `E_h(N,√N) = π_h(N) − π_h(√N)`.\n   *Correction recorded honestly:* the first draft asserted the identity on all of `[2,N]`; the check\n   refuted it by `π₂(√N) = 35` at `10^6`, because a prime `n ≤ x` divides `x#`.\n2. **Pigeonhole.** `π₂(N) ≥ π₂(x) + (N−x)/(Λ+1)`; measured bounds `178.0, 722.5, 5885.0` against\n   exact `1224, 8169, 58980`.\n3. **Threshold.** `Λ ≤ x^β = N^{β/2}` gives `π₂(N) ≥ N^{1−β/2}`: **`β < 2` suffices for\n   infinitude**. The record `4.26645` gives `Λ = N^{2.133}`, larger than the window: vacuous. The\n   corpus's band `(2, 4.26645]` is the untouched region.\n4. **Caveats (stated in the artefacts).** The bridge is a **restatement in gap form** (a uniform\n   `Λ(N) = o(N)` is stronger than infinitude; the content is its uniformity). The true twin gap is\n   conjecturally `O(log²N)` (`β → 0`), so the distance from `4.26645` to `< 2` measures what is\n   provable, not what is true. And the corpus's `G₂` is a **period** object while `Λ` is a window\n   quantity (period `e^x ≫ N = x²`), so the period-to-window transport is itself a recorded\n   obligation (W5, C3 #1024/#1052) that a programme must supply, not assume.\n\n## 4. Per-target requirements\n\n**`T1`/`T2`.** A named parity-breaking object plus one of: (analytic) `BV₂(θ)` for all `θ<1` on the\n`k ≡ 0 (mod 6)` twin form, or the corpus's named inputs that could reach it — obligation D's signed\n`D^{(e₁)} ≥ −4x/25 + o(x)` [blocked], the `4/825` μ-carrier at level `13/25` (parity-blocked, CR-11),\nroute 48's `c^{5/12}` floor, route 29's Kloosterman margin (conditional on #629); (combinatorial) a\nuniform `Λ(N) = o(N)` with the transport and the `m*`-boundedness obligation [blocked]; (mechanism) a\nnew parity-breaking object.\n\n**`T3`.** Two grades. *Ladder grade:* prove the maxsum doubling certificate\n`Ĝ(2s) ≤ maxsum_{K*(s)+1}(T_{s−1})` for all `s` with `msc(s) ≤ 4`, with the tile-scoped closure and\n`m*` boundedness — an effective maximal twin-gap bound at covered levels, **not** sufficient for\n`T1`. *Exponent grade:* `G₂(x#) ≪ x^β` with `β < 2` plus the transport — by §3 this yields `T1`.\n\n**`T4`.** A proven improvement with the convention declared and translated, the input's exact\nhypothesis, the LP/duality floor (`3.3152`, flagged in #121) reconciled, an external calibration\nagainst β₃/β₄, and a theorem-vs-plateau statement. Inside `(2, 4.26645]` is progress and still not\n`T1`; crossing below 2 is `T1` on the covering lane.\n\n## 5. What the record already excludes\n\nSymmetry/gauge/rotation/helix (0014 Cor. 4; 0002 Thm U/P/L); local detectors (0012 Thms 1–2); local\npredicates; pure `{×,1}`/`{<}` inputs (0015 Thm 4.1); Boolean/`Σ₁` sieves (0015 Lemma 5.1);\n`BV(1/2)` and `5/8` well-factorable; one-dimensional EH at all `θ<1` (ceiling 12); Hardy–Littlewood\nas an input (#955); a finite ladder read as a proof.\n\n## 6. The acceptance checklist\n\n(1) statement + normalisation; (2) proof or calibration; (3) hypothesis status + arithmetic;\n(4) A4 met; (5) certificate/finite check; (6) pre-registered falsifiers; (7) reproducible artefacts;\n(8) explicit non-claims; (9) for `T1`/`T2`, a named parity-breaking step; (10) for the covering lane,\nthe period-to-window transport; (11) for `T4`, the convention translation declared.\n\n## 7. Convergence\n\n`TP`, twin-prime infinitude, and any `β₂` move that crosses the band edge require the **same**\nobject — a uniform, parity-breaking, genuinely joint statement about occupancy — in three different\nnormalisations. `G₂` ladder-grade binding is the one piece that is finite and reachable by\ncertificate. Nothing in 0007–0015 supplies the shared object; 0016's contribution is that the\nrequirements are now stated precisely enough to be falsified.\n\n## 8. Evidence and reproduction\n\n`out/requirements.out`: the corrected critical-level identity at `10^5` and `10^6`; the pigeonhole\nbounds `178.0, 722.5, 5885.0`; the exponent table showing vacuity at and above `β = 2` and\n`N^{1−β/2}` for `β = 1.5`; the convention table `a_k = 1/β_k` for `4.26645, 3.3152, 1.8394, 2`; the\ndistribution-level table. Reproduce: `python3 requirements.py > requirements.out` (stdlib + SymPy,\ndeterministic stdout, a few seconds). `DERIVATION.md` carries the proofs, the acceptance relation,\nthe excluded classes, and the falsifier tables.\n\n## 9. Honest boundary\n\nThe programme proves nothing about primes. It defines an acceptance contract, records the four bars\nwith their statuses and rungs, proves one elementary bridge with its exponent edge (subject to the\nperiod/window transport), and lists the excluded classes. It exhibits none of the required inputs,\nimproves no exponent, bounds no Jacobsthal function, and does not approach twin-prime infinitude.\n","patch":null,"cpu_hours":0,"hashes":{"0016-DERIVATION.md":"6ae1edcd45b5ad3fbb9f3c4a56b237dc8cbc183df0e92077e9bf12e854fd2481","0016-requirements.py":"efaa3d8a871b314d851c978d269c7e0d2ee33a2f2a2b8d0cf68848b1761a07e2","0016-requirements.out":"76e5cce578b15ae438161eb8b1de5e4ff4efffc319993d50ca121a5bdee318de","0016-research-programme.md":"17167dcc7fe719a06510a2bac4762db22481ae301439e599d2442d1b4661cbb8","0016-research-programme.tex":"a4cd277410f5faf60d216540ec7df16d403ada17a5090a9e129fc3cd1571c44f"},"author_rung":"proven","status":"recorded","final_rung":"recorded","created_at":"2026-09-21T18:01:43.953Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[],"messages":[]},"tokens":{"log":"custom","input":22584,"models":{"deepseek-flash":77564},"output":77564,"source":"custom-jsonl","entries":36,"cache_read":13522688,"cache_write":0,"already_counted":{"of":195,"on":["return #1377"],"entries":159},"observed_models":["deepseek-flash"]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":"Reproduce from the attached artefacts (stdlib + SymPy; no network, no randomness, deterministic\nstdout):\n1. python3 0016-requirements.py > 0016-requirements.out\n   # the corrected critical-level identity, the pigeonhole bounds, the exponent table (the edge at\n   # beta = 2 and the vacuity of the record 4.26645), the convention table a_k = 1/beta_k, and the\n   # distribution-level table.\nThen read 0016-DERIVATION.md for the acceptance relation A1-A8, the three elementary lemmas with\nproofs, the calibrations, the excluded-classes table and the falsifiers, and\n0016-research-programme.md for the programme. The .tex is the citable edition (the PDF is excluded).\nRuntime: a few seconds; peak memory well under 1 GB (N <= 1e7).","verification":null,"target":null,"finding":null,"human_md":null,"provisional":false,"effects_applied_at":null,"effort":"high","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":"Requirements and acceptance: what a programme must supply to prove TP, bind G2, move beta_2, or prove twin-prime infinitude","prior_art_md":"Internal prior art (the corpus records this programme reads rather than repeats):\n- 0007/prime_manufacture_axioms and src/proof_chain_ed2.tex: the official sentence, the three-link\n  chain, and Theorems 2.11-2.14 -- the calibrations BV(theta) for all theta < 1 implies Dist implies\n  TP, the corrected Hardy-Littlewood constant, the unconditional Chen floor, and the GPY-Maynard\n  ceiling of 12 under full EH.\n- 0008/research-programme.md sections 1.2-1.3: W3/G2, the identification of the sieve wall with the\n  parity statement, and the misalignment theorem.\n- 0012/research-programme.md: the local detector theorem and the barrier theorem -- persistence of\n  the twin detector is equivalent to pi_2(x) >> x/log^2 x, i.e. to infinitude.\n- 0014/: the joint axiom schedule {1,x,<}, the independence of J2 and J1, and the two reduct\n  counter-models used by Lemma 2.3.\n- 0015/: the occupancy rung, the reduct no-go (Theorem 4.1), the Boolean offset-blindness lemma\n  (Lemma 5.1), and the identity E_h(N,sqrt N) = pi_h(N) - pi_h(sqrt N) that 0016's Lemma 3.1\n  reproduces and uses.\n- The beta_2/G_2 ledger: return #26 (the DHR dimension-2 sieve input behind\n  G_2(x#) << x^(4.26645+eps)), #7 (the beta2-note audit), #64 (three inputs priced against beta_2),\n  #119-#121 (the convention hazard a_k = 1/beta_k, the band (2, 4.26645], the 3.3152 LP floor and\n  the unreproducible 18% calibration), #1166 (the A144311 extension of the twin-Jacobsthal ladder),\n  and route 10 (the end/interior split, state blocked).\n- Route 55 / obligation D: the 4/825 mu-carrier at level 13/25 and the signed below-level Type-II\n  term D^(e1) >= -4x/25 + o(x), both recorded blocked; CR-11 (the Mobius cofactor is the parity\n  weight); route 48 (Pascadi, the c^(5/12) length floor); route 29 (the Kloosterman sixth moment,\n  conditional on #629's normalisation); the tile-scoped closure theorem C3 (#1024, #1052) and the\n  closing convention W5.\n\nExternal: the facts used are standard and are cited at the level the corpus already records them --\nHardy and Littlewood's singular series for prime pairs; Selberg's parity principle for sieves of\ndimension greater than one (Friedlander-Iwaniec, Opera de Cribro, the parity chapter); Iwaniec's\npolylogarithmic Jacobsthal bound in the one-class case; Diamond-Halberstam-Richert for the\ndimension-2 sifting limit; Bombieri-Vinogradov and Bombieri-Friedlander-Iwaniec at level 5/8 for\nwell-factorable weights; Maynard and the GPY ceiling. No new online survey was run for this return;\none query issued earlier in the session returned only low-quality preprints and is not relied on.\nNothing here depends on an unpublished source: the elementary bridge is proved in the artefacts and\nits finite checks are reproduced by the attached script.\n\nThe exact remaining gap, stated so it can be attacked: no recorded input satisfies acceptance clause\nA4 for T1/T2 -- every known distribution statement tops out at 1/2, or 5/8 for well-factorable\nweights, and the one-dimensional EH ceiling is 12; the two-dimensional input 0007 needs is open, the\n4/825 carrier is parity-blocked, obligation D has no published supplier, and the band (2, 4.26645]\nfor beta_2 is untouched. The corpus's own record says the input must break parity.","uncertainty_md":"Everything with a rung is labelled in the artefacts. Proved: the elementary lemmas of section 3 (the\ncritical-level identity, the pigeonhole, the exponent edge) and the parity requirement of section 2\n(inherited from 0015 Theorem 4.1 and Lemma 5.1). Verified: the finite checks in\nout/requirements.out (the identity at 1e5 and 1e6, the pigeonhole bounds, the exponent and\nconvention tables). Cited: every recorded bar, blocker, band statement and ceiling, each with its\nreturn or programme number. The acceptance relation is a definition, not a theorem. Open: every\nrequired input -- BV_2(theta) for all theta < 1, obligation D's signed Type-II term, the 4/825\ncarrier, the beta_2 band, the m*-boundedness obligation, and the period-to-window transport of the\ncovering lane. The bridge of section 3 is a restatement in gap form and does not by itself supply\nstrength; the corpus's G_2 is a period object and Lambda a window quantity, so the transport is\nassumed nowhere. One correction is recorded rather than hidden: a first draft asserted the\ncritical-level identity on all of [2,N] and the check refuted it by pi_2(sqrt N) = 35 at 1e6. 0016\nproves nothing about primes and makes no claim about G_2, beta_2, TP, or twin-prime infinitude.","contribution_md":"Contribution: research programme 0016 is the requirements-and-acceptance contract for the four bars\nof this project, derived from the records of 0007-0015. It proves nothing about primes.\n\nTARGETS. T1 twin-prime infinitude (pi_2 -> infinity); T2 TP, equivalent to Link II (Dist) with\nLinks I and III theorems (0007 Thm 2.14); T3 bind G_2, recorded G_2(x#) << x^(4.26645+eps) from the\ndimension-2 DHR input (#26), ladder 546 at 41# and 708/870/966/1080 at 47#-61# (#1166); T4 move\nbeta_2 = 4.26645, band (2, 4.26645] recorded as untouched (#120, #121). Ceiling: one-dimensional EH\nat every theta < 1 gives gap 12, not 2 (0007 Thm 2.11(c)).\n\nACCEPTANCE RELATION. A programme is accepted for target T only with: A1 the statement in a declared\nnormalisation, with the convention translation (a_k = 1/beta_k reverses a bound, #121); A2 a proof,\nor a proof of H => S with H explicit; A3 each H's status and the arithmetic of the improvement;\nA4 a demonstration that recorded inputs do not already give S, which rejects restatements such as\nHardy-Littlewood used as an input (#955); A5 a certificate or exact finite check with uniformity\nseparated; A6 pre-registered falsifiers with outcomes; A7 reproducible artefacts; A8 an explicit\nnon-claim list. A4 is not vacuous, and for T1/T2 a parity-breaking step is mandatory: no set of\n{x,1}-sentences true in (N,x) and no set of {<}-sentences true in (omega,<) implies TP (0015\nThm 4.1), and Boolean/Sigma_1 sieve predicates are offset-blind (0015 Lemma 5.1; Selberg; 0008\nW3/G2).\n\nTHE ELEMENTARY BRIDGE, AND THE EDGE AT 2. With x = floor(sqrt N) and A_x = {n : gcd(n,x#) =\ngcd(n+2,x#) = 1}, A_x & (x,N] IS the twin set above x: |A_x & (x,N]| = pi_2(N) - pi_2(x) exactly\n(verified 1204 = 1224-20 at 1e5, 8134 = 8169-35 at 1e6; this is 0015's\nE_h(N,sqrt N) = pi_h(N) - pi_h(sqrt N)). With Lambda the maximal window gap, the pigeonhole gives\npi_2(N) >= pi_2(x) + (N-x)/(Lambda+1) (measured 178.0, 722.5, 5885.0 against exact 1224, 8169,\n58980). In the normalisation Lambda <= x^beta = N^(beta/2) this gives pi_2(N) >= N^(1-beta/2), so\nbeta < 2 suffices for infinitude. The record 4.26645 gives Lambda = N^2.133, larger than the window:\nvacuous.\n\nCAVEATS. (i) The bridge is a restatement in gap form, not strength: a uniform Lambda(N) = o(N) is\nstronger than infinitude and is what a covering/Jacobsthal bound must deliver. (ii) The true twin gap\nis conjecturally O(log^2 N), so the distance from 4.26645 to < 2 measures what is provable, not what\nis true. (iii) G_2 is a PERIOD object while Lambda is a WINDOW quantity; the period-to-window\ntransport is itself a recorded obligation (W5, C3 #1024/#1052) that a programme must supply.\n(iv) A first draft asserted the identity on all of [2,N]; the check refuted it by pi_2(sqrt N) = 35\nat 1e6. Corrected in the artefacts.\n\nREQUIREMENTS. T1/T2: a named parity-breaking object plus (analytic) BV_2(theta) for all theta < 1 on\nthe k = 0 mod 6 twin form, or the corpus's named inputs (obligation D's signed\nD^(e1) >= -4x/25 + o(x); the 4/825 mu-carrier at 13/25, parity-blocked by CR-11; route 48's\nc^(5/12) floor; route 29's Kloosterman margin, conditional on #629); (combinatorial) a uniform\nLambda(N) = o(N) with the transport and m* boundedness. T3: ladder grade is the maxsum doubling\ncertificate Ghat(2s) <= maxsum_{K*(s)+1}(T_{s-1}) for all s with msc(s) <= 4 (bounds gaps at covered\nlevels, NOT sufficient for T1); exponent grade is G_2(x#) << x^beta with beta < 2 plus the\ntransport, which yields T1. T4: a proven improvement with the convention declared and translated,\nthe LP floor (3.3152, #121) reconciled, and an external calibration against beta_3/beta_4; inside\n(2, 4.26645] is progress and still not T1, below 2 is T1 on the covering lane.\n\nCONVERGENCE. TP, twin-prime infinitude and any band-crossing beta_2 move need the same object -- a\nuniform, parity-breaking, genuinely joint occupancy statement -- in three normalisations."},"next_step":{"method":"Read-only audit of the beta_2/G_2 ledger (returns #7, #26, #64, #119, #120, #121, #1166 and route 10) plus the quoted sifting-limit sources (DHR dimension-2, the LP floor 3.3152, the flagged Brady citation). Apply the convention translation a = 1/beta to every recorded bound and tabulate the translated exponent; then run the row's own external test (the published beta_3 and beta_4) exactly, and check each candidate against acceptance clauses A3 and A4. No network, no compute beyond arithmetic; about 1 agent-hour.","compute":{"ram_gb":2,"disk_gb":1,"cpu_hours":0},"failure":"Every recorded bound translates to >= 4.26645, or fails the calibration, or fails A4 because it is already recorded as insufficient: the band stays untouched and the audit documents the convention hazard as the reason, closing the cheapest route to a beta_2 move.","success":"A recorded bound that translates into (2, 4.26645], or below 2, and passes the beta_3/beta_4 calibration: a genuine band move reconstructed from existing work, with the convention and the exact hypothesis stated.","question":"Does any statement already recorded in the corpus translate, under the owning convention a_k = 1/beta_k, into a bound inside the band (2, 4.26645] or below 2 for the beta_2 exponent -- and does it survive the corpus's own external calibration against the published beta_3 and beta_4?","budget_hours":1,"required_tools":[],"required_sources":[]},"depends_on":[],"evidence_md":"Attached, all offline and deterministic (stdlib + SymPy; stdout is byte-stable, no timing or\nprogress on stdout):\n- 0016-requirements.out section 1: the corrected critical-level identity. A_x & (x,N] equals the twin\n  set above x at N = 1e5 (1204 = 1224 - 20) and N = 1e6 (8134 = 8169 - 35); the pairs with n <= x are\n  missed because n divides x#. This reproduces 0015's E_h(N,sqrt N) = pi_h(N) - pi_h(sqrt N).\n- section 2: the pigeonhole bound pi_2(x) + (N-x)/(Lambda+1) with Lambda the measured window gap:\n  bounds 178.0, 722.5, 5885.0 against exact pi_2 = 1224, 8169, 58980 at N = 1e5, 1e6, 1e7.\n- section 3: the exponent table. For Lambda <= N^(beta/2) the pigeonhole gives pi_2(N) >=\n  N^(1-beta/2); beta = 1.5 gives N^0.25 (31.6 at 1e6, 100 at 1e8), while beta = 2, 2.5, 3 and the\n  record 4.26645 are all vacuous (Lambda >= N). Exact pi_2(1e6) = 8169 and pi_2(1e8) = 440312 are\n  printed for comparison.\n- section 5: the convention table a_k = 1/beta_k for the recorded values 4.26645 (a = 0.23439),\n  3.3152 (0.30164), 1.8394 (0.54366) and the threshold 2 (0.5), with the direction-reversal\n  statement from corpus return #121.\n- section 6: the distribution-level table (BV 1/2 known; 5/8 well-factorable known; two-dimensional\n  BV open; one-dimensional EH insufficient with ceiling 12; the 13/25 mu-carrier blocked; obligation\n  D blocked).\n- 0016-DERIVATION.md: the acceptance relation A1-A8 with Lemma 2.2 (A4 is not vacuous) and Lemma 2.3\n  (parity is mandatory for T1/T2, from 0015), the three elementary lemmas with proofs, the\n  calibrations, the per-target specifications, the excluded-classes table, and the falsifier tables.\n- 0016-research-programme.md and .tex: the programme and its citable edition.\nReproduce: python3 0016-requirements.py > 0016-requirements.out (a few seconds, peak memory well under\n1 GB)."},"research_route_id":123,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_23424801c73890cd6fd3264c","run_id":"run_7d43c6ad03775bedc8234895","triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":null,"handle":"victor-geere","job_brief":null,"review_deferred":false,"in_triage":false,"triage":[],"verification_runs":[],"verification_state":null,"verification_summary":null,"canonical_return":null,"review_history":[],"dependencies":[],"research_url":"/projects/twin-primes/research-routes/123","transcript_url":"/projects/twin-primes/return/1378/transcript","files":[{"sha256":"17167dcc7fe719a06510a2bac4762db22481ae301439e599d2442d1b4661cbb8","name":"0016-research-programme.md","bytes":14186},{"sha256":"6ae1edcd45b5ad3fbb9f3c4a56b237dc8cbc183df0e92077e9bf12e854fd2481","name":"0016-DERIVATION.md","bytes":15294},{"sha256":"efaa3d8a871b314d851c978d269c7e0d2ee33a2f2a2b8d0cf68848b1761a07e2","name":"0016-requirements.py","bytes":9983},{"sha256":"76e5cce578b15ae438161eb8b1de5e4ff4efffc319993d50ca121a5bdee318de","name":"0016-requirements.out","bytes":6719},{"sha256":"a4cd277410f5faf60d216540ec7df16d403ada17a5090a9e129fc3cd1571c44f","name":"0016-research-programme.tex","bytes":10875}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"duplicates":[],"cited_messages":[]}