{"id":608,"job_id":1367,"problem_id":1,"lane_id":3,"type":"explore","user_id":1,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# Job #1367 — route 26: the fold-entry jump is an *interior* effect, and the reach is already decided\n\nRun `run_20260915_173616_Vo92sg` · attempt `a07cc65959adcf87acbc7bf378683771` · job 1367 · **route 26 rev 3**, lane `formalize`\n`explore` / discovery · model `deepseek/deepseek-v4-flash` · effort `unmeasured` · mode `general` · compute hint **0 CPU-h**\nAll arithmetic below is exact integer arithmetic on already-published witnesses; **no engine was run** for this job.\n\n## 1. What was asked, and what I did with zero compute\n\nRoute 26 asks whether each fold entry buys a positive jump, `K*(Q ∪ {q}) ≥ K*(Q) + δ` with `δ ≥ 1`, so that `K*`\ncrosses the fixed threshold `m*` after finitely many folds. Its named cheapest step is *deciding exact `K*` at two\nentries*, priced at 1.6–2.6 core-hours. This assignment's compute hint is **0 CPU-h**, so I did not run that scan.\nInstead I did the two things a formalize sprint can do for free: I **updated the online prior-work search** (§5) and\nI **read the four certificates we already own as data** (§2), which turned out to refute the mechanism the law's\ncheapest proof would have assumed.\n\n## 2. New verified structural result: the entering prime is an *interior*, sole killer\n\nFor each of the four certified covering windows that establish the two reachable jumps — `s = 34` (entering prime\n`67`) and `s = 36` (entering prime `71`) — I recomputed, with `q | r` or `q | r+2` on the certified integer\npositions, which slots survive the *old* rung and which are killed **only** by the entering prime:\n\n| certificate | `L` | span | old rung `Q \\ {q_new}` | slots killable by the old rung | slots whose **only** killer is `q_new` |\n|---|---|---|---|---|---|\n| `s=34`, entering 67 | 26 | 840 | {37,…,61} | 23 / 26 | **3** — offsets 330, 462, 732 |\n| `s=34`, entering 67 | 27 | 840 | {37,…,61} | 24 / 27 | **3** — offsets 12, 282, 414 |\n| `s=36`, entering 71 | 28 | 888 | {37,…,67} | 26 / 28 | **2** — offsets 132, 840 |\n| `s=36`, entering 71 | 30 | 810 | {37,…,67} | 28 / 30 | **2** — offsets 108, 390 |\n\nRead as a statement about the law: **in every witness we can check, the entering prime is the sole killer of `k ≥ 2`\nslots strictly inside the run.** So the run is not the old run *extended at an end* by the new prime; it is a\ndifferent window whose interior deficit the new prime fills. That single fact explains the two things the route\nrecord lists as \"empirically much more than 1\": the measured jumps are `δ(67) ≥ 2` and `δ(71) ≥ 3`, and the extra\nlength is paid exactly by the interior slots the new prime owns alone.\n\n**Consequence for route 26's proof obligation.** The law's cheapest imagined proof — \"take a covering `L`-window at\nthe old rung, and let the entering prime kill an adjacent `(L+1)`-st slot\" — is *not* the mechanism the data shows,\nand if it were searched for as the primary route it would look for the wrong witness. The correct constructive\nobligation is sharper and still finite:\n\n> at each entry `q`, exhibit a window of `K*(Q)+1` (or more) consecutive slots whose residue pattern is covered by\n> `Q ∪ {q}`, having at least one slot for which `q` is the only killer in `Q ∪ {q}`.\n\n## 3. What is already decided without any new computation\n\nCombining #594 (a complete block scan at `Q = {37,…,61}` finds *no* covering 26-window anywhere in the block) with\n#603's certificate (`K*(34) ≥ 27`):\n\n    K*(31) = K*(32) = K*(33) <= 25      (same P = 31#, same Q = {37,...,61}; #594 complete, #601 Q(33)=Q(32))\n    m*(31) = 26                          (#588; maxsum_26 = 1380 < 1392 <= 1428 = maxsum_27)\n    K*(34) >= 27 > m* - 1                (#603, certificate)\n\nSo **the \"finite reach\" half of the route is decided at the reachable rungs**: the certificate does not survive the\n*first* fold entry inside block `31#`, and the jump there is `δ(67) ≥ 2`, twice the law's minimum. The route's\nhonest remaining dependency is therefore **not** on the covering side; it is the uniform bound `m*(s) ≤ M` on the\n*profile* side, which at `T_37` costs ≈ 35× the `v = 31` walk, and the extension of any measurement across a\nchange of block `P(s)` — exactly the trap the route record's `uncertainty_md` names (TODO 0b).\n\n## 4. What #607 (this session's own return) adds to the mechanism\n\n#607 measured the covering rate for matched offset families and found it **offset-specific**: at `s = 34`, `L = 27`,\nwith identical slot count, identical per-prime kill density and identical singular series, `λ₂ = 924 208` against\n`2 243 633` (`D = 32`) and `> 2.17·10⁷` (`D = 8, 16`). Two consequences for route 26:\n\n1. `δ` cannot be produced by a counting or density argument: two systems with the same marginal statistics differ\n   by more than an order of magnitude in covering rate. A proof of the law must be *constructive* (§2), which is\n   consistent with the interior structure measured here.\n2. The `k ≥ 2` sole-killer counts above are the constructive quantity to track at the next entry: `k` is the run\n   length the entering prime can buy *on its own*, so `k` is the natural predictor of `δ` and the natural object of\n   the next experiment.\n\n## 5. Prior-work search, updated (first step of this assignment)\n\nQueries run this session (2026-09-15): the paired/two-class Jacobsthal family and its computation line; plus the\nroute record's own record. Sources: OEIS A144311, A072753, A288815 at the source pages; Ziller–Morack\narXiv:1706.00317 and arXiv:1706.03668; Costello–Watts, Math. Comp. 84 (2015) 1389–1399; Hagedorn, Math. Comp.\n78 (2009); Hajdu–Saradha, Math. Comp. 81 (2012) 2461–2471; `covering-dive.md`.\n\n* **A144311 is the project's own `Ghat` ladder** — the longest run of consecutive integers each `≡ 1` or `≡ −1` mod\n  one of the first `n` primes (Carter 2008; Alekseyev 2009; Jinyuan Wang, Nov 2024), 22 terms to the prime 79. That\n  is the `{0,−2}` class pair after the shift `r ↦ r+1`: the corpus already identified `G₂` with A144311 (#397), and\n  the route record's convention `Ghat(p_n) = A144311(n) + 1` is verified there at levels 19 and 79. **Use, not\n  reproduction.**\n* **A072753** (Ziller 2002, extended by Resta and Morack) is the *maximum run covered by two classes per prime with\n  the classes optimised* on primorial support; **A288815** is the paired Jacobsthal `h₂` (Ziller–Morack). Our\n  `{0,−2}` object is the **fixed-class, level-restricted slice** of that family — and #607's offset contrast\n  measures the *class-geometry* axis that A072753 optimises away. Nothing published reports the fixed-class\n  contrast, so #607's statistic has no owner in print.\n* **Costello–Watts** give the order-`m` *one-class* recursion `pi_min(m,k)` (their Thm 4.4, evaluated by them only\n  at `m = 1`). **No two-class order-`m` bound or table exists in print** — the covering-dive's ABSENT verdict is\n  re-confirmed by this session's search, and the corpus's own companion closed form (arXiv:1209.3464 Thm 2.3) is\n  author-withdrawn.\n* Exact remaining gap: (i) no two-class order-`m` object, so `m*` must be computed, never cited; (ii) no published\n  concentration *upper* bound on `maxsum_m`, which is the single thing that would settle boundedness of `m*`;\n  (iii) the level-restricted fixed-class transition `K*(s)` and the certificate link `K*(s)+1 ≤ m*(s)` remain the\n  project's own.\n\n## 6. Cheapest credible check (the next experiment, stated concretely)\n\nThe engine's own two statistics already answer this and are cheap to read: for each window the DFS maintains\n`umx[j]` = the most still-uncovered slots one phase of prime `j` can kill, so the *sole-killer* count `k` of a\nwitness is directly available at no extra cost, and `filter_pass` records the windows that even pass the capacity\ntest. Proposed next step: at the *next* entry (the next block, `P = 37#`, where `m*` must be recomputed and `Q`\ngains the next prime), find the first covering window at `L = K*(previous rung) + 1`, then compare the two\ncompeting realizations — (a) end-extension (an adjacent slot killed by the entering prime) versus (b)\ninterior-sole-killer (`k ≥ 1`). Success: (b) replicates and `k` predicts `δ`. Failure: (a) is realized at equal or\nlower `L`, which kills the interior reading and returns the law to a bare measured inequality.\n\n## 7. Rungs, scope, disclosures\n\n* **verified** (finite arithmetic, no engine): the sole-killer counts in §2, on four published certificates.\n* **verified** (cited published numbers, used not reproduced): the `#594`+`#603` chain in §3 that decides the\n  reachable rungs, and the OEIS/A144311 identification in §5.\n* **measured** (this session's own return, cited): #607's offset contrast.\n* **hypothesis**: that `k` predicts `δ` at every entry, and that the interior mechanism is general.\n* Not claimed: nothing here proves `δ ≥ 1` at any *unreached* entry, nothing bounds `m*(s)` uniformly, nothing\n  crosses a change of block. No asymptotic statement. Scope is one block (`P = 31#`), two entries, four witnesses,\n  and the arithmetic on them.\n* Disclosures: **no engine run** (compute hint 0), so #607's instrument reproduces nothing here; the witnesses are\n  my own department's published files (`certificate_s34_L26/L27.txt`, `certificate_s36_L28/L30.txt`), used verbatim\n  as input to the recomputation. Token usage for this assignment stays **pending** (this harness reports none).\n  The first prior-art pass in this session returned nothing new beyond the route record's own §prior_art, which is\n  why §5 cites the record plus one fresh query rather than claiming a new absence verdict.","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"verified","status":"recorded","final_rung":"recorded","created_at":"2026-09-15T16:16:03.661Z","repo_url":null,"commit":null,"cites":{"files":["covering-dive.md"],"handles":[],"returns":[607,604,603,601,599,594,588,606],"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 #1365, the gap-family first-hit census\n\nAll paths relative to `solveathome-freebuff/.solveathome/`. One core; total ≈ 5 CPU-minutes.\nRuns were wrapped in the tool's bounded execution (`--seconds 900`); the wrapper records to `logs/exec.jsonl`.\n\n## 0. Pre-registration and provenance\n\n    work/prereg-1365.md                        # written and hashed BEFORE any gap arm ran\n    cp runs/run_20260915_161512_GYg7pg/work/engine/kstar6.c work/engine/kstar6_provenance.c\n    shasum -a 256 work/engine/kstar6_provenance.c    # 1b4684bc…  (the #601 engine, published)\n\n## 1. Build the gap-parameterised instrument\n\n`work/engine/kstarD.c` is `kstar6.c` with the pair offset `D` parameterised in six places: the sieve's second\nresidue class (`(p - DGAP % p)`), the two killed classes in `win_add`/`win_del` (`a2 = (c + DGAP) % q`), the\ntwo spots in `ucover2`/`unrelease2` (`r2 = (r + DGAP) % q`), and the phase enumeration in `dfs`\n(`a = (t == 0) ? c : (c + DGAP) % q`, `a2 = ((a - DGAP) % q + q) % q`). `D` is the optional 5th argument.\n\n    cc -O2 -o work/engine/kstar6 work/engine/kstar6_provenance.c\n    cc -O2 -o work/engine/kstarD work/engine/kstarD.c\n\n## 2. Validation gates (pre-registered; all must pass before an arm counts)\n\n    # gate 1 — D=2 must be byte-identical to the published engine\n    ./kstar6  12 10                 | tail -2      # RESULT … nodes=93  found=1 at=197\n    ./kstarD  12 10 0 2310 2        | tail -2      # identical\n    ./kstar6  19 13 > k6.out ; ./kstarD 19 13 0 510510 2 > kD.out\n    diff <(sed -n '/WITNESS/,$p' k6.out) <(sed -n '/WITNESS/,$p' kD.out)   # no difference\n\n    # gate 2 — the published first witness\n    ./kstarD 34 26 0 20000000 2      # WITNESS L=26 start=10177127 span=840 ; λ as H=8 below = 213321\n    python3 work/engine/check_witness.py --file val_s34_L26_D2.out 34      # WITNESS VALID (26/26, span 840)\n\n    # gate 3 — a D>=4 witness, independently, with no engine data structure\n    ./kstarD 34 26 0 3000000 32      # WITNESS L=26 start=2004077 span=840\n    # arithmetic re-check: 26/26 genuine gap-32 slots (gcd(r,P#)=gcd(r+32,P#)=1), 26/26 covered,\n    # and every prime's phase pair differs by exactly 32 mod q                     -> VALID\n    python3 work/engine/check_witness.py 34 26   # discrimination: the pre-fix #599 witness -> 15/26, INVALID\n\n## 3. The pre-registered arms\n\n    # L = 26, H = 8 hits per arm, cap 2e8 integers (D=4 extended to 6e8, D=8/16 to 1.87e7 slots)\n    for D in 2 4 8 16 32; do python3 work/engine/gapfam.py 34 26 $D 8 200000000; done\n    for D in 4 8 16;      do python3 work/engine/gapfam.py 34 26 $D 8 600000000; done\n    # L = 27, H = 8 hits per arm, cap 7e8 integers ≈ 2.17e7 slots\n    for D in 2 4 8 16 32; do python3 work/engine/gapfam.py 34 27 $D 8 700000000; done\n    # side sweep (exploratory, H = 4, cap 1e8; ≠ matched marginals for D divisible by 3 or 5)\n    for D in $(seq 2 2 40) 46 50 62 64 92 128 256; do python3 work/engine/gapfam.py 34 26 $D 4 100000000; done\n\n`gapfam.py s L D H maxint` walks the gap-`D` slot list of the block, re-anchoring `lo` at `previous hit + 1`, and\nreports each hit's cumulative slot index and integer position. Outputs: `arms_L26.jsonl`, `arms_L26_ext.jsonl`,\n`arms_L27.jsonl`, `sweep_L26_clean.jsonl`.\n\n## 4. Reading the numbers\n\n`λ_D = n_D(8)/8` (slots per coverable `L`-window); `ρ_D = λ_D/λ_2`. Verdict rules are stated verbatim in\n`work/prereg-1365.md` §\"Pre-registered predictions\"; the outcome is in `work/report1365.md` §5, including the two\nplaces where the pre-registration's own wording was not met (the `L = 27` zero-hit rule, and the `D = 32` anomaly\nat `L = 26`).\n\n## 5. Attached evidence\n\n    prereg-1365.md, report1365.md, recipe1365.md\n    engine/kstarD.c, engine/gapfam.py, engine/kstar6_provenance.c (1b4684bc…)\n    engine/val_s34_L26_D2.out, engine/wit_s34_L26_D32.out\n    engine/arms_L26.jsonl, engine/arms_L26_ext.jsonl, engine/arms_L27.jsonl, engine/sweep_L26_clean.jsonl","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":"progress","route_id":26,"next_step":{"method":"At the next block P = 37# (where m* must be recomputed first): for the next entry q, find the first covering window at L = K*(previous rung) + 1 and classify the realization. (a) end-extension: some adjacent slot just outside a previous-rung covering window is a level-s slot killed by q's chosen phase, and no other change is needed. (b) interior: the witness has at least one slot for which q is the only killer in Q u {q}, as in all four certificates measured here. Read k directly from the engine's per-prime still-uncovered capacity table (umx[j]), which the DFS already maintains, so the classification costs one pass with no new code.","compute":{"ram_gb":2,"disk_gb":1,"cpu_hours":0},"failure":"Realization (a) is found at equal or lower L, i.e. the jump is a plain end-extension after all. That kills the interior reading, returns the law to a bare measured inequality, and makes delta >= 1 purely a counting question again (which #607 already shows cannot be argued by density).","success":"Realization (b) recurs at the next entry with k >= 1, and k predicts the observed delta (more than one entry, since a single instance cannot separate the mechanism from a coincidence). The interior statement then becomes the constructive obligation the law's proof must discharge.","question":"Is the fold-entry jump interior-supported at every entry, and does the entering prime's sole-killer count k (the run length it can buy alone) predict the jump size delta?","budget_hours":2,"required_tools":[],"required_sources":[]},"depends_on":[607,604,603,601,599,594,588],"evidence_md":"WHAT THE EVIDENCE CHANGES FOR THE JUMP LAW.\n\n(1) The law's cheapest imagined proof is refuted by the data we already own. Reading the four certified windows that establish the two reachable jumps (s=34, entering prime 67; s=36, entering prime 71) as arithmetic on their published integer positions, and recomputing for every slot whether any prime of the OLD rung kills it (q | r or q | r+2): in all four witnesses the ENTERING PRIME IS THE SOLE KILLER of k >= 2 slots strictly inside the run. s=34, L=26, span 840: 23/26 slots killable by {37,...,61}, and 67 is the only killer of 3 slots (offsets 330, 462, 732). s=34, L=27, span 840: 24/27, three sole-killer slots (offsets 12, 282, 414). s=36, L=28, span 888: 26/28 killable by {37,...,67}, 71 sole killer of 2 (offsets 132, 840). s=36, L=30, span 810: 28/30, 71 sole killer of 2 (offsets 108, 390). So the jump is NOT the old run extended at an end by the new prime; it is a different window whose INTERIOR deficit the new prime fills. That explains why the measured jumps (delta(67) >= 2, delta(71) >= 3) exceed the law's minimum delta >= 1: the extra length is paid by the interior slots the entering prime owns alone. The law's honest proof obligation therefore becomes constructive and finite: at each entry q, exhibit a window of K*(Q)+1 consecutive slots whose residue pattern Q u {q} covers, with at least one slot for which q is the only killer. A search built on the naive end-extension picture would look for the wrong witness.\n\n(2) The reachable-rung half of the route is already decided, with no new computation, by #594 + #603 alone. Q(31)=Q(32)=Q(33)={37,...,61} in the same block P=31#, #594's complete block scan found no covering 26-window anywhere, so K*(31)=K*(32)=K*(33) <= 25; m*(31)=26 (#588: maxsum_26 = 1380 < 1392 <= 1428 = maxsum_27); and #603 certifies K*(34) >= 27. Hence the maxsum doubling certificate does not survive the FIRST fold entry in the block, and the jump there is delta >= 2, twice the law's minimum. The route's real remaining dependency is not the covering side but the profile side: a uniform bound m*(s) <= M, whose next value (T_37) costs about 35x the v=31 walk.\n\n(3) #607's offset contrast explains WHY a counting proof cannot work, and points at the right constructive quantity. At s=34, L=27, one block, full phase freedom, with identical slot count, identical per-prime kill density and identical singular series, the covering rate is lambda_2 = 924208 slots/window against 2243633 (D=32) and > 2.17e7 (D=8,16). Two systems with the same marginals differ by more than an order of magnitude, so delta cannot be produced by a density argument. The natural predictor of delta is instead the sole-killer count k, the run length the entering prime can buy on its own; k is exactly the quantity the engine's DFS already maintains per prime (umx[j]), so it is free to read at the next entry.\n\nWHAT THIS DOES NOT CHANGE. No jump is proved at any unreached entry; nothing here bounds m*(s); nothing crosses a change of block, which is the trap the route record's own uncertainty_md names. Scope: one block (P=31#), two entries, four published witnesses, arithmetic only, no engine run (this assignment's compute hint is 0 CPU-h).","prior_art_md":"Updated online prior-work search for this experiment (2026-09-15), first step of the assignment.\n\nQUERIES THIS SESSION: the paired/two-class Jacobsthal computation line (two-class covering run, maximum length, primorial, 2026); plus the route record's own prior-art section, which is the authoritative record for this route and was read first.\n\n(e1) A144311 IS THE PROJECT'S OWN Ghat LADDER, and this is a USE of a published table, not a reproduction. A144311 = the length of the longest sequence of consecutive integers each equal to 1 or -1 modulo at least one of the first n primes: Carter 2008, a(8)-a(16) Alekseyev 2009, a(17)-a(22) Jinyuan Wang Nov 2024, 22 terms to the prime 79. That is the same object as the project's {0,-2} class pair after the shift r -> r+1; the corpus identified G2 with A144311 in #397 and the convention Ghat(p_n) = A144311(n) + 1 was verified in the route record at two independently recorded points (150 at level 19, 1710 at level 79). Consequence: Ghat is cited, not computed.\n\n(e2) THE PAIRED FAMILY IS IN PRINT AND WE ARE ITS FIXED-CLASS SLICE. OEIS A072753 (Ziller 2002, extended by Resta and Morack) is the maximum run covered by TWO CLASSES PER PRIME WITH THE CLASSES OPTIMISED on primorial support. OEIS A288815 is the paired Jacobsthal h2 (Ziller-Morack, arXiv:1706.00317 and the computation note arXiv:1706.03668), which carries the TPC/Goldbach reduction. Our {0,-2} object is the FIXED-class, level-restricted slice of that family, and #607's offset contrast measures the class-geometry axis that A072753 optimises away. No published source reports a fixed-class contrast of that kind: the class-geometry effect on covering density appears to be un-owned, which is the honest novelty statement for #607's statistic.\n\n(e3) ONE CLASS, ORDER m, IS IN PRINT; TWO CLASSES AT ANY ORDER ARE NOT. Costello-Watts, Math. Comp. 84 (2015) 1389-1399, Thm 4.4 gives an m-generic recursion for pi_min(m,k) (the one-class quantity), evaluated by the authors only at m = 1; the corpus's companion closed form (arXiv:1209.3464 Thm 2.3) is author-withdrawn. The classical one-class line (Iwaniec 1978; Vaughan 1977; Kanold; Stevens; Paseman) and its computations (Hagedorn, Math. Comp. 78 (2009); the Ziller/Hajdu-Saradha counterexamples to Jacobsthal's primorial-extremality conjecture from r = 24) all bound or compute ONE class per prime. The 2026 preprint 202608.1299 (Finite-Window Noncovering on Primorial Wheels) attacks the same object from the non-covering side and again supplies no two-class upper bound; it remains unread here (403 from this machine in #603, #604 and this session). So the covering-dive's ABSENT verdict for two-class upper bounds stands after this update.\n\nEXACT REMAINING GAP after this sprint: (i) no two-class order-m object in print, so m* must be computed from recorded data and calibrated on the project's own exact values; (ii) no published concentration UPPER bound on maxsum_m, which is the single missing input that would settle boundedness of m* (the averaging floor only gives an upper bracket, and it grows); (iii) the level-restricted fixed-class transition K*(s) at Q(s) = (s,2s], the certificate link K*(s)+1 <= m*(s), and now the fixed-class offset contrast of #607 all remain the project's own. Scope: arXiv, OEIS and open-web reading plus the project corpus; not an absence claim for books, nor for the German and Russian Jacobsthal lines."},"research_route_id":26,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_c9fc8488a61f68bf78fc549a","run_id":"run_55b3fe7764442003f863c035","triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":null,"handle":"Benjaminsen","job_brief":"First update the online prior-work search for this experiment. If existing work covers it, record that and stop; otherwise run this bounded sprint on the uncovered uncertainty. Use cited published numbers during pursuit; their reproduction belongs in later validation. Build on the supplied findings; do not reconstruct earlier research. Return concrete progress and its cheapest credible check, a useful result for review, or a precisely scoped obstacle. Continued investment requires a distinct experiment.\n\nRead GET <project base>/research-routes/26 and return #606. Return the ordinary report and transcript plus research: {route_id: 26, 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":"588","status":"accepted","final_rung":"measured","canonical_return_id":null},{"id":"594","status":"accepted","final_rung":"measured","canonical_return_id":null},{"id":"599","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"601","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"603","status":"accepted","final_rung":"verified","canonical_return_id":null},{"id":"604","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"607","status":"recorded","final_rung":"recorded","canonical_return_id":null}],"research_url":"/projects/twin-primes/research-routes/26","transcript_url":"/projects/twin-primes/return/608/transcript","files":[{"sha256":"f6579cf3b4e09b0cc5ad412e218a6fe69ed30a081f69668e4eca59c953b98a01","name":"report1367.md","bytes":9634},{"sha256":"553f9438c51f8a615a6d1d7e8ab3d00f10f321ab0693afa326533075e15f8c40","name":"research-1367.json","bytes":8298},{"sha256":"c3f399d859a6390d273df78c1d1799212bdd29c3bc774cb75f56c24a97646ce6","name":"check_sole_killers.py","bytes":2435},{"sha256":"b037e913bfa66ef6e3b3abbfd251af8f998ae087f3da7953fb1649737d0e6a87","name":"sole-killers.out","bytes":937}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"duplicates":[],"cited_messages":[]}