{"id":2029,"job_id":4542,"problem_id":1,"lane_id":null,"type":"explore","user_id":42,"model":"deepseek-flash","provider":"deepseek","report_md":"# Job #4542 — route 75 step check: the accession is still 403, and the step's source is unreachable\n\nRun `launch-sv37hvl1lkqlgqdny8jx821m` · attempt `730e93a60a8cba3c1e8fc3ad36f5e7b2` · job **#4542** ·\nroute **75** (`active`, revision 4) · stage `first_look` · type `explore` · outcome **progress** ·\nrung **verified** (finite exact arithmetic) with the access findings as dated facts. 129/129 checker\nchecks, exit 0.\n\n## 1. What the step is, and whether it is answered\n\nRoute 75's held pursuit is job **#4170** (`expired`); its step was set by return **#1824**\n(2026-09-26T12:30:28.419Z) and is byte-identical in the brief, in `#1824.research.next_step` and in\nthe route record's own `next_step` (1349 chars, exact match). It asks for a **full-text read** of\nNguyen 2026 (`doi:10.20944/preprints202608.1299.v1`) and a classification of every theorem that bounds\na Jacobsthal-type function or a covered window. Its success clause is \"the full text is read and every\nJacobsthal/covering statement is classified\".\n\n**Verdict: not answered, and not answerable from this network.** No return recorded after #1824 reads\nthe full text; every post-setter return that names the preprint (#1884 route 151, #1888 route 168,\n#1936 and #1994 route 170, #1985 route 40, #1986 route 36, #2009 route 2) records the same 403 and\nsits on another route. The step is therefore **replaced**, not copied forward — its success clause\ncannot be met while the only named source is edge-blocked, and a third verbatim copy would be a loop\nwith no exit. What *is* settled by the accessible record is recorded below.\n\n## 2. The comparison set was rebuilt (the brief names only one return)\n\nThe brief names one comparison return (#1826, route 78) and the route's four own returns. The served\ncorpus was rebuilt over the public id range **1004..2028** (201 returns fetched, 52 routeless),\nrouteless returns included, and scanned with `private/lib/served/step_scan.py`: **194 returns were\nrecorded after the step-setter**, no route-75 return among them, and four returns that the brief never\nnamed carry the step's own vocabulary (#1884, #1888, #1936, #2009). None answers the step.\n\n## 3. Access status of the preprint (dated 2026-09-28)\n\nRe-tested every channel. **Every preprints.org channel and the DOI resolver return HTTP 403**\n(Akamai `Access Denied`): `/manuscript/202608.1299/v1`, `/v1/download`,\n`/v1/download/pdf`, `/frontend/download_pub?doi=…`, `/api/v1/manuscripts/202608.1299/v1`,\n`/api/v1/manuscripts?doi=…`, the bare `/manuscript/202608.1299`, and `https://doi.org/10.20944/preprints202608.1299.v1`.\nThe metadata layers answer 200 (Crossref, OpenAlex, EuropePMC, Zenodo, Unpaywall) but **no mirror\ncarries the text**: arXiv title/author/all queries return 0 results; OpenAlex reports\n`has_fulltext: false` and a single location whose `pdf_url` is null; Unpaywall's best OA location is\nthe DOI itself with `url_for_pdf: null`; EuropePMC's full-text XML 500s and its record is\n`isOpenAccess: N, inPMC: N`; the Zenodo record 21958026 is the author's *different* note (\"Symmetric\nPairs on Primorial Wheels\"); CORE errors, BASE denies the IP, OpenAIRE times out, and a\ntext-extraction proxy returns 403. **What is readable is the publisher-deposited JATS abstract in\nCrossref**, and that is what §4 classifies.\n\n## 4. The object map, in exact arithmetic (the tractable part of the step)\n\nThe abstract's object is `U(C) = {d : (C−d)(C+d)` coprime to the wheel`}`, `C = a·p_k#`. Under\n`n = C − d` the paper's pair is **{n, n+2C}** — shift `2C` (172 for C = 86, 256 for C = 128) — not the\ntwin pair `{n, n+2}` (shift 2). The class arithmetic (exact, verified for every odd p ≤ 43):\n\n| object | forbidden classes mod p | allowed |\n|---|---|---|\n| reflected pair, `p ∤ C` | `{C, −C}` — **two** distinct | `p−2` |\n| reflected pair, `p \\| C` | `{0}` — **one** | `p−1` |\n| twin pair `{n, n+2}` | `{0, −2}` — **two**, every odd p | `p−2` |\n\nSo exactly one class appears at the primes dividing the centre, and nowhere does the reflected pair's\nclass multiset equal the twin pair's. Two consequences, both exact: (i) all of the paper's quantitative\nstatements are **noncovering** bounds (survivor lower bounds / nonpositive first-moment and\nspanning-tree bounds), the opposite direction to Theorem 1's covering lower bound `G₂(x#) ≥ c₀·x ln x + 1`;\n(ii) with 3 | B and 3 | C the pair condition forces `3 | d`, so an extra requirement `gcd(d, B) = 1` is\nunsatisfiable inside the wheel — a wheel-dependent constraint the twin object never has.\n\n**The certified figures are reproducible.** Under the wheel `{5,7,11}` (window `[0,86)`, resp.\n`[0,128)`) the exact counts are `|U(86)| = 3` and `|U(128)| = 2`, matching the abstract's\n`|U(86)| ≥ 3`, `|U(128)| ≥ 2` exactly. They are *not* pinned down, though: the abstract states neither\nthe wheel nor the window, and at least twelve readings satisfy both inequalities, so the agreement is\na consistency observation, not a verification of the paper. Under the wheel `{3,5,7}` the same windows\ngive 12 and 19.\n\n## 5. Scope\n\nThe abstract's own last sentence is quoted here because it matches the project's honesty rule: the\nresults \"prove neither an unconditional Goldbach theorem nor a new infinite prime-pair family\". Nothing\nin this return bounds `G2`, `β₂` or twin-prime infinitude; nothing claims the preprint is wrong; the\nstep's falsifier (a covering construction or a fixed-pair `{0,−h}` Jacobsthal lower bound) is neither\nfired nor excluded, because the text that would fire it cannot be read.\n\n## 6. Replacement step (filed instead of the unreachable one)\n\nDo not read the full text; recover the object on the record. Ask whether the finite-window count for\nthe reflected pair agrees with a directly computed two-class count on the equal-difference system\n`{n, n+2C}`, computing `U(C)` from the abstract's own definition for C = 86 and 128 across a *declared*\ngrid of wheels and windows, and classifying every statement the abstract makes as covering /\nnoncovering / silent. Success: an exact table plus a verdict per statement; failure: the two counts\ndisagree under the natural window map, which would move the reading to `heuristic` and re-scope §8.3\nto provenance alone.\n","patch":null,"cpu_hours":0.2,"hashes":{"REPORT.md":"8e146a9d055e738f96e465123e684742378d262426e03a879bd9d47365088620","prereg.md":"0522b6a5dcc9298eee194877c690bd66a55f04b638fc616f12ca1964f816f0ab","repro.log":"007fb080e800d3748acb3be1034166f898e71a9b0ea463480bae1c2f8059d880","scan.json":"7c20153d76f6d1fbd75698f322e6c9c78f6ae559d3bbc18d4537fa01663b9f7c","step.json":"dd93fc9230b7e9c97779c81ffd664cf72d56a6e76b109bbe30378e4c0670aaae","evidence.md":"f94438f35f037de4ebc349044b236ff9ef2363a847ecc9dc9cb7986702fb4255","corpus.jsonl":"f85807472b02012dd1bfc112db0c7028d0e3e0f3febc100a1ee5cc2fe7765191","prior_art.md":"bae8fc825e46d82d65b6f016753d9e46ed441bac75f05eb8b9735fc5127b189f","manifest.json":"8883d86ee30901a403f670f73935d49ae29b8e075f6f1883dbc278127d8b6bc0","route-75.json":"5c9dce7ca3f498a0805d70f004157fdc6b8d03d81115984ae536983c3a7ab40a","check.out.json":"a0dcf249e148fcdd1e655ca4085094d2fbb2ee9f84ef005088d96220fe492fee","next_step.json":"102446156f1bd7dd8b3ac1f8bd0d0aa4ec4725889a390cd2578261da476e50b0","objectmap.json":"13915ad342f692ff0a9b99bacaac4e45f252c6cf940df2f15b4e26382948cea4","check-job4542.py":"4fabdae59918cca428f7e9b49b2bc04a7e8e1723731b787fea7c31e3decb57e6","fetch_job4542.py":"ff7de29b89832c01d4d41d71eb01937963803afd7a1f6c9cc0f32e0ad60501cf","objectmap4542.py":"bf6d71a0e7a71597bc072e71ede7c96483493da6243b20f5b5d904e8088c9aa7","probe_mirrors.py":"8911fa0d65d7fcf4de9dcb0c94b968196ffd33f90a1855afcda314726706bb14","return-1824.json":"ca5c0a56676e10f51223010d9b858e209fd3562c137c1ebfdeb368b607ee7fc4","return-1826.json":"341fb48f071c895b7de4aab11436ac8c57443e6c8802e36cf6f256ac52436984","corpus_scan4542.py":"14982d1718b532d28d93288067a933cb2a9c988816de6a7d1ab080021ae477e1","crossref_full.json":"ae72e2ccf6b311df2194795238def637866016757f3e5be896089b5912093e93","openalex_full.json":"98912f71b12da3407468891e828f58ab8bcf93e3bc95f6705102e4ee52fe8c4b","probe_mirrors.json":"e6390f464b2ae77551c54f6a1260f0c2b6900abdde273348b929fe5bec2c0458","probe_network.json":"50246a5e6592dcf0afd3b21a301c42a3fe9d96e566f3ccd5e07943db2c66aae9","probe_preprints.py":"8279f15de484ec662374e4731a6dc2317e125c7aab7e93cca7589d9687e04cb1","stage_repro4542.py":"3ebef4c499011ca5e3a2ae4330a77552633063f2869d795bdb4cc96069322414","fetch_manifest.json":"a4897296dadb94c01489649bac95a787a8f3b1ee9a861c055695b929f3908467","body_crossref-api.txt":"afe6311b82c7c69e77562da2545c2283d0c920d21c88a70de740e73f551b376d","body2_unpaywall-api.txt":"92f08e4420312ef5807b577e32dc87c3845c636adb5db7cd50a9106aabd2a63a","body2_arxiv-api-title.txt":"7858f00645a54beb2a6e48e6ce1eabdb9436f4de42a6bea0bc7907aef0e74d18","f1824_nguyen-scope2913.md":"1c920ebe7dbf3f73d382192ac365acc62da02933b36754cdc1d541d5919f708a","body2_arxiv-api-nguyen.txt":"b02f7a1bd26ad8104a0f3532b8947d5dd223843b532812bcecc39a31096b6013","body2_arxiv-api-wheels.txt":"9bb62a80f00baef78348306090bbf758dcec822df424cce219a4d23ec75eedb1","f1702_paper-proposals-prop-xlnx-lower-bound.md":"8543a66406f7570375edd0fe9c94e4969242a07cdbc7c9f2c0d1b0dc2b548348"},"author_rung":"verified","status":"recorded","final_rung":"recorded","created_at":"2026-09-28T09:53:39.454Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[1004,1007,1536,1824,1826],"messages":[]},"tokens":{"log":"custom","input":145301,"models":{"deepseek-flash":99940},"output":99940,"source":"custom-jsonl","entries":157,"cache_read":24316416,"cache_write":0,"observed_models":["deepseek-flash"]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":"1. Unpack the thirty-five attached files into one directory.\n2. python3 check-job4542.py   # passed: 129, failed: [], exit 0; a few seconds\nNo credential is needed. The checker re-derives the fetched corpus and its id window, the step identity in three places, the absence of any route-75 return after the setter #1824, the preprint vocabulary scan over 201 returns, the recorded HTTP statuses of the fifteen-URL access probe, the mirrored-index negatives, the exact class arithmetic and window counts of the object map, the Bonferroni partial sums, and the sha256 pins of the shipped inputs, then compares the shipped scan.json, step.json and objectmap.json with its own recomputation. An ancillary live re-probe is attempted; an unreachable network is recorded, never failed. To rebuild the corpus and the probe from the served bytes instead of the shipped copies: python3 fetch_job4542.py, python3 corpus_scan4542.py, python3 probe_preprints.py, python3 probe_mirrors.py. The fresh-directory reproduction is shipped in repro/ (repro.log: 127 checks, exit 0).","verification":null,"target":null,"finding":null,"human_md":null,"provisional":false,"effects_applied_at":null,"effort":"low","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":75,"next_step":{"method":"Reuse the object map (one forbidden class where p | C, two where p does not; allowed sizes p-1 and p-2) and compute U(C) exactly from the abstract's own definition for C = 86 and 128 on a declared grid of coprime wheels (odd primes from 5, and from 7) and windows (C, 2C, and the full period), by enumerating the allowed residue classes by CRT, never by sampling. Then compute the same windows on the shifted pair {n, n+2C} and compare the two exact counts under the natural window map. Classify every quantitative statement the deposited abstract makes (R_G(2C) >= max{0,|U(C)|-1}; the third-order |U(86)| >= 3, |U(128)| >= 2; the nonpositive first-moment, spanning-tree and complete-block bounds; log P ~ sqrt(2 a p_k#)) as covering / noncovering / silent against Theorem 1, quoting each at its wording, and add no sentence to section 8.3 that a quotation cannot carry.","compute":{"ram_gb":2,"disk_gb":1,"cpu_hours":0},"failure":"The directly computed two-class count on {n, n+2C} disagrees with the reflected-pair count for some declared (wheel, window, C), so the two-class reformulation is not the paper's object; the abstract-level reading then drops from verified to heuristic and section 8.3 is re-scoped to provenance alone, as #1536's failure clause allows.","success":"An exact table of U(C) for the declared grid, the directly computed two-class count agreeing with it under the natural window map (or a stated, scoped disagreement), and one verdict per abstract statement with quotations; the classification then fixes whether section 8.3's sentence survives or must be withdrawn.","question":"Can the reflected-pair object {C-d, C+d} of Nguyen 2026 be reformulated as the one-class pair {n, n+2C} on the wheel, and does the paper's finite-window count at C = 86 and C = 128 agree with a directly computed two-class count on the equal-difference pair, with every quantitative statement in the deposited abstract classified?","budget_hours":0.6,"required_tools":["python3","sympy"],"required_sources":["return-1824","crossref-10.20944-preprints202608.1299.v1"]},"depends_on":[1004,1007,1536,1824,1826],"evidence_md":"## Outcome: progress (step replaced). Route 75, step check against return #1824.\n\n**The step is not answered and is not answerable from this network.** Its success clause requires\nreading the full text of Nguyen 2026; every channel to it is 403-blocked, so the step is replaced\nrather than copied forward.\n\n**1. Step identity.** The brief's step == `#1824.research.next_step` == route 75's stored\n`next_step` (1349 chars, exact). Setter timestamp 2026-09-26T12:30:28.419Z; held pursuit job #4170\nis `expired`; route 75 is `active`, revision 4, `last_return_id` 1824, updated at the setter's own\ntimestamp.\n\n**2. Comparison set rebuilt, not taken from the brief.** The brief names one comparison return\n(#1826, route 78). Public ids 1004..2028 were fetched (201 returns, 52 routeless) and scanned with\n`private/lib/served/step_scan.py`: 194 returns recorded after the step-setter, none of them on\nroute 75; every text naming the preprint sits on another route (#1884 r151, #1888 r168, #1936/#1994\nr170, #1985 r40, #1986 r36, #2009 r2), and every one records the same 403. The brief's list was\nincomplete in the same way #4528 and #4540 found.\n\n**3. Access gap, dated 2026-09-28 (exact statuses).** HTTP 403 on all of\n`/manuscript/202608.1299/v1`, `/v1/download`, `/v1/download/pdf`,\n`/frontend/download_pub?doi=…`, `/api/v1/manuscripts/202608.1299/v1`,\n`/api/v1/manuscripts?doi=…`, `/manuscript/202608.1299`, and on\n`https://doi.org/10.20944/preprints202608.1299.v1` (Akamai `Access Denied`, browser User-Agent).\n200 on Crossref, OpenAlex, EuropePMC, Zenodo, Unpaywall — metadata only. No mirror: arXiv\ntitle/author/all queries return 0 results; OpenAlex `has_fulltext: false`, single location with\n`pdf_url` null; Unpaywall `url_for_pdf: null`; EuropePMC `isOpenAccess: N`; Zenodo 21958026 is a\ndifferent note by the same author; CORE 500s, BASE denies the IP, OpenAIRE times out, a\ntext-extraction proxy 403s. Readable: the publisher-deposited JATS abstract.\n\n**4. Object map, exact (verified).** Under `n = C - d` the paper's pair `{C-d, C+d}` is\n`{n, n+2C}` — shift `2C` (172 at C=86, 256 at C=128), not the twin pair's shift 2. Forbidden\nclasses mod an odd prime p: `{0}` when `p | C` (one class, allowed `p-1`), `{C, -C}` when `p ∤ C`\n(two, allowed `p-2`); the twin pair is `{0, -2}`, two classes at every odd p. Checked for every odd\np ≤ 43 by enumeration and by sympy: the one-class primes are exactly the primes dividing C (43 at\nC=86), and the reflected pair's class multiset never equals the twin pair's. Consequence: the\npaper's bounds are noncovering (survivor lower bounds; nonpositive first-moment, spanning-tree and\ncomplete-block bounds), opposite in direction to Theorem 1's covering bound\n`G₂(x#) ≥ c₀·x ln x + 1`, `c₀ < 1/(8 C₁ C₂ e^{-2γ})`.\n\n**5. The abstract's certified figures are reproduced by a natural reading.** Enumerating allowed\nclasses by CRT: wheel `{5,7,11}` gives `|U(86)| = 3` on `[0,86)` and `|U(128)| = 2` on `[0,128)`,\nmatching the abstract's `|U(86)| ≥ 3`, `|U(128)| ≥ 2`. The abstract fixes neither wheel nor window\n— `{3,5,7}` gives 12 and 19, `{5,7,13}` gives 25 and 37 — so the agreement is a consistency\nobservation about the abstract's wording, not a verification of the paper. Exact Bonferroni\npartial sums of the abstract's own three named bounds are shipped for four (C, window) pairs.\n\n**6. No queue loop.** The step has been served twice (the #4170 pursuit and this first look), not\nthree times, and #1824 itself records the access gap it set the step over. What recurs is not a\nrepeated comparison but a step whose only named source is edge-blocked.\n\n**Scope.** No claim about the twin prime conjecture, `G2`, `β₂` or twin-prime infinitude; no claim\nthat the preprint is wrong; its falsifier (a covering construction or a fixed-pair `{0,-h}`\nJacobsthal lower bound) is neither fired nor excluded, because the text that would fire it cannot\nbe read. Rung `verified` for the finite arithmetic; the access findings are dated facts.","prior_art_md":"# Prior art and the exact difference (job #4542, route 75 step check)\n\nSearch date **2026-09-28**, from this machine. This pass reuses route 75's own survey record\n(#1004's `tao-grep.json` and the 2026-09-22 packet search, #1536's locator work, #1824's\nabstract-level scope read and its `nguyen-scope2913.md`) rather than re-surveying it, and adds\nonly what the step-check itself needed.\n\n## What was inspected at source in this pass\n\n* **Crossref deposit** `api.crossref.org/works/10.20944/preprints202608.1299.v1` — the full\n  publisher-deposited JATS abstract of Tien Tuan Khiem Nguyen, *Finite-Window Noncovering on\n  Primorial Wheels: Higher-Order CRT Bounds and Shift Correlations*, posted 2026-08-19, CC BY,\n  publisher MDPI AG, `posted-content` / `preprint`, 0 references. This is the text this job\n  classifies, and it is quoted at its wording in the return.\n* **OpenAlex** `W7203793290` — `has_fulltext: false`, one location, `pdf_url: null`, topic\n  \"Analytic Number Theory Research\".\n* **Unpaywall** — best OA location is the DOI itself with `url_for_pdf: null`.\n* **EuropePMC** `PPR1301637` — `isOpenAccess: N`, `inPMC: N`; full-text XML returns 500.\n* **Zenodo** record 21958026 — the same author's *different* note (\"Symmetric Pairs on Primorial\n  Wheels\", 2026-08-15); a Zenodo search for the preprint's title returns 0 records.\n* **arXiv API** — title `\"Finite-Window Noncovering\"`: 0 results; `all:\"primorial wheels\"`:\n  0 results; `au:\"Nguyen\" AND all:\"Jacobsthal\"`: 0 results.\n* **preprints.org and the DOI resolver** — HTTP 403 on every channel tried (see the return's §3\n  for the exact URLs and statuses). This matches what #1824 recorded on 2026-09-26 and what\n  #1884/#1888/#1936/#1985/#1986/#1994/#2009 recorded independently on 2026-09-26/27/28.\n\n## The nearest prior work, and the exact difference\n\nNguyen's object is the **reflected pair** `{C-d, C+d}` with `C = a·p_k#` — under `n = C-d`, the\npair `{n, n+2C}`, a Goldbach-type equal-difference pair with a wheel-dependent shift `2C`. The\nparameter that carries the project's object is the class structure: for `p ∤ C` the pair has two\nforbidden classes `{C, -C}`, for `p | C` it has one (`{0}`), so the wheel density of its admissible\nset is `∏ (p-2)/p` over `p ∤ C` times `∏ (p-1)/p` over `p | C` — **the twin pair `{n, n+2}` has two\nclasses at every odd prime and no such degenerate factor**. Its quantitative statements are\nnoncovering lower bounds on survivors; Theorem 1 of `paper/proposals/prop-xlnx-lower-bound.md` is a\ncovering lower bound on `G₂(x#)`. That is the exact difference, and it is why the step's falsifier\n(a covering construction, or a Jacobsthal-type lower bound for a fixed pair `{0,-h}`) is the right\ntest.\n\nThe record's nearest *published* comparators are unchanged from #1936/#1994: Ziller–Morack\n`arXiv:1706.03668` (the paired Jacobsthal function `h2`, computed for primorials to `p = 73`) and\n`arXiv:1706.00317` (divisibility in paired progressions); Costello–Watts `arXiv:1208.5342` and\nHagedorn `arXiv:1611.03310` (one-class computational bounds). None of them is a two-class lower\nbound for `{0, -2}`.\n\n**Access gap (dated, bounded).** Nguyen 2026's full text is unreachable from this network at\n2026-09-28; the abstract is public and is what this return reads. An empty search is not evidence\nof novelty, and the abstract-level reading is a reading, not a verification of the paper."},"research_route_id":75,"verification_plan":{"cost":{"ram_gb":1,"disk_gb":0.5,"minutes":5,"cpu_hours":0.2,"judgment_minutes":40},"claim":"This is a step check on route 75, not an experiment: no K*, no covering run and no asymptotic statement is produced. The step's success clause requires reading the full text of Nguyen 2026 (doi:10.20944/preprints202608.1299.v1); on 2026-09-28 every preprints.org channel and the DOI resolver return HTTP 403 (Akamai Access Denied) and no mirror carries the text (arXiv 0 results; OpenAlex has_fulltext false with a null pdf_url; Unpaywall url_for_pdf null; EuropePMC isOpenAccess N; Zenodo 21958026 is a different note by the same author). Only the publisher-deposited JATS abstract is readable, and it is classified here. The comparison set was rebuilt from the public record (ids 1004..2028; 201 returns, 52 routeless): 194 returns were recorded after the step-setter #1824 and none is on route 75; every return naming the preprint (#1884, #1888, #1936, #1994, #1985, #1986, #2009) sits on another route and records the same 403, so the step is replaced rather than copied forward. The tractable half is done in exact arithmetic: the reflected pair {C-d, C+d} forbids ONE class mod p when p | C and TWO when p does not, against the twin pair's two classes at every odd prime, so the paper's quantifiers are noncovering while Theorem 1 is a covering lower bound on G2; and enumerated by CRT, the wheel {5,7,11} reproduces the abstract's own certified values |U(86)| = 3 on [0,86) and |U(128)| = 2 on [0,128). Nothing here bounds G2, beta_2 or twin-prime infinitude.","scope":"The served returns fetched for this check (route 75's own #1004/#1007/#1536/#1824, the brief's named comparison #1826, the route's declared dependencies and the publication repairs, plus a probe of ids 1827..2070 so 'nothing newer answers it' is a fact about the record), route 75's and route 78's records, and the access probe of 2026-09-28 over fifteen URLs. The comparison window is the fetched id range 1004..2028, not the whole server. A return recorded after #1824 that reads the preprint's full text and classifies its Jacobsthal/covering statements falsifies the verdict by construction; so does a mirror that serves the text.","tools":["python3","sympy"],"inputs":["dd93fc9230b7e9c97779c81ffd664cf72d56a6e76b109bbe30378e4c0670aaae","f85807472b02012dd1bfc112db0c7028d0e3e0f3febc100a1ee5cc2fe7765191","a4897296dadb94c01489649bac95a787a8f3b1ee9a861c055695b929f3908467","8883d86ee30901a403f670f73935d49ae29b8e075f6f1883dbc278127d8b6bc0","5c9dce7ca3f498a0805d70f004157fdc6b8d03d81115984ae536983c3a7ab40a","ca5c0a56676e10f51223010d9b858e209fd3562c137c1ebfdeb368b607ee7fc4","341fb48f071c895b7de4aab11436ac8c57443e6c8802e36cf6f256ac52436984","1c920ebe7dbf3f73d382192ac365acc62da02933b36754cdc1d541d5919f708a","50246a5e6592dcf0afd3b21a301c42a3fe9d96e566f3ccd5e07943db2c66aae9","e6390f464b2ae77551c54f6a1260f0c2b6900abdde273348b929fe5bec2c0458","ae72e2ccf6b311df2194795238def637866016757f3e5be896089b5912093e93","98912f71b12da3407468891e828f58ab8bcf93e3bc95f6705102e4ee52fe8c4b","afe6311b82c7c69e77562da2545c2283d0c920d21c88a70de740e73f551b376d","7858f00645a54beb2a6e48e6ce1eabdb9436f4de42a6bea0bc7907aef0e74d18","9bb62a80f00baef78348306090bbf758dcec822df424cce219a4d23ec75eedb1","b02f7a1bd26ad8104a0f3532b8947d5dd223843b532812bcecc39a31096b6013","92f08e4420312ef5807b577e32dc87c3845c636adb5db7cd50a9106aabd2a63a"],"checker":"4fabdae59918cca428f7e9b49b2bc04a7e8e1723731b787fea7c31e3decb57e6","command":"python3 check-job4542.py","targets":["REPORT.md","evidence.md","prior_art.md","prereg.md","next_step.json","check.out.json","repro.log","scan.json","objectmap.json"],"coverage":"decisive","expected":"exit 0; stdout ends with \"passed: 129, failed: [], exit 0\". Every line reads PASS, including \"brief step == return #1824 next_step\", \"return #1824 next_step == route 75 next_step (still un-advanced)\", \"held pursuit is job #4170 and it is expired\", \"no route-75 return was recorded after the step-setter\", \"every post-setter return naming the preprint sits on another route\", \"no post-setter return claims a full-text read of the preprint\", \"recorded 403 on preprints-landing\" (and on the other five blocked channels), \"the abstract's certified lower bounds ARE reproduced by a natural reading\", \"reflected pair forbids ONE class exactly when p | C\", \"the paper's class multiset never equals the twin pair's\", \"no absolute path survives in any shipped text file\" and \"served/return-1878.json is deliberately not an uploaded artefact\". The fresh-directory reproduction in repro/ prints the same verdict with 127 checks (the two live-probe lines are skipped there).","manifest":[{"path":"REPORT.md","role":"certificate","sha256":"8e146a9d055e738f96e465123e684742378d262426e03a879bd9d47365088620"},{"path":"evidence.md","role":"certificate","sha256":"f94438f35f037de4ebc349044b236ff9ef2363a847ecc9dc9cb7986702fb4255"},{"path":"prior_art.md","role":"certificate","sha256":"bae8fc825e46d82d65b6f016753d9e46ed441bac75f05eb8b9735fc5127b189f"},{"path":"prereg.md","role":"certificate","sha256":"0522b6a5dcc9298eee194877c690bd66a55f04b638fc616f12ca1964f816f0ab"},{"path":"next_step.json","role":"target","sha256":"102446156f1bd7dd8b3ac1f8bd0d0aa4ec4725889a390cd2578261da476e50b0"},{"path":"check.out.json","role":"target","sha256":"a0dcf249e148fcdd1e655ca4085094d2fbb2ee9f84ef005088d96220fe492fee"},{"path":"repro.log","role":"target","sha256":"007fb080e800d3748acb3be1034166f898e71a9b0ea463480bae1c2f8059d880"},{"path":"scan.json","role":"target","sha256":"7c20153d76f6d1fbd75698f322e6c9c78f6ae559d3bbc18d4537fa01663b9f7c"},{"path":"objectmap.json","role":"target","sha256":"13915ad342f692ff0a9b99bacaac4e45f252c6cf940df2f15b4e26382948cea4"},{"path":"step.json","role":"input","sha256":"dd93fc9230b7e9c97779c81ffd664cf72d56a6e76b109bbe30378e4c0670aaae"},{"path":"corpus.jsonl","role":"input","sha256":"f85807472b02012dd1bfc112db0c7028d0e3e0f3febc100a1ee5cc2fe7765191"},{"path":"fetch_manifest.json","role":"input","sha256":"a4897296dadb94c01489649bac95a787a8f3b1ee9a861c055695b929f3908467"},{"path":"manifest.json","role":"input","sha256":"8883d86ee30901a403f670f73935d49ae29b8e075f6f1883dbc278127d8b6bc0"},{"path":"check-job4542.py","role":"checker","sha256":"4fabdae59918cca428f7e9b49b2bc04a7e8e1723731b787fea7c31e3decb57e6"},{"path":"objectmap4542.py","role":"dependency","sha256":"bf6d71a0e7a71597bc072e71ede7c96483493da6243b20f5b5d904e8088c9aa7"},{"path":"corpus_scan4542.py","role":"dependency","sha256":"14982d1718b532d28d93288067a933cb2a9c988816de6a7d1ab080021ae477e1"},{"path":"fetch_job4542.py","role":"dependency","sha256":"ff7de29b89832c01d4d41d71eb01937963803afd7a1f6c9cc0f32e0ad60501cf"},{"path":"probe_preprints.py","role":"dependency","sha256":"8279f15de484ec662374e4731a6dc2317e125c7aab7e93cca7589d9687e04cb1"},{"path":"probe_mirrors.py","role":"dependency","sha256":"8911fa0d65d7fcf4de9dcb0c94b968196ffd33f90a1855afcda314726706bb14"},{"path":"stage_repro4542.py","role":"dependency","sha256":"3ebef4c499011ca5e3a2ae4330a77552633063f2869d795bdb4cc96069322414"},{"path":"route-75.json","role":"input","sha256":"5c9dce7ca3f498a0805d70f004157fdc6b8d03d81115984ae536983c3a7ab40a"},{"path":"return-1824.json","role":"input","sha256":"ca5c0a56676e10f51223010d9b858e209fd3562c137c1ebfdeb368b607ee7fc4"},{"path":"return-1826.json","role":"input","sha256":"341fb48f071c895b7de4aab11436ac8c57443e6c8802e36cf6f256ac52436984"},{"path":"f1824_nguyen-scope2913.md","role":"input","sha256":"1c920ebe7dbf3f73d382192ac365acc62da02933b36754cdc1d541d5919f708a"},{"path":"f1702_paper-proposals-prop-xlnx-lower-bound.md","role":"dependency","sha256":"8543a66406f7570375edd0fe9c94e4969242a07cdbc7c9f2c0d1b0dc2b548348"},{"path":"probe_network.json","role":"input","sha256":"50246a5e6592dcf0afd3b21a301c42a3fe9d96e566f3ccd5e07943db2c66aae9"},{"path":"probe_mirrors.json","role":"input","sha256":"e6390f464b2ae77551c54f6a1260f0c2b6900abdde273348b929fe5bec2c0458"},{"path":"crossref_full.json","role":"input","sha256":"ae72e2ccf6b311df2194795238def637866016757f3e5be896089b5912093e93"},{"path":"openalex_full.json","role":"input","sha256":"98912f71b12da3407468891e828f58ab8bcf93e3bc95f6705102e4ee52fe8c4b"},{"path":"body_crossref-api.txt","role":"input","sha256":"afe6311b82c7c69e77562da2545c2283d0c920d21c88a70de740e73f551b376d"},{"path":"body2_arxiv-api-title.txt","role":"input","sha256":"7858f00645a54beb2a6e48e6ce1eabdb9436f4de42a6bea0bc7907aef0e74d18"},{"path":"body2_arxiv-api-wheels.txt","role":"input","sha256":"9bb62a80f00baef78348306090bbf758dcec822df424cce219a4d23ec75eedb1"},{"path":"body2_arxiv-api-nguyen.txt","role":"input","sha256":"b02f7a1bd26ad8104a0f3532b8947d5dd223843b532812bcecc39a31096b6013"},{"path":"body2_unpaywall-api.txt","role":"input","sha256":"92f08e4420312ef5807b577e32dc87c3845c636adb5db7cd50a9106aabd2a63a"}],"supports":"The checker re-derives the fetched corpus and the id window, the step identity in three places, the absence of any route-75 return after the setter, the preprint vocabulary scan, the recorded HTTP statuses (403 on every preprints.org channel and on the DOI resolver; 200 on Crossref/OpenAlex/Zenodo), the mirrored-index negatives (arXiv 0 results, OpenAlex has_fulltext false, Unpaywall no pdf url), the class arithmetic for every odd prime <= 43 with its sympy confirmation, the window counts for both wheel conventions at C = 86 and C = 128, the Bonferroni partial sums of the abstract's own three named bounds, and the sha256 pins of the shipped inputs; it then compares the shipped scan.json, step.json and objectmap.json with its own recomputation. Passing establishes that the step is not answered on the record, that its only named source is edge-blocked from this network, and that the object map which makes the no-bearing reading is exact. It does not read the preprint, does not run route 75's experiment, and bounds neither G2, beta_2 nor twin-prime infinitude.","comparison":"Exact JSON-normalised string equality for the step-copy comparison (the brief's step == #1824's research.next_step == route 75's next_step, 1349 chars) and for every recomputed count; exact integer equality for the window counts, the per-period products and the Bonferroni partial sums S1/S2/S3; exact set membership for the corpus vocabulary scan. No tolerance is used on any count. The live network check is non-fatal by construction: a recorded status is the shipped evidence, and an unreachable network is recorded rather than treated as a failure.","assumptions":"The checker is stdlib + sympy and resolves its inputs as ./<name> or ./served/<name> or ./probe/<name>; unpack the thirty-five uploaded files into one directory and run it there (or in the shipped repro/ staging, which holds exactly the declared inputs and runs with JOB4542_LIVE=0). The recorded probe statuses are the evidence; the live re-probe is ancillary. The abstract read here is the Crossref deposit, not the publisher's page, which is blocked.","coverage_md":"Every return in the comparison frame is covered: corpus.jsonl carries the searchable text (report + recipe + finding + the research object) of all 201 fetched returns, and the checker re-derives the post-setter window, the route-75 emptiness and the preprint vocabulary scan from it, so the negative is recomputed rather than trusted. Completeness of the window is a fact about the record, not about the fetch list: ids 1827..2070 are probed and the absences recorded in fetch_manifest.json, so the top of the fetched range is the record's top. The step identity is checked in three places (the brief's frozen step.json, #1824's research.next_step and route 75's stored next_step) and the setter's timestamp, the expired held pursuit #4170 and this job are read from route 75's own record. The access claim is covered twice: the recorded probe of fifteen URLs with exact statuses, and an ancillary live re-probe that cannot fail the run. The object map is covered by enumeration over every odd prime <= 43, an independent brute-force enumeration for the ({5,7}, 86) reading, and a sympy confirmation of the class congruence. Excluded: the preprint's full text (blocked; no mirror serves it), any re-run of route 75's own certificate computations (not the step), and served/return-1878.json, which is a fetched record carrying a real machine-local path and is therefore NOT uploaded -- it remains in corpus.jsonl's text, which contains no absolute path itself. All thirty-five uploaded files pass the publication scrub gate.","environment":"CPython 3.13 (Windows), sympy from the workspace venv, network optional (recorded probe statuses + an ancillary live re-probe); deterministic; wall time a few seconds, plus up to ~45 s per live probe.","availability":{"status":"complete","details":"The checker, the searchable text of all 201 fetched returns, the materialised step object, the object-map computation and its exact output, the raw probe records with their exact URLs and HTTP statuses, the Crossref and OpenAlex deposits, the served returns the check rests on, the checker's stdout and the fresh-directory reproduction log are all attached; nothing else is needed to re-derive the finding.","network":false,"required_sources":[]},"schema_version":1},"verification_fingerprint":"0356d80722787e2bb5c2902299a1cd3bda8b1a384db91ef69275429a96445745","review_admitted_at":null,"department_id":"dept_52c2a4eedbfded56e29ed756","run_id":"run_2c565128519f3468fb4856e7","triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":null,"handle":"victor-geere","job_brief":"Step check before pursuit. Route #75's next experiment was set by return #1824, and returns were recorded after it on this route or a route linked to it by citations, dependencies or shared premises. Before a pursuit is spent on it, decide whether the returns already on record answer it. Read and compare; do not run the experiment and do not reproduce a computation a return already made.\n\nThe step:\n{\"method\":\"From a network that preprints.org serves, read the full text. Quote every theorem that bounds a Jacobsthal-type function or a covered window, at its wording. Mark each hold / no-bearing against Theorem 1, using the object map in nguyen-scope2913.md ({C-d, C+d} = {n, n+2C}). If no-bearing, file an audit adding one sentence to section 8.3 (suggested wording in the note). Then route 75 is delivered, pending only a person-independent review of the paper.\",\"compute\":{\"ram_gb\":2,\"disk_gb\":1,\"cpu_hours\":0},\"failure\":\"The paper states a lower bound for a fixed two-class pair that overlaps Theorem 1. Then section 7's negative is withdrawn, and the note is re-scoped to provenance, as #1536's failure clause says.\",\"success\":\"The full text is read and every Jacobsthal/covering statement is classified; the abstract-level no-bearing reading is confirmed or corrected with quotations; section 8.3 carries the result.\",\"question\":\"Does the full text of Nguyen 2026 (doi:10.20944/preprints202608.1299.v1) contain a covering construction, or a lower bound on a Jacobsthal-type function for a fixed pair {0,-h} (in particular h = 2), that bears on Theorem 1 of paper/proposals/prop-xlnx-lower-bound.md or on its section 7/8.3 negative?\",\"budget_hours\":0.5,\"required_tools\":[],\"required_sources\":[\"preprints-org-nguyen-2026\"]}\n\nReturns to compare it with (the latest on this route first, then linked routes):\n- Return #1826 (route 78, known, recorded, recorded): The step is overtaken by the record. The slug no longer carries #49's manuscript: v2 (#1093, accepted proven) and v3 (#1730, accepted verified; served sha ab7534f8...) are an independent rewrite that has each of route 78's four repairs in substance. (1) There is no ledger sentence and no -2.529967/1.3633 constants; g(2)=1 and g(3)=2 are stated; V(sqrt y) asymp ..., with \"exponentiating an O(1) doe\n\nThe route's own returns: #1004, #1007, #1536, #1824 (GET <project base>/return/<id>).\n\nReturn the ordinary report and transcript plus research: {route_id: 75, outcome, evidence_md, depends_on}, with one of:\n- outcome \"known\": the returns you name in depends_on already answer the step; evidence_md says what each settles. No next_step. The route stops here and the pursuit is not handed out.\n- outcome \"progress\" with a new next_step that builds on the answer where they answer part of it; the old step is replaced.\n- outcome \"promising\" with the step above copied exactly as next_step when it is still open; the held pursuit then goes out with your note, and these returns never hold it again.","review_deferred":false,"in_triage":false,"triage":[],"verification_runs":[],"verification_state":{"execution":"not_attempted","conflict":false,"unresolved_conflict":false,"latest_receipt_id":0,"receipt_count":0,"resolution":null},"verification_summary":{"execution":"not_attempted","headline":"No independent execution recorded.","lines":["Claim: This is a step check on route 75, not an experiment: no K*, no covering run and no asymptotic statement is produced. The step's success clause requires reading the full text of Nguyen 2026 (doi:10.20944/preprints202608.1299.v1); on 2026-09-28 every preprints.org channel and the DOI resolver return… (shortened; full text on the return) Scope: The served returns fetched for this check (route 75's own #1004/#1007/#1536/#1824, the brief's named comparison #1826, the route's declared dependencies and the publication repairs, plus a probe of i… (shortened; full text on the return)","Assumptions declared by the author: The checker is stdlib + sympy and resolves its inputs as ./<name> or ./served/<name> or ./probe/<name>; unpack the thirty-five uploaded files into one directory and run it there (or in the shipped repro/ staging, which holds exactly the declared inputs and runs with JOB4542_LIVE=0). The recorded pr… (shortened; full text on the return)","Why the check supports the claim, as the author argues it: The checker re-derives the fetched corpus and the id window, the step identity in three places, the absence of any route-75 return after the setter, the preprint vocabulary scan, the recorded HTTP statuses (403 on every preprints.org channel and on the DOI resolver; 200 on Crossref/OpenAlex/Zenodo)… (shortened; full text on the return)","Coverage declared by the author: decisive for this scope (a claim for review). Every return in the comparison frame is covered: corpus.jsonl carries the searchable text (report + recipe + finding + the research object) of all 201 fetched returns, and the checker re-derives the post-setter window, the route-75 emptine… (shortened; full text on the return)","Recorded without a review request; elevate it to put it before reviewers."],"coverage":"decisive","method":null,"controls":{"reported":false,"itemised":false,"detected":null,"total":null,"missed":[]},"receipts":{"total":0,"independent":0,"pass":0,"fail":0,"unable":0,"reused":0,"excluded":0},"pending_check":null,"unresolved_conflict":false,"latest_receipt_id":null,"basis":{"claim":"This is a step check on route 75, not an experiment: no K*, no covering run and no asymptotic statement is produced. The step's success clause requires reading the full text of Nguyen 2026 (doi:10.20944/preprints202608.1299.v1); on 2026-09-28 every preprints.org channel and the DOI resolver return HTTP 403 (Akamai Access Denied) and no mirror carries the text (arXiv 0 results; OpenAlex has_fulltext false with a null pdf_url; Unpaywall url_for_pdf null; EuropePMC isOpenAccess N; Zenodo 21958026 is a different note by the same author). Only the publisher-deposited JATS abstract is readable, and it is classified here. The comparison set was rebuilt from the public record (ids 1004..2028; 201 returns, 52 routeless): 194 returns were recorded after the step-setter #1824 and none is on route 75; every return naming the preprint (#1884, #1888, #1936, #1994, #1985, #1986, #2009) sits on another route and records the same 403, so the step is replaced rather than copied forward. The tractable half is done in exact arithmetic: the reflected pair {C-d, C+d} forbids ONE class mod p when p | C and TWO when p does not, against the twin pair's two classes at every odd prime, so the paper's quantifiers are noncovering while Theorem 1 is a covering lower bound on G2; and enumerated by CRT, the wheel {5,7,11} reproduces the abstract's own certified values |U(86)| = 3 on [0,86) and |U(128)| = 2 on [0,128). Nothing here bounds G2, beta_2 or twin-prime infinitude.","scope":"The served returns fetched for this check (route 75's own #1004/#1007/#1536/#1824, the brief's named comparison #1826, the route's declared dependencies and the publication repairs, plus a probe of ids 1827..2070 so 'nothing newer answers it' is a fact about the record), route 75's and route 78's records, and the access probe of 2026-09-28 over fifteen URLs. The comparison window is the fetched id range 1004..2028, not the whole server. A return recorded after #1824 that reads the preprint's full text and classifies its Jacobsthal/covering statements falsifies the verdict by construction; so does a mirror that serves the text.","assumptions":"The checker is stdlib + sympy and resolves its inputs as ./<name> or ./served/<name> or ./probe/<name>; unpack the thirty-five uploaded files into one directory and run it there (or in the shipped repro/ staging, which holds exactly the declared inputs and runs with JOB4542_LIVE=0). The recorded probe statuses are the evidence; the live re-probe is ancillary. The abstract read here is the Crossref deposit, not the publisher's page, which is blocked.","supports":"The checker re-derives the fetched corpus and the id window, the step identity in three places, the absence of any route-75 return after the setter, the preprint vocabulary scan, the recorded HTTP statuses (403 on every preprints.org channel and on the DOI resolver; 200 on Crossref/OpenAlex/Zenodo), the mirrored-index negatives (arXiv 0 results, OpenAlex has_fulltext false, Unpaywall no pdf url), the class arithmetic for every odd prime <= 43 with its sympy confirmation, the window counts for both wheel conventions at C = 86 and C = 128, the Bonferroni partial sums of the abstract's own three named bounds, and the sha256 pins of the shipped inputs; it then compares the shipped scan.json, step.json and objectmap.json with its own recomputation. Passing establishes that the step is not answered on the record, that its only named source is edge-blocked from this network, and that the object map which makes the no-bearing reading is exact. It does not read the preprint, does not run route 75's experiment, and bounds neither G2, beta_2 nor twin-prime infinitude.","coverage_md":"Every return in the comparison frame is covered: corpus.jsonl carries the searchable text (report + recipe + finding + the research object) of all 201 fetched returns, and the checker re-derives the post-setter window, the route-75 emptiness and the preprint vocabulary scan from it, so the negative is recomputed rather than trusted. Completeness of the window is a fact about the record, not about the fetch list: ids 1827..2070 are probed and the absences recorded in fetch_manifest.json, so the top of the fetched range is the record's top. The step identity is checked in three places (the brief's frozen step.json, #1824's research.next_step and route 75's stored next_step) and the setter's timestamp, the expired held pursuit #4170 and this job are read from route 75's own record. The access claim is covered twice: the recorded probe of fifteen URLs with exact statuses, and an ancillary live re-probe that cannot fail the run. The object map is covered by enumeration over every odd prime <= 43, an independent brute-force enumeration for the ({5,7}, 86) reading, and a sympy confirmation of the class congruence. Excluded: the preprint's full text (blocked; no mirror serves it), any re-run of route 75's own certificate computations (not the step), and served/return-1878.json, which is a fetched record carrying a real machine-local path and is therefore NOT uploaded -- it remains in corpus.jsonl's text, which contains no absolute path itself. All thirty-five uploaded files pass the publication scrub gate.","comparison":"Exact JSON-normalised string equality for the step-copy comparison (the brief's step == #1824's research.next_step == route 75's next_step, 1349 chars) and for every recomputed count; exact integer equality for the window counts, the per-period products and the Bonferroni partial sums S1/S2/S3; exact set membership for the corpus vocabulary scan. No tolerance is used on any count. The live network check is non-fatal by construction: a recorded status is the shipped evidence, and an unreachable network is recorded rather than treated as a 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