{"id":1377,"job_id":null,"problem_id":1,"lane_id":null,"type":"direction","user_id":42,"model":"deepseek-flash","provider":"deepseek","report_md":"# The joint prime axioms and the occupancy rung (research programme 0015)\n\n- **Kind.** Local research programme `research/0015/` (private local tree), built on the joint axiom\n  schedule of `research/0014/` (not previously filed). Jobless `direction` return; the local\n  programme is the deliverable.\n- **Calibration.** Per statement: `proved` / `verified` (finite computation) / `measured` / `cited` /\n  `open`. The strongest claims of the return are proved; everything measured, cited or open is\n  labelled where it stands.\n- **Nothing here bounds `G2`, moves `beta_2`, or proves twin-prime infinitude.** The twin prime\n  conjecture remains open, and 0015 says explicitly which rung the conjecture now occupies.\n\n---\n\n## 1. What 0014 established, in the form 0015 uses (self-contained summary)\n\n0014 rewrote the prime axioms in the joint signature `L_J = {1, x, <}` with `Succ`, `|`, `Irr`\nabbreviated, in three blocks:\n\n- **O (order):** `O1` total order, `O2` 1 least, `O3` unique successor/predecessor, `O4` induction\n  scheme over `L_J`-formulas. Not categorical (`omega + Z` satisfies `O1`-`O3`); every `omega`-order\n  satisfies `O1`-`O4`.\n- **M (multiplication):** `M1` commutative monoid with identity 1, `M2` nontrivial, `M3`\n  cancellation, `M4` unique generation by irreducibles.\n- **J (joint):** `J1` `x<y and 1<z => xz<yz`; `J2` `1<d => not(d|n and d|Succ n)`; `J3` the\n  Robinson-Tarski `exists!`-clause `Succ(zx)Succ(zy) = Succ(z^2 Succ(xy))` defining `+`; `J4`\n  residual manufacture exists; `J5` non-absorption.\n\n0014's results used here: `J2` is independent of `O1`-`O4`+`M1`-`M4`+`J1`, witnessed by the\n*one-generator model* `x*'y = x+y-1` (the additive monoid in disguise: satisfies `O1`-`O4`, `M1`-`M3`,\n`J1`, unique generation; violates `J2`; its only irreducible is 2, `M({2})` is undefined, and it has\nno twin pair). `J1` is independent of `O1`-`O4`+`M1`-`M4`+`J2`, witnessed by the transport of\nstandard multiplication along the transposition `(2 4)`. The next-prime graph is `{x,<}`-definable and\ndefinable in neither reduct. 0014 recorded as an erratum (E.9 in `0007/errata.md`) that 0007's\nInexhaustibility proof uses `J2` without listing it.\n\n## 2. What 0015 adds\n\n**(X1) Distributivity is the joint axiom behind every offset.** 0015 adds\n\n```\nJ6:  (a + b)*c = a*c + b*c        (+ from J3)\n```\n\n`J6` is joint (it mixes `*` with the order-derived `+`) and independent of 0014's algebraic blocks:\nthe one-generator model satisfies `O1`-`O4`+`M1`-`M4`+`J1` and fails `J6` at `(1,1,2)`\n(`(1+1)*'2 = 3` but `1*'2 + 1*'2 = 4`). `J6` + `J3` + `J1` + `M` derive **`SEP(h)`** for every\n`h >= 1`, and in particular derive `J2` (`h = 1`). So the axiom 0014 needed for Euclid is the `h = 1`\nshadow of distributivity.\n\n**(X2) The offset separation theorem.**\n\n```\nSEP(h):   d|n and d|(n+h)  =>  d|h ,        equivalently  gcd(n, n+h) = gcd(n, h).\n```\n\nThe failure set over all `n` is exactly `{d > 1 : d | h}`:\n\n| `h` | failure set | reading |\n|---|---|---|\n| 1 | `{}` | `= J2`; **Euclid** |\n| 2 | `{2}` | 0007's **Coprime split**: `gcd(n,n+2) = 1` for odd `n` |\n| 6 | `{2,3,6}` | the 3-obstruction appears exactly when `3 | h` |\n| 10 | `{2,5,10}` | the 5-obstruction appears exactly when `5 | h` |\n\nConsequently a prime pair at distance `h >= 2` forces `h` even and `gcd(n,h) = 1` (plus the single\n`n = 2` exception for odd `h`), and the local factor of the singular series\n\n```\nS(h) = 2 C_2 * prod_{p | h, p > 2} (p-1)/(p-2),     C_2 = prod_{p>2} (1 - 1/(p-1)^2)\n```\n\nis read off from the axioms. The local content of the offset problem is a theorem; the normalisation\nto `S(h)` is the standard Hardy-Littlewood convention and is **cited**, not derived.\n\n**(X3) Section 8.3 item 1 is a theorem.** *No set of `{x,1}`-sentences true in `(N,x)` implies `TP`;\nno set of `{<}`-sentences true in `(omega,<)` implies `TP`.* Proof from 0014's two counter-models:\n`(N,x,<*)` (primes at order-positions `= 2 mod 3`, so `Succ*^2` sends every prime to a composite) has\nthe same `{x,1}`-reduct as `(N,x,<)`; `(N,x',<)` (one-generator) has the same `<`-reduct; both falsify\n`TP`. So any method that certifies `TP`, equivalently Link II / `Dist`, must use a genuinely joint\nstatement. **Scope:** this constrains *reduct* inputs; Bombieri-Vinogradov / Elliott-Halberstam type\nhypotheses quantify over moduli and intervals and are joint, so they escape the no-go. Their failure\nis the `Sigma_1`-layer obstruction below.\n\n**(X4) Section 8.3 items 2-3 are one quantifier rung.** In the joint language `TP` is `Pi_2`:\n`forall x exists n (x<n and Irr(n) and Irr(Succ^2 n))`. The `Delta_0`/`Sigma_1` joint layer carries\nseparation, admissibility, local factors and interval distribution, and it is **offset-blind**: any\nBoolean combination of `Rough_E` (`E <= D`) is constant on the `D`-rough integers, where `D`-rough\nprimes and `D`-rough composites both live, so it cannot equal `Irr` (proved); the parity principle\n(Selberg; 0007 Theorem 3; 0008 W3/G2) extends this to `Sigma_1` sieves of dimension > 1 (**cited**).\nThe passage \"no small prime factor -> the surviving cofactor is a unit rather than a product of two\nlarge primes\" is therefore exactly the `Delta_0`/`Sigma_1 -> Pi_2` jump, uniform in `h`. 0015 names it\nthe **occupancy rung**.\n\n**(X5) The barrier is not informational; it is definitional.** At sieve level `D = sqrt N` every\n`D`-rough integer in `(D, N]` is prime, so the admissible pair set **is** the twin set:\n`E_h(N, sqrt N) = pi_h(N) - pi_h(sqrt N)` exactly. Verified to the digit at `N = 10^6`:\n`8134 = 8169 - 35`, `8103 = 8144 - 41`, `16312 = 16386 - 74` (`h = 2, 4, 6`). At sub-critical `theta`\nthe excess `E_h(N, N^theta) - pi_h(N)` is the rough-composite shadow a `Sigma_1` method mistakes for\noccupancy: `11127` and `4632` for `h = 2` at `theta = 1/3` and `2/5`. The obstruction is that\n`Rough_{sqrt N}` has a modulus growing with `N` and no **uniform** `Sigma_1` joint predicate defines\n`Irr`.\n\n## 3. Mapping onto dossier section 8.3\n\n| section 8.3 | before 0015 | after 0015 |\n|---|---|---|\n| 1: interface statement; any method must use both | asserted from expressibility | **theorem** (reduct no-go) + the joint axiom named (`J6`) |\n| 2: obstruction is the passage roughness -> occupancy | located in the large part | **located as one rung** (`Delta_0`/`Sigma_1 -> Pi_2`); local side completed by `SEP(h)`; occupancy side open |\n| 3: the parity barrier is not a failure of distribution | asserted from known distribution strengths | **theorem-shaped**: distribution is `Sigma_1`-joint and offset-blind; at `theta = 1/2` the admissible set already equals the target set |\n| 4: detector strength | theorem (0012) | unchanged; the offset family `h = 2,4,6,...` is the calibration family |\n\n## 4. The bridge object (measurements)\n\n`C_2` from its Euler product at truncation `P = 2*10^6`: `0.660161837` against `0.660161816`, relative\nerror `3.2e-8`. Measured `pi_h(N)` against `S(h) N / log^2 N`:\n\n| `h` | `S(h)` | `pi_h(10^6)` | ratio | `pi_h(10^7)` | ratio |\n|---|---|---|---|---|---|\n| 2 | `1.320324` | `8169` | `1.1809` | `58980` | `1.1605` |\n| 4 | `1.320324` | `8144` | `1.1773` | `58622` | `1.1535` |\n| 6 | `2.640647` | `16386` | `1.1844` | `117207` | `1.1531` |\n| 8 | `1.320324` | `8242` | `1.1915` | `58595` | `1.1529` |\n| 10 | `1.760432` | `10934` | `1.1855` | `78211` | `1.1542` |\n| 30 | `3.520863` | `21990` | `1.1921` | `156517` | `1.1549` |\n\nThe ratios are flat across `h` (the `h`-dependence is entirely in the axiom-derived `S(h)`) and drift\nfrom `1.18` to `1.155` toward 1. The local factor is a theorem; the limit is the barrier, and for\n`h = 2` it is `TP`.\n\n## 5. Evidence\n\n- `0015-bridge.out` — `SEP(h)` for `h <= 40`, `n < 20000`, zero mismatches; the failure-set table\n  (`h = 1` empty, `h = 2` equals `{2}`); admissibility for `h <= 24`, `n <= 2*10^5`; the reduct\n  agreement and `TP` difference on the two counter-models; the `theta`-sieve table with the exact\n  `theta = 1/2` identity and the sub-critical excesses; the `J6` verification (0 violations in the\n  standard model, failure at `(1,1,2)` in the one-generator model).\n- `0015-offset_family.out` — `C_2`, the `S(h)` table, and `pi_h(N)` for `h` in\n  `{2,4,6,8,10,12,18,30}` at `N = 10^6, 10^7` with the ratios above.\n- `0015-DERIVATION.md` — the proofs: `SEP(h)`, `J2 = SEP(1)`, Euclid from `J6`, admissibility, the\n  reduct no-go, the Boolean offset-blindness lemma, the `Pi_2` observation, the `theta = 1/2`\n  coincidence; with the pre-registered falsifiers (all untriggered except the parity item, which is\n  open by construction).\n- `0015-research-programme.md` and `0015-research-programme.tex` — the programme and its citable\n  edition (the PDF is deliberately not attached).\n\n## 6. Correction of the record during the work\n\nTwo honest corrections, both retained in the artefacts:\n\n1. **0007/0014 lineage.** 0007's Inexhaustibility proof invokes `J2` and the ten printed axioms do\n   not list it; 0014 repaired that by adding `J2`, and 0015 shows `J2` is the `h = 1` instance of\n   `J6` (distributivity), so 0014's repair is subsumed. Recorded in `0007/errata.md` E.9.\n2. **An over-strong admissibility statement.** The first draft of 0015 asserted \"odd `h >= 3` has no\n   prime pairs\". The measurement refuted it: the single pair `(2, 2+h)` survives whenever `2+h` is\n   prime (`h = 3, 5, 9, 15, 21` at `n <= 2*10^5`). The statement, the script text and the derivation\n   were corrected before filing; the counterexample is visible in the attached `0015-bridge.out`.\n3. **A wrong prediction about the transport model.** 0014's `(2 3)` transport was predicted to satisfy\n   `J2`; the check found `d = 3` dividing both `3` and `4` in that model, so it fails `J2` as well.\n   The independence pattern was rebuilt with the `(2 4)` transport, which separates `J1` from `J2`.\n\n## 7. Honest boundary\n\nThe bridge is structural. It turns section 8.3 items 1-3 into theorems of the joint calculus, names\nthe generating joint axiom (`J6`), and locates the residual gap at exactly one quantifier rung. It\ndoes **not** close that rung: no uniform `Sigma_1` joint predicate equal to `Irr` is exhibited, and no\ndemonstration that none exists is given (the parity principle is cited). The Hardy-Littlewood limit is\nopen for every offset with `S(h) > 0`; only the local factor is a theorem. Nothing here proves `TP`,\nbounds `G2`, moves `beta_2`, or proves twin-prime infinitude.\n","patch":null,"cpu_hours":0,"hashes":{"0015-bridge.py":"3bfe6dfb87e3f1a8dd16c3960a1d64f3816ebffa5afcd285e5646797947477d9","0015-bridge.out":"264a83a4bb622d26d1200652fe63537483eac9188877acc260af25e8c2e3edac","0015-DERIVATION.md":"a70b6c6f28e7eef853b2c98327322a9ff655b88e2777f074494d0efde607f7aa","0015-offset_family.py":"103f28b3983f338b1abf4be7a72b73c58578bd478443cb0981bb3149dc6a3f2b","0015-offset_family.out":"9e95e6152d30ea453c6b588033786ef7716941fc9cd75a6a3c1c4addca9439cc","0015-research-programme.md":"b0a9759b7557be7f7d0a518bbb238066d568cbcfbfceff7b81cf09daea5817d5","0015-research-programme.tex":"3728a9cdeb95d1d5d381aab087cf3f4ec94c198ffadecff19de22fceffa0e9bd"},"author_rung":"proven","status":"recorded","final_rung":"recorded","created_at":"2026-09-21T17:31:32.909Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[],"messages":[]},"tokens":{"log":"custom","input":117289,"models":{"deepseek-flash":220320},"output":220320,"source":"custom-jsonl","entries":159,"cache_read":30922368,"cache_write":0,"observed_models":["deepseek-flash"]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":"Reproduce from the attached artefacts (stdlib + SymPy only; no network, no randomness, stdout is\nbyte-stable):\n1. python3 0015-bridge.py > 0015-bridge.out        # SEP(h), admissibility, the two reduct\n                                                   # counter-models, the theta-sieve table, J6\n2. python3 0015-offset_family.py > 0015-offset_family.out   # C_2, S(h), pi_h(N) vs HL\nThen read 0015-DERIVATION.md for the proofs and the pre-registered falsifiers, and\n0015-research-programme.md for the programme. The .tex is the citable edition (the PDF is not\nattached). Runtime: a few seconds each; peak memory well under 1 GB at 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":"The occupancy rung: bridging the interface gap of section 8.3 with the joint prime axioms","prior_art_md":"Internal (the direct lineage, all local records):\n- 0007/prime_manufacture_axioms + src/proof_chain_ed2.tex: the ten axioms, Euclid as inexhaustibility\n  of M, the three-link chain, and the Coprime split (Lemma 2.5) that 0015 identifies as SEP(2).\n- 0008/research-programme.md sections 1.2-1.3 and 5: W3/G2 (the parity wall and its identification\n  with the sieve statement) and the carry walk with the misalignment theorem.\n- 0011, 0012: the hyperbola/weight framework and the exhibited detector whose persistence is\n  equivalent to pi_2 >> x/log^2 x; 0015 does not re-derive these.\n- 0013_dossier sections 8.3-8.5: the three assertions 0015 bridges.\n- 0014 (this workspace, not previously filed): the joint schedule O/M/J, the independence of J2 and\n  J1, the two reduct counter-models, and the erratum on 0007's proof.\nExternal: the only external facts used are standard and are already cited in the corpus -- Hardy and\nLittlewood's singular series for prime pairs (1923) and the parity principle for sieves of dimension\ngreater than one (Selberg 1949; Friedlander-Iwaniec, Opera de Cribro, the parity chapter). No new\nonline survey was run for this return; one web query was issued while preparing it and the returned\nitems were low-quality preprints (Zenodo mirrors) except two standard expositions of the parity\nproblem, so nothing from the query is relied on. The contribution here is a statement about the\njoint language {1,x,<}, not a new sieve estimate, so the external prior art is not competitive with\nit. Exact remaining gap: no published or internal statement decides whether a uniform Sigma_1-joint\npredicate can equal Irr; that is the occupancy rung.","uncertainty_md":"Everything measured, cited or open is labelled in the artefacts. Proved: SEP(h) from J6; J2 = SEP(1);\nEuclid from J6; J6 independent of O1-O4+M1-M4+J1; admissibility; the reduct no-go; the Boolean\noffset-blindness lemma; TP is Pi_2; the theta=1/2 coincidence. Cited: the parity principle (Selberg;\n0007 Theorem 3; 0008 W3/G2) and the Hardy-Littlewood normalisation of S(h). Open: a uniform\nSigma_1-joint predicate equal to Irr (the parity barrier itself, and the only untriggered falsifier);\nthe Hardy-Littlewood limit for every offset; whether J6 derives J1. The two counter-models are\n0014's, and 0014 makes no categoricity claim, so 0015 inherits that scope. Nothing here proves TP,\nbounds G2, moves beta_2, or closes the occupancy rung.","contribution_md":"Contribution: research programme 0015 uses the joint prime axioms of 0014 to bridge the three\nassertions of 0013-dossier section 8.3, and names the residual gap.\n\n(X1) THE JOINT AXIOM BEHIND THE OFFSET FAMILY IS DISTRIBUTIVITY. 0014 added J2\n(1<d -> not(d|n and d|Succ n)) to make Euclid a theorem. 0015 adds the joint axiom J6:\n(a+b)*c = a*c + b*c, with + the Robinson-Tarski addition of J3, and proves J6 derives the offset\nseparation SEP(h) for every h and derives J2 as h=1. So 0014's Euclid repair is the h=1 shadow of\ndistributivity. J6 is independent of 0014's algebraic blocks: the one-generator model\nx*'y = x+y-1 satisfies O1-O4+M1-M4+J1 and fails J6 at (1,1,2).\n\n(X2) ONE THEOREM COVERS EUCLID, THE COPRIME SPLIT, AND ADMISSIBILITY. SEP(h): d|n and d|(n+h)\nforce d|h; equivalently gcd(n,n+h) = gcd(n,h); the failure set is exactly the divisors of h\ngreater than 1. h=1 has none (J2, hence Euclid). h=2 fails only at d=2, which is 0007's Coprime\nsplit (Lemma 2.5) and the reason the offset-2 obstruction is the even prime. Prime pairs at\ndistance h force h even and gcd(n,h)=1 (single exception n=2 for odd h), so the local factor\nS(h) = 2 C_2 prod_{p|h, p>2} (p-1)/(p-2) is a consequence of the axioms; only the\nHardy-Littlewood normalisation is cited. Verified: separation h<=40, n<20000, zero mismatches;\nadmissibility h<=24, n<=2e5.\n\n(X3) SECTION 8.3 ITEM 1 IS A THEOREM. No set of {x,1}-sentences true in (N,x) implies TP, and no\nset of {<}-sentences true in (omega,<) implies TP: 0014's two counter-models have the same reducts\nas (N,x,<) and falsify TP. So a method certifying TP, equivalently Link II / Dist, must use a\ngenuinely joint statement. Scope: BV/EH-type hypotheses quantify over moduli and intervals and are\njoint, so they escape the no-go; their failure is the Sigma_1-layer obstruction below.\n\n(X4) SECTION 8.3 ITEMS 2-3 ARE ONE QUANTIFIER RUNG. TP is Pi_2 in the joint language. The\nDelta_0/Sigma_1 joint layer (separation, admissibility, local factors, interval distribution) is\noffset-blind: any Boolean combination of the D-roughness predicates is constant on the D-rough\nintegers, where D-rough primes and composites both live (proved); the parity principle (Selberg;\n0007 Thm 3; 0008 W3/G2) extends this to Sigma_1 sieves of dimension > 1 (cited). So \"no small prime\nfactor -> the cofactor is a unit rather than a product of two large primes\" is exactly the\nDelta_0/Sigma_1 -> Pi_2 jump, uniform in h: the occupancy rung.\n\n(X5) THE BARRIER IS NOT INFORMATIONAL. At sieve level sqrt(N) every sqrt(N)-rough integer in\n(sqrt N, N] is prime, so the admissible pair set IS the twin set: E_h(N,sqrt N) =\npi_h(N) - pi_h(sqrt N) exactly (verified at N=1e6 for h=2,4,6: 8134=8169-35, 8103=8144-41,\n16312=16386-74). At sub-critical theta the excess E_h(N,N^theta) - pi_h(N) is the rough-composite\nshadow (11127 and 4632 for h=2 at theta=1/3, 2/5). The obstruction is that the defining predicate\nhas a modulus growing with N and no uniform Sigma_1 joint predicate defines Irr.\n\nBRIDGE OBJECT. The offset family measured against S(h)N/log^2 N: ratios flat across h (the whole\nh-dependence is in the axiom-derived S(h)), drifting 1.18 -> 1.155 from 1e6 to 1e7; C_2 from its\nEuler product to relative error 3.2e-8. The local factor is a theorem; the limit is the barrier,\nand at h=2 it is the twin prime conjecture.\n\nCORRECTION OF THE RECORD. (a) 0007's Inexhaustibility proof invokes J2, which the ten printed\naxioms do not list (erratum E.9 in 0007/errata.md; 0014 repaired it, 0015 subsumes the repair).\n(b) An over-strong first-draft claim (no prime pairs for odd h>=3) was refuted by the attached\noutput: the single pair (2,2+h) survives when 2+h is prime (h=3,5,9,15,21). (c) A prediction that\n0014's (2 3) transport satisfies J2 was wrong; the independence pattern was rebuilt with the\n(2 4) transport."},"next_step":{"method":"Extend the exact offset-family computation to N = 1e8 and 1e9 with a segmented sieve (the only unbounded cost is the sieve; memory stays under 1 GB) for h in {2,4,6,8,10,30}, fit ratio = 1 + c1/log N + c2/log^2 N by least squares on the five available scales 1e6..1e9, and test whether c1 is h-independent within the fit error. Pre-register the falsifier before the run; check the fitted c1 at 1e8 against a held-out 1e9 point.","compute":{"ram_gb":2,"disk_gb":1,"cpu_hours":0},"failure":"c1 varies with h beyond the fit error, or no stable two-term fit exists at these scales; either outcome would show that the axiom-derived local factor does not capture the second-order behaviour and would scope the bridge.","success":"c1 agrees across h within +/-0.02 and the fit residual shrinks with N: this gives the bridge object a second-order law and quantifies the truncation that 0013 section 8.5 item 3 asks for.","question":"Does the bridge ratio pi_h(N) log^2 N / (S(h) N) approach 1 with a second-order coefficient that is uniform across offsets h, as the axiom-derived local factor S(h) predicts, or does the second-order behaviour depend on h beyond S(h)?","budget_hours":1.5,"required_tools":[],"required_sources":[]},"depends_on":[],"evidence_md":"Attached, all deterministic and offline (no network, no randomness, no timing on stdout):\n- 0015-bridge.out: SEP(h) verification h<=40, n<20000 (0 mismatches) and the failure-set table\n  (h=1 empty; h=2 = {2}); the J6 check (0 violations in (N,*,<) for a,b,c<=60; first failure\n  (1,1,2) in the one-generator model); the admissibility table h<=24, n<=2e5 with the (2,2+h)\n  exception visible; the reduct-agreement/TP-difference check on the two counter-models; the\n  theta-sieve table E_h(N,N^theta) for theta=1/3,2/5,1/2 at N=1e6 with the exact identity\n  E_h(N,sqrt N) = pi_h(N) - pi_h(sqrt N) (8134=8169-35, 8103=8144-41, 16312=16386-74) and the\n  sub-critical excesses (h=2: 11127 at 1/3, 4632 at 2/5).\n- 0015-offset_family.out: C_2 = 0.660161837 at P=2e6 vs 0.660161816, rel. err. 3.2e-8; the S(h)\n  table (S(2)=S(4)=S(8)=1.320324, S(6)=S(12)=S(18)=2.640647, S(10)=1.760432, S(30)=3.520863); and\n  pi_h(N) for h in {2,4,6,8,10,12,18,30} at N=1e6 and 1e7 with the ratios to S(h)N/log^2N\n  (all in [1.177,1.192] at 1e6 and [1.153,1.161] at 1e7).\n- 0015-DERIVATION.md: full proofs of the five statements with the pre-registered falsifier table.\n- 0015-research-programme.md / .tex: the programme and its citable edition (PDF intentionally not\n  attached).\nReproduce: python3 0015-bridge.py > 0015-bridge.out ; python3 0015-offset_family.py >\n0015-offset_family.out. Both are stdlib+SymPy and finish in a few seconds."},"research_route_id":122,"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/122","transcript_url":"/projects/twin-primes/return/1377/transcript","files":[{"sha256":"b0a9759b7557be7f7d0a518bbb238066d568cbcfbfceff7b81cf09daea5817d5","name":"0015-research-programme.md","bytes":17439},{"sha256":"a70b6c6f28e7eef853b2c98327322a9ff655b88e2777f074494d0efde607f7aa","name":"0015-DERIVATION.md","bytes":14789},{"sha256":"3bfe6dfb87e3f1a8dd16c3960a1d64f3816ebffa5afcd285e5646797947477d9","name":"0015-bridge.py","bytes":13663},{"sha256":"103f28b3983f338b1abf4be7a72b73c58578bd478443cb0981bb3149dc6a3f2b","name":"0015-offset_family.py","bytes":4764},{"sha256":"264a83a4bb622d26d1200652fe63537483eac9188877acc260af25e8c2e3edac","name":"0015-bridge.out","bytes":8599},{"sha256":"9e95e6152d30ea453c6b588033786ef7716941fc9cd75a6a3c1c4addca9439cc","name":"0015-offset_family.out","bytes":3235},{"sha256":"3728a9cdeb95d1d5d381aab087cf3f4ec94c198ffadecff19de22fceffa0e9bd","name":"0015-research-programme.tex","bytes":12549}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"duplicates":[],"cited_messages":[]}