{"id":1299,"job_id":2648,"problem_id":1,"lane_id":null,"type":"explore","user_id":42,"model":"deepseek-flash","provider":"deepseek","report_md":"# Job #2648 (explore, triage) — route 106: **known**\n\n**Verdict: `known`.** Route 106's headline (every layer of the 3-D radix tower is core-homologous, so\nall linking numbers vanish) is a correct but *textbook* statement about closed curves in a solid\ntorus; the route's own written proofs of Theorems 1 and 2 are not valid as they stand (a false core\ncoefficient, an ill-posed relative pairing, and a closure that routes every layer through the axis).\nThe one open item, Conjecture T3, has a pre-registered test that its own smoke test already runs\n*without the radix index `b`*, and whose band `[0.1, 0.9]` is passed by independent fair coin signs\nwith probability `≈ 2/3` — so it cannot separate the claimed structure from noise. The statistic it\nmeasures is already on record. No bounded experiment on the recorded next step would change the\nrecord.\n\nNo claim here bounds `G2`, moves `beta2`, or approaches twin-prime infinitude. Every number below is\nan exact finite computation or arithmetic on the route's own published checks; a script output is\nnever a proof.\n\n## 1. What I inspected\n\n* Route 106 (`research-routes/106`); its origin return **#1294** (direction 5 of programme 0002);\n  its basis/dependencies `893, 904, 946, 1273`.\n* Local sources: `paper-5-tower-linking.md`, `paper-4-parity-cocycle.md`, the whole\n  `numerical-verification/` suite, `paper-verify-parity-cocycle.json`,\n  `evidence/verify_5_tower.json`.\n* Docs: `research/OUTCOMES.md` (closed-routes register) and `research/README.md` (router).\n* Online: three search batches, queries and links recorded in the `prior_art_md` of this return.\n\n## 2. Theorem L — the conclusion is right, the proofs are not\n\nThe route grades Theorems 1, 2 and 6 **proved**. The *conclusion* (all pairwise and self-linking\nnumbers of the tower vanish) is true, but the derivations given do not establish it, and one stated\ntheorem is false as written.\n\n**(a) The core coefficient is not 1.** Theorem 1 states `[L_b] = 1·[c] + 0·[m]`, \"the core\ncoefficient is `v_*[S¹] = 1` because a layer winds once around the axis per traversal\". The same\npaper's §1.2 and its own check V5.4 say `arg z_n = Θ_n` and the layer wraps `Θ_N/2π` times. My\nindependent float64 sum gives\n\n| N | `Θ_N/2π` | so `[L_b]` |\n|---|---|---|\n| 1e2 | 2.858 | 3·[c] |\n| 1e4 | 31.489 | 31·[c] |\n| 1e6 | 317.967 | **318·[c]**, not 1·[c] |\n\nThe winding is the internal contradiction: §1 says \"unbounded\", Theorem 1's proof says \"once\".\nThe `meridian coefficient 0` half is also content-free: `H₁(D²×S¹) = H₁(D²) ⊕ H₁(S¹) = 0 ⊕ Z`, so\n*u_*[S¹] = 0* for **any** map `u : S¹ → D²`, telescoping or not (V5.3 checks the telescoping\nidentity, which is exact but not the point).\n\n**(b) The relative-homology bookkeeping is wrong.** The Theorem 2 proof pairs\n`H₁(V) × H₁(V,∂V) → Z` and calls the meridian `[m]` a generator of `H₁(V,∂V)`. For\n`V = D²×S¹` the long exact sequence of `(V,∂V)`, with `H₂(V,∂V)=Z --∂--> H₁(∂V)=Z² --i--> H₁(V)=Z`\n(`i` kills the meridian, sends the longitude to the core) and `H₀(∂V) ≅ H₀(V)=Z`, gives\n`rank H₁(V,∂V) = 1 − 1 = 0`: **`H₁(V,∂V) = 0`**. The meridian class `m` lives in `H₁(∂V)=Z²`, not\nin `H₁(V,∂V)`. The correct non-degenerate pairing is `H₂(V,∂V) × H₁(V) → Z` with\n`⟨meridian disk, core⟩ = 1`. The claimed pairing is degenerate/ill-posed.\n\n**(c) The closure routes every layer through the axis.** The stated closure is \"the radial segment\nfrom `Emb_b(N)` to the axis and the radial segment from the axis to `Emb_b(1)`\". Those two segments\nmeet the axis at `(0,t_N)` and `(0,t_1)`, so the curve closes only by adding the axis segment between\nthem — and then *every* layer's closure contains an axis segment. Layers whose height ranges overlap\n(any two with close `t_b`, and certainly equal `t_b`) intersect on the axis, so their linking number\nis undefined. The \"for every base height `t_b`\" quantifier of Theorem 1 is therefore too strong.\n\n**What survives, and why it is textbook.** The conclusion `lk = 0` follows independently and\nelementarily: a layer is asymptotically confined to its own horizontal slab (V5.2: vertical spread\n`3.7e-43` at `ρ=1, N=1e4`), and disjoint curves lying in distinct slabs — equivalently, two disjoint\nplanar curves — are unlinked. That is the standard \"a planar curve has linking number zero with\nanything disjoint from it\" fact; no solid-torus homology is needed. The route itself concedes the\ningredients are textbook (§7, prior art). So the lane closure is **valid and worth having on the\nrecord, but not new mathematics**, and the recorded rung `proved` overstates what the written proofs\nestablish.\n\n## 3. Register and project-goal fit\n\nThe closed-routes register has **no entry** for this lane: `research/OUTCOMES.md` contains zero\noccurrences of `0002`, `co-rotation`, `spiral gauge`, `parity holonomy`, `TASK E` or `3-D tower`, and\nthe router does not mention it. Route 106 therefore re-opens nothing closed and closes nothing the\nregister already carried. Its *class* of statement — a geometric observable cannot see the\ntwin/composite split — is already on the record twice over: algebraically by returns #893/#946 (any\nfixed-modulus kernel is a function of `n mod lcm`), and geometrically by paper 0002.4, Theorem 3\n(*every* spiral gauge is flat, so every gauge-invariant functional of the phases is blind). Route 106\nadds the position-lattice companion: the tower's rotation is real but homologically invisible. The\nproject's own object (the `K*`/`L(T_x,p)` ladder, `G2`, `beta2`) is untouched by either direction.\n\n## 4. Conjecture T3 — not well-posed, and non-diagnostic\n\nT3: the `Z/2` holonomy of the parity local system around a layer (product of\n`a_n = λ(n)λ(n+2)` along `A_P`-restricted twin bonds) is `-1` for a positive proportion of closures;\nfalsifier: `-1` fraction in `[0.1,0.9]` **at every `(b,N)`**, `b ∈ {2,3,10}`,\n`N ∈ {1e4,1e5,1e6}`, offsets `{0,1,2,3}`.\n\n**(i) `b` does not enter the computation.** The route's own smoke test (V5.6) builds `A_P` at `z=13`\n(`P = 15015`), computes `a_n` on every admissible `n < 1e6`, and multiplies `bond[offset::4]` — the\nradix `b` appears nowhere, and the layer is never used. The pre-registered `(b,N)` table therefore\nhas three identical rows per `N`, and no map from the layer's parameter to a closed set of twin\nbonds is defined anywhere in the route. I reproduced V5.6 and extended it to the full `N` grid:\n\n| N | four offset products | `-1` fraction | in band? | whole-layer product |\n|---|---|---|---|---|\n| 1e4 | `[+1,+1,-1,-1]` | 0.50 | yes | `+1` |\n| 1e5 | `[-1,+1,+1,+1]` | 0.25 | yes | `-1` |\n| 1e6 | `[+1,+1,-1,+1]` | 0.25 | yes | `-1` |\n\n**(ii) The band is passed by noise.** With four offsets the fraction takes values in\n`{0, 1/4, 1/2, 3/4, 1}`, so a cell passes unless *all four* products are `+1` or *all four* are `-1`.\nUnder iid fair signs that is probability `1 − 2/16 = 7/8` per cell; across the pre-registered grid\nthis is `≈ 0.67` (the `b` index is inert, so only the three `N` cells are effective), `≈ 0.30` even\nif the nine cells were independent. A 200 000-draw simulation gives `0.8764` per cell. So a\n\"successful\" T3 run would confirm the conjecture for *any* near-balanced `±1` bond assignment,\nincluding a randomized one: the falsifier has no power against the null it exists to exclude.\n\n**(iii) The statistic is already measured.** On `A_P` below `1e6` the bond variable is balanced\n(`-1` fraction `0.4575 / 0.4991 / 0.5008` at `N = 1e4/1e5/1e6`), the plaquette\n`F_n = a_n a_{n+1}` is balanced (`0.5001` at `1e6`), and explicit window-product holonomies of\n`m = 1,2,3,5` bonds over 200 starts give `-1` frequencies `0.40, 0.46, 0.465, 0.50`. Paper 0002.4\n(Prop. 6) already reports exactly this: loop holonomies of length `1,2,3,5` bonds are `-1` with\nfrequencies `0.4826, 0.4776, 0.5323, 0.4975`, and Theorem 4(iii) records `F_n = -1` for\n`1 499 092 / 3 000 000` values. **Provenance gap noticed:** paper 0002.4 attributes the loop-holonomy\nnumbers to `paper-verify-parity-cocycle.json`, but that file contains only the `F_n` census — the\nloop family is not retained, and the committed suite never recomputes it. The numbers are therefore\nplausible and independently reproduced in direction here, but their provenance should be repaired.\n\n**Net.** The route's only live conjecture is either already answered by its own basis paper (the\nparity local system is non-flat and its loop holonomies are mixed) or rests on an undefined\nlayer-to-bond map. Running the recorded next step as written would return a spurious success. That is\na defect of the *test*, not evidence for the tower; the honest triage call is that no experiment is\nwarranted.\n\n## 5. Independent checks run for this triage (≈ 0.05 CPU-h)\n\n* The 0002 finite suite, re-run from a clean copy (`outputs/2648/nv`, deleted after capture; log\n  retained): **63 passed, 0 failed, 3 informational** in ≈ 64 s, including all seven of the route's\n  own V5.1–V5.7 checks. V5.7 keeps the three failed discrete Gauss implementations visible rather\n  than hiding them — good discipline.\n* `triage_checks.py` (this job): layer winding at `N = 1e2,1e4,1e6`; the relative-homology rank\n  count; the T3 census on the full pre-registered `(N, offset)` grid with the `b`-inertness noted;\n  the iid-sign power calculation and simulation; the bond/plaquette/window-product censuses;\n  `triage_rows.json` holds the machine-readable rows.\n* `nv_run_all.log`: the independent suite re-run transcript.\n\n## 6. Prior art and the exact remaining gap\n\nOnline search (2026-09-19; exact queries and links in `prior_art_md`). The route's two ingredients\nare covered:\n\n* **Vanishing linking form.** Textbook: the torus-knot formula `lk = p₁q₂ − p₂q₁`, the homology\n  `H₁(D²×S¹) = Z`, the intersection form, and \"a planar curve is unlinked from any disjoint curve\".\n  Nothing here is new, and the route says so.\n* **Non-flat parity local system.** The Liouville bond variable as the parity/Selberg obstruction is\n  classical; the route's own paper 0002.4 states and measures it (Theorem 4, Prop. 6). What is *not*\n  in the literature is a linking-form or lattice-`U(1)` computation specific to this tower — because\n  the linking form is identically zero for a textbook reason, so there is nothing to compute.\n  Kim's arithmetic gauge theory and Kapustin–Witten are Diophantine/geometric-Langlands and yield no\n  gap bound (the route's own verdict, confirmed by my searches); arithmetic BF theory / the\n  Cassels–Tate pairing is a different class-field pairing.\n\n**Exact remaining gap:** none for the linking lane (closed). For the parity-holonomy lane the missing\npieces are a canonical layer-to-bond-loop map and a discriminating null; the route supplies neither,\nand with the linking lane closed, a repair would only re-measure an object already on record. That is\nwhy this return is `known` rather than `promising`: there is no bounded experiment worth funding.\n\n## 7. Calibration\n\n| claim | route's rung | triage rung |\n|---|---|---|\n| every layer is asymptotically planar; height damping | verified (V5.1–V5.2) | verified (reproduced) |\n| Theorem 1: `[L_b] = 1·[c] + 0·[m]`, same for every radix/decay/height | proved | **refuted as stated** (`[L_b] = winding·[c]`, 318 at `N=1e6`; the meridian half is content-free) |\n| Theorem 2 proof via `H₁(V)×H₁(V,∂V)` and the meridian `[m]` | proved | **invalid proof** (`H₁(V,∂V)=0`; correct pairing `H₂(V,∂V)×H₁(V)`) |\n| Theorem 2 conclusion `lk(L_b,L_b') = 0` | proved | **true, elementary/known** (slab separation); proof as written does not give it |\n| closure \"in the horizontal plane\", for every height | definition | **under-specified** (axis segment shared by all layers; overlapping heights intersect) |\n| Theorem 6 self-linking 0 | proved | true only in the Seifert framing; stated proof flabby |\n| V5.1–V5.7 finite checks | verified | verified (independent re-run, 63/0/3) |\n| Observation 7 (Milnor / Arf / non-abelian candidates) | observation | valid pointer, unsettled |\n| Conjecture T3 | conjectured | **not well-posed + non-diagnostic**; the underlying mixed-holonomy statistic is already measured in paper 0002.4 |\n| nothing bounds `G2`, `beta2`, twin-prime infinitude | scope | scope respected |\n\n## 8. Files\n\n`report.md`, `triage_checks.py`, `triage_rows.json`, `nv_run_all.log`.\n\n## 9. Outstanding\n\nThe run ledger's outstanding-work check lists exactly one outstanding attempt, this job #2648; all\nprior attempts in this run have verified receipts. After submission the only remaining item is this\nreturn's own recording. 13 returns of the author's handle wait for a verdict (from the brief); none is\nthis session's work, and no agent of this person's can decide them.\n","patch":null,"cpu_hours":0.05,"hashes":{"report.md":"fa001c9a453217cdc8252ff5e8c18d46206db6c5a2cfebded6e445346cba71bc","nv_run_all.log":"24bda8f213bd9d309a90aab74b3f16d1cb82c3ae6ee7ec9298a4fe051b0022ac","triage_checks.py":"37f659404f9a9e0dde0b147b397199372caf007e39fed5a42196f16e930a1bc5","triage_rows.json":"5bdbd8b55ed6dd50f045ef076d5e59edced28b9b1c122a4db26bdc05d3ab02c2"},"author_rung":"verified","status":"recorded","final_rung":"recorded","created_at":"2026-09-19T17:16:42.736Z","repo_url":null,"commit":null,"cites":{"files":["research/OUTCOMES.md","research/README.md"],"handles":[],"returns":[1294],"messages":[]},"tokens":{"log":"custom","input":82982,"models":{"deepseek-flash":61168},"output":61168,"source":"custom-jsonl","entries":45,"cache_read":4268160,"cache_write":0,"observed_models":["deepseek-flash"]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":"All checks are seconds to ~1 minute and run from the workspace root with ./.venv/bin/python3. (1) Copy the 0002 suite to a scratch dir under outputs/ and re-run it, so the archived artifacts are untouched: `cp -R .solveathome/private/research/0002/numerical-verification outputs/2648/nv && (cd outputs/2648/nv && ../../../.venv/bin/python3 run_all.py)` -> 63 passed / 0 failed / 3 informational (log retained as nv_run_all.log). (2) `./.venv/bin/python3 outputs/2648/triage_checks.py` -> layer winding at N=1e2,1e4,1e6; the H_1(V,dV) rank count; the T3 census on the full pre-registered (N,offset) grid with the b-inertness noted; the iid-sign power calculation and 200000-draw simulation; the bond / plaquette / window-product censuses; writes triage_rows.json. numpy is used for the sieve and the grid; all arithmetic is exact integers except the float64 Theodorus sum (whose rounded winding is what the paper's own V5.4 reports). No large computation was run: the route's whole next step is a product of +-1 along a prefix and is not worth executing as specified.","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":"known","route_id":106,"depends_on":[1294],"evidence_md":"Triage of route 106 (origin return #1294, direction 5 of programme 0002). Outcome: known -- the linking lane is closed, correctly but by textbook means, and the one open conjecture's test is neither well-posed nor discriminating, so no experiment is warranted.\n\n(1) Theorem L. The conclusion lk=0 for every pair is TRUE and elementary: a layer is asymptotically confined to its own horizontal slab (V5.2: spread 3.7e-43 at rho=1,N=1e4) and slab-separated (equivalently planar) disjoint curves are unlinked. But the route's \"proved\" derivations are not valid. (a) Theorem 1 asserts [L_b]=1[c]+0[m] because a layer \"winds once around the axis\"; the same paper's S1.2 and check V5.4 give arg z_n=Theta_n and winding Theta_N/2pi = 2.858 / 31.489 / 317.967 at N=1e2/1e4/1e6, so [L_b]=318[c] at N=1e6, not 1[c]. The meridian half is content-free: H_1(D^2xS^1)=H_1(D^2)+H_1(S^1)=0+Z, so u_*=0 for ANY u:S^1->D^2. (b) Theorem 2's proof pairs H_1(V) with H_1(V,dV) and calls the meridian a generator of H_1(V,dV); the LES of (V,dV) gives H_1(V,dV)=0 (rank 1-1), the meridian lives in H_1(dV)=Z^2, and the correct pairing is H_2(V,dV)xH_1(V)->Z with <meridian disk, core>=1. (c) The stated closure sends every layer through the axis ((0,t_N)->(0,t_1)), so layers with overlapping height ranges intersect and lk is undefined; \"for every base height\" is too strong.\n\n(2) Conjecture T3. (i) The radix b enters neither the definition nor the route's V5.6 smoke test; the (b,N) table has three identical rows per N, and no map from the layer parameter to a closed set of twin bonds is given. I reproduced V5.6 and extended it to the pre-registered grid: four offset products [1,1,-1,-1] (frac 0.50) at N=1e4, [-1,1,1,1] (0.25) at 1e5, [1,1,-1,1] (0.25) at 1e6 -- all \"pass\". (ii) With four offsets the band admits {1/4,1/2,3/4}; under iid fair signs a cell passes with p=7/8, the grid with p~0.67 (b inert) or ~0.30 (nine independent cells); a 200000-draw simulation gives 0.8764 per cell. Any near-balanced +-1 assignment passes, so the falsifier has no power against the null it must exclude, and the recorded next step would return a spurious success. (iii) The statistic is already on record: bond -1 fractions 0.4575/0.4991/0.5008 at N=1e4/1e5/1e6, plaquette F 0.5001 at 1e6, explicit window products m=1,2,3,5 = 0.40/0.46/0.465/0.50, whole-layer product +1/-1/-1; paper 0002.4 Prop. 6 already reports loop holonomies -1 at 0.4826/0.4776/0.5323/0.4975 and Theorem 4(iii) F_n=-1 for 1499092/3000000. Provenance gap: 0002.4 attributes the loop numbers to paper-verify-parity-cocycle.json, which holds only the F_n census; the committed suite never recomputes them.\n\n(3) Positive checks. The 0002 suite re-runs clean from a clean copy (63 pass / 0 fail / 3 info, ~64 s), including V5.1-V5.7; V5.7 keeps the three failed discrete Gauss-linking implementations visible.\n\n(4) Register and goal. OUTCOMES.md has no entry for 0002 / co-rotation / spiral gauge / parity holonomy / 3-D tower, so route 106 re-opens nothing; its statement class is already carried by returns #893/#946 (fixed-modulus kernels) and paper 0002.4 Theorem 3 (every spiral gauge flat). The project's K*/G2 object is untouched. Net: the lane closure is valid and useful but not new mathematics, and T3 is already measured or undefined.","prior_art_md":"Updated online search record, 2026-09-19. Three batches; queries: \"linking number torus knots solid torus homology textbook\", \"lattice U(1) gauge theory arithmetic primes Wilson loop number theory\", \"Kim gauge theory number theory Diophantine 2018 review\", \"Kapustin Witten electric-magnetic duality geometric Langlands\", \"arithmetic gauge theory Minhyong Kim introduction link invariant Selmer\", \"quadratic refinement linking form Arf invariant Z/2 spin 3-manifold\", \"Milnor triple linking number higher order invariants Brunnian\", \"Liouville function holonomy flat bundle integers parity obstruction\", \"Selberg parity obstruction Liouville function sieve twin primes\", \"Theodorus spiral square root spiral phase asymptotics\", \"linking number two disjoint planar curves zero separation surface\", plus variants.\n\nInspected closest sources. (a) Vanishing linking form: standard algebraic topology -- H_1(D^2xS^1)=Z, the torus-knot formula lk=p1q2-p2q1 [Stosic, Homology of torus knots and links](https://www.kurims.kyoto-u.ac.jp/~nakajima/07_Link%20homology%20and%20categorification/20070515%20M.Stosic%20Homology%20of%20torus%20knots%20and%20links.pdf), the intersection form and self-linking [Cochran-Orr-Teichner](http://math.uchicago.edu/~shmuel/L%5E2%20cohomology%20readings/Cochran-Orr-Teichner.pdf). (b) Gauge-theoretic number theory: Kim, [Arithmetic gauge theory: a brief introduction](https://zbmath.org/pdf/06951000.pdf) and [arithmetic BF theory / Cassels-Tate pairing](https://arxiv.org/pdf/2602.19621) are Diophantine/class-field and give no analytic gap bound; [Kapustin-Witten](https://ar5iv.labs.arxiv.org/html/0911.4586), Comm. Number Theory Phys. 1 (2007) 1-236, is 't Hooft/Hecke-eigensheaf (geometric Langlands), no gap bound either. (c) Phase: [Waldvogel, The Theodorus Spiral](https://people.math.ethz.ch/~joergw/Papers/basel_waldvogel.pdf) covers the phase asymptotics used in the embedding. (d) Parity: the Selberg parity obstruction / Liouville sign is classical ([Tao's parity notes](https://terrytao.wordpress.com/wp-content/uploads/2008/04/whatsnew1.pdf)); the route's own paper 0002.4 Theorem 4 / Prop. 6 already measures the non-flatness (F_n=-1 for 1499092/3000000; loop holonomies mixed). (e) Higher-order candidates: [Milnor triple linking and Pontryagin formulas](https://ar5iv.labs.arxiv.org/html/1101.3374); the Arf/quadratic refinement needs a spin structure.\n\nExact remaining gap. No source computes a lattice-U(1)/Wilson-loop or linking-form invariant of this tower, because the linking form is identically zero for a textbook reason (planar/slab-separated disjoint curves are unlinked) -- there is nothing to compute, so the route's novelty claim is true but empty. Remaining gap: (1) linking lane -- none, closed; (2) parity-holonomy lane -- a canonical layer-to-bond-loop map and a discriminating null, neither supplied by the route. No published table, OEIS entry or dataset bears on Conjecture T3 as stated."},"research_route_id":106,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_23424801c73890cd6fd3264c","run_id":"run_1e3cac2821ce0a9ce994625b","triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":null,"handle":"victor-geere","job_brief":"Search online for existing attempts, results, tables and datasets before testing feasibility. Reuse the recorded search and inspect the closest sources and weakest assumption. Use published numbers with citations; do not reproduce them in triage. Seek the smallest experiment on the uncovered step. Recommend promising only with specific evidence and a bounded next step; do not claim the route is proved. Map the assumptions of any borrowed method onto this problem.\n\nRead GET <project base>/research-routes/106 and return #1294. Return the ordinary report and transcript plus research: {route_id: 106, outcome: \"promising|progress|blocked|inconclusive|known|result\", evidence_md: \"what the evidence changes, <=4000 chars\", prior_art_md: \"updated online search record, sources and exact remaining gap, <=4000\", next_step: {question, method, success, failure, budget_hours} <only for continued pursuit>, obstacle: {kind, statement, assumptions, evidence, revisit_when} <for blocked/inconclusive>, depends_on: [<return ids actually required>]}. A result with a distinct next_step requests review and continues pursuit concurrently; omit next_step when no further experiment is warranted. Use known with prior_art_md and no next_step or obstacle when cited prior work already covers the proposed contribution; it stops automatic investigation without requesting review. The evidence grade is separate. Do not close a broad route because one proof attempt failed.","review_deferred":false,"in_triage":false,"triage":[],"verification_runs":[],"verification_state":null,"verification_summary":null,"canonical_return":null,"review_history":[],"dependencies":[{"id":"1294","status":"recorded","final_rung":"recorded","canonical_return_id":null}],"research_url":"/projects/twin-primes/research-routes/106","transcript_url":"/projects/twin-primes/return/1299/transcript","files":[{"sha256":"fa001c9a453217cdc8252ff5e8c18d46206db6c5a2cfebded6e445346cba71bc","name":"report.md","bytes":12847},{"sha256":"37f659404f9a9e0dde0b147b397199372caf007e39fed5a42196f16e930a1bc5","name":"triage_checks.py","bytes":9207},{"sha256":"5bdbd8b55ed6dd50f045ef076d5e59edced28b9b1c122a4db26bdc05d3ab02c2","name":"triage_rows.json","bytes":6528},{"sha256":"24bda8f213bd9d309a90aab74b3f16d1cb82c3ae6ee7ec9298a4fe051b0022ac","name":"nv_run_all.log","bytes":9716}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"duplicates":[],"cited_messages":[]}