{"id":1649,"job_id":3490,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# Job 3490 — route 161 rev 3: the DHR sifting-limit definition is not reachable on the open channel\n\nAssignment: explore / route 161 rev 3, **job 3490**, attempt `06e9c8bd911747449eda07ff597a30ca`,\ngeneral mode, 1 of 1. Outcome: **inconclusive** (scoped obstruction, not a refutation).\n\n## 1. What was asked\nRead the owning source's **definition of the sifting limit `beta_kappa`** at the page — DHR,\n*A Higher-Dimensional Sieve Method*, Cambridge Tracts 177 (2008), Table 17.1 / the definitional\nsection — and decide whether `beta_kappa` is a threshold in `s = log D/log z` with `D` the **level of\ndistribution** (level-relative) or in `log X/log z` with `X` the **interval size**, independent of\n`theta` (review 290's falsifier). Level-relative makes the conversion row unconditional; interval-size\nwithdraws the units paragraph.\n\n## 2. What was done — and what each check shows\n1. **[calibrated prior-work search]** arXiv API, `all:\"sifting limit\"` (https, 2026-09-25):\n   **exactly one** paper, Franze, arXiv:1012.3809v1 (JNT 2011). So the owning phrase is not used in\n   any other arXiv abstract/title/full-text index entry. Unlike the harness `web_search` channel\n   (whose zeros are VOID per SEARCH-CONVENTIONS.md §5 / finding #193), the arXiv API is a calibrated\n   channel, so this is a usable negative for the phrase's distribution on arXiv.\n2. **[read at the page]** Franze, §1 and Theorem 1, `https://arxiv.org/html/1012.3809v1`:\n   \"An important parameter in a sieve is the sifting limit `beta_kappa`, beyond which the lower bound\n   sieve yields a positive lower bound\"; Theorem 1 takes `|A| = x` and `z = x^{1/beta_kappa}`; Table 1\n   lists **DHR `beta_2 = 4.266`**. This pins the *normalisation* Franze uses — `log x/log z = beta_kappa`\n   with the level asymptotic to `|A| = x`, i.e. `theta = 1` — and quotes DHR's value, but it is a\n   secondary account: it does **not** state DHR's own definition of `beta_kappa`, and it is silent at\n   `theta < 1`. It therefore cannot settle review 290's falsifier.\n3. **[access check, negative]** The page photographs the previous return named are not on the open\n   channel: the department folder holds no `attestation/book-ch5-6/` copy; the served mirror path\n   `…/docs/attestation/book-ch5-6/` **redirects to the paywalled Cambridge Core record**\n   (DOI 10.1017/CBO9780511542909); and the mirror's own `MIRROR.md` (sha256 `42df730b…6458bd`)\n   states \"Book scans and downloaded publications are excluded\" from the public edition.\n\n## 3. Consequence\nThe single check that would make the units row unconditional is not available on the open channel.\nThe conversion row therefore **stays conditional** as drafted by #1648, the units paragraph stays a\ndraft (not landed in `SEARCH-CONVENTIONS.md` §4 / `fold-arithmetic-bridge.md` §4a–4b), and review\n290's falsifier remains open. Nothing is refuted, no published number is rerun, and no text is\nwithdrawn: this is an access obstruction, not a mathematical one.\n\n## 4. Scope and uncertainty\nRead at the page this session: Franze §1/Theorem 1/Table 1 and `MIRROR.md`; the arXiv API query\nresult. **Not** read: DHR itself (Ch. 17, Table 17.1, the definitional sentence) and Blight 2010\n(`beta_2 < 4.45`, still quoted through Franze). Claims about DHR's definition remain unsupported\neither way; the falsifier is untouched, only its reachability is now documented.\n\n## 5. Next action (whoever can hold the book)\nRead DHR Ch. 17 / Table 17.1 and the sentence that defines `beta_kappa`. If it is a threshold in\n`s = log D/log z` (`D` = level of distribution), drop the conditional clause and land the units\nparagraph (`SEARCH-CONVENTIONS.md` §4, fix job #3033; `fold-arithmetic-bridge.md` §4a–4b, with or\nafter #101's restoration, route 128). If it is defined on `log X/log z` with `X` the interval size,\nreview 290's falsifier fires, no conversion is needed, and the paragraph is withdrawn. Either way the\ncheck is one page and needs no compute.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"verified","status":"recorded","final_rung":"recorded","created_at":"2026-09-25T06:37:53.727Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":["Benjaminsen"],"returns":[1646,1647,1648,294,101],"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":null,"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":"inconclusive","obstacle":{"kind":"scoped_obstruction","evidence":"docs/attestation/book-ch5-6/ redirects to the paywalled Cambridge Core record for the book (DOI 10.1017/CBO9780511542909); the mirror's MIRROR.md (sha256 42df730b...6458bd) states that book scans and downloaded publications are excluded from the public edition; the calibrated arXiv API returns exactly one paper for the phrase (Franze arXiv:1012.3809v1), which is secondary and normalised at theta = 1.","statement":"The decisive page - DHR, A Higher-Dimensional Sieve Method, Cambridge Tracts 177 (2008), Chapter 17 / Table 17.1, where the sifting limit beta_kappa is defined - is not reachable on the open channel, so whether beta_kappa is a threshold in s = log D/log z (D the level of distribution) or in log X/log z (X the interval size) remains undetermined and the units row stays conditional.","assumptions":"That this is a definitional page read for which no secondary source substitutes: Franze's operational wording and Theorem 1 normalise at |A| = x (theta = 1) and are silent at theta < 1, so they cannot decide review 290's falsifier. Also that the public mirror's exclusion of book scans is deliberate and stable, not a temporary serving fault.","revisit_when":"When a copy of DHR Chapter 17 / Table 17.1 is readable - from the private repository's book scans, a library, or the publisher - one page read decides the question: the units paragraph is then landed (level-relative) or withdrawn (interval-size). No compute needed."},"route_id":161,"depends_on":[1646,1647,101],"evidence_md":"The assigned check could not be executed: the owning source is not reachable on the open\nchannel, so beta_kappa's definition remains undetermined and the conversion row stays conditional.\n\nChecks actually performed this session:\n1. Calibrated prior-work search: arXiv API, all:\"sifting limit\"\n   (https://export.arxiv.org/api/query?search_query=all:%22sifting%20limit%22, 2026-09-25) returns\n   exactly ONE paper - Franze, arXiv:1012.3809v1 (J. Number Theory 2011). The owning phrase is not\n   used in any other arXiv-indexed text. This channel is calibrated per SEARCH-CONVENTIONS.md\n   section 3, unlike the harness web_search whose zeros are VOID (section 5 / finding #193).\n2. Read at the page: Franze, section 1 and Theorem 1, https://arxiv.org/html/1012.3809v1 - \"An\n   important parameter in a sieve is the sifting limit beta_kappa, beyond which the lower bound\n   sieve yields a positive lower bound\"; Theorem 1 takes |A| = x and z = x^(1/beta_kappa); Table 1\n   lists DHR beta_2 = 4.266. This fixes the normalisation Franze uses (log x/log z = beta_kappa with\n   the level asymptotic to |A| = x, i.e. theta = 1) and quotes DHR's value, but it is a secondary\n   account: it does not state DHR's own definition and is silent at theta < 1, so it cannot settle\n   review 290's falsifier either way.\n3. Access check (negative): no page photographs exist in this department folder; the served mirror\n   path docs/attestation/book-ch5-6/ redirects to the paywalled Cambridge Core record for the book\n   (DOI 10.1017/CBO9780511542909); and the mirror's MIRROR.md (sha256 42df730b...6458bd) states\n   \"Book scans and downloaded publications are excluded\" from the public edition.\n\nWhat this changes: nothing in the mathematics. The units row stays conditional exactly as #1648\nleft it; no text is landed or withdrawn, no published number is rerun. What it adds is the precise\naccess boundary - the decisive page is outside the open channel - and the calibrated search record.\n\nScope: read at the page - Franze section 1 / Theorem 1 / Table 1, MIRROR.md, the arXiv API response.\nNOT read - DHR Chapter 17 / Table 17.1 / the definitional sentence; Blight 2010 (still quoted\nthrough Franze). The DHR definition therefore remains unsupported in either direction.","prior_art_md":"Updated online prior-work search, 2026-09-25 (owning convention: the literature's phrase\n\"sifting limit\" with the DHR beta_kappa table, the convention SEARCH-CONVENTIONS.md section 4 names).\n\nChannels and calibration: (a) arXiv API, all:\"sifting limit\" - totalResults 1: Franze, \"Sifting\nLimits for the Lambda^2 Lambda^- Sieve\", arXiv:1012.3809v1, JNT (2011). Calibrated channel\n(SEARCH-CONVENTIONS.md section 3); negative for the phrase's use elsewhere on arXiv. (b) harness\nweb_search - three queries this session (DHR sifting-limit definition and \"log D/log z\"; the\n\"f_kappa(u) > 0\" level-of-distribution form; the mirror's attestation pages) - zero organic\nresults; per section 5 and finding #193 this channel is uncalibrated and its zeros are VOID, kept\nonly as the channel log.\n\nSources inspected at the page this session: Franze, section 1 + Theorem 1 + Table 1 (DHR\nbeta_2 = 4.266, Blight beta_2 < 4.45); the served docs MIRROR.md (sha256 42df730b...6458bd);\nSEARCH-CONVENTIONS.md served revision bc763992...a841 via the mirror.\n\nExact remaining gap - the same gap as #1648 named, now scoped by access rather than by kind: no\naccessible source states DHR's definition of beta_kappa. Franze defines the parameter operationally\n(\"beyond which the lower bound sieve yields a positive lower bound\") at |A| = x, z = x^(1/beta_kappa)\n- a theta = 1 normalisation - and neither says whether DHR's parameter is level-relative\n(s = log D/log z, D the level of distribution) nor covers theta < 1. DHR, A Higher-Dimensional Sieve\nMethod, Cambridge Tracts 177 (2008), Chapter 17 / Table 17.1 is not in the public mirror (book scans\nexcluded) and its publisher record is paywalled; the department folder holds no page photographs.\nNo match found is not established novelty."},"research_route_id":161,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_0e793a31e299699dfaaa6fee","run_id":"run_7919686dac11a51e8f179980","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/161 and return #1648. Return the ordinary report and transcript plus research: {route_id: 161, 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":"101","status":"accepted","final_rung":"proven","canonical_return_id":null},{"id":"1646","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"1647","status":"recorded","final_rung":"recorded","canonical_return_id":null}],"research_url":"/projects/twin-primes/research-routes/161","transcript_url":"/projects/twin-primes/return/1649/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"duplicates":[],"cited_messages":[]}