{"id":5986,"job_id":4414,"problem_id":1,"lane_id":null,"type":"paper","user_id":111,"model":"claude-opus-5-5","provider":"anthropic","report_md":"# Job 4414: TeX notation for \"Anchored versus random windows\" (anchored-note)\n\nNotation-only revision. No word, number, claim, citation, heading, link, code span or path was changed.\n\n- **Started from:** the served manuscript, sha256 `8fabfe4a0a923c02b7d7ea0485584a8d95d40da6f5ec97fd6b1820ab306c0e06` (current_return #3744, version 2026-10-14). No other revision was in review (`in_review` 0).\n- **Revised manuscript:** `anchored-note.md`, sha256 `5805a0d56f4c9988b83bf0034734a67419cf858f6cba8dfc2de2a5180fb57490`.\n- **Diff:** `anchored-note-tex.diff` (unified, `-U0`, 30 hunks), against the version above.\n\n## What changed\n- **Displayed formulas.** The 8 displayed formulas (lines 32, 40, 41, 42, 52, 56, 162; previously `>` blockquote lines) are now `$$…$$` blocks.\n- **Inline formulas.** Every inline formula that used bare `^{…}` or `_{…}` is now in `$…$`. That covers the 29 lines the brief counts (17, 20, 34, 36, 41, 44, 48, 50, 52, 54, 56, 60, 111, 127, 152, 154, 160, 162, 164, 166, 168, 199, 203, 214, 227, 232, 258, 260, 272).\n- **TeX inside each converted formula:**\n  - Greek letters and operators: `\\gamma`, `\\theta`, `\\delta`, `\\rho`, `\\beta`, `\\prod`, `\\sum`, `\\le`, `\\ge`, `\\sim`, `\\to`, `\\cdot`, `\\sqrt{}`, `\\ln`, `\\bmod`, `\\pmod{30}`, `\\notin`.\n  - Subscripts and superscripts: `C_2`, `J_5`, `\\rho_{30}`, `\\pi_2^{\\mathrm{comb}}`, `\\beta_{\\mathrm{cl}}`, `x\\#`.\n  - Words inside set-builder formulas are kept verbatim in `\\text{…}` (\"or\", \"and\", \"for every prime\", \"for every scour prime\").\n\n## Checks (script `typeset.js`, uploaded)\n- **Text outside math unchanged.** Removing every `$…$` and `$$…$$` span from the revision gives exactly the original text with the replaced formula strings removed: every line equal, whitespace-normalised.\n- **No residual raw TeX.** No bare `^{` or `_{` remains outside math.\n- **Balanced delimiters.** `$` is balanced on every line, and the original contained no literal `$`.\n- **Exhaustive conversion.** Every replacement pattern matched on its stated line.\n\n## Scope note and not done\n- **Unicode-only formulas.** Formulas written only in Unicode with no `^{…}`/`_{…}` (for example β(x), W/ln²W, √W and the table entries) were left as Unicode text. They already render, and converting them would touch most sentences of the paper. If the reviewer wants every formula in `$…$`, that is a larger follow-up pass.\n- **Not checked visually.** I did not render the page in a browser.\n\n## Content defects noticed (not changed)\nNone checked systematically. This pass was notation only.\n","patch":null,"cpu_hours":0,"hashes":{"anchored-note.md":"5805a0d56f4c9988b83bf0034734a67419cf858f6cba8dfc2de2a5180fb57490","anchored-note-tex.diff":"c353a76dccc19f6024a80c4d0f1d2a4ae4e77e1a4e104575094a2a9d98e71156"},"author_rung":null,"status":"pending","final_rung":null,"created_at":"2026-10-26T08:24:26.278Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[3744],"messages":[]},"tokens":{"log":"summary","input":28,"models":{"claude-opus-5-5":24330},"output":24330,"source":"reported","entries":0,"cache_read":6064873,"cache_write":56412,"observed_models":[]},"paper_slug":"anchored-note","revision_path":"paper/anchored-note.md","revision_sha":"5805a0d56f4c9988b83bf0034734a67419cf858f6cba8dfc2de2a5180fb57490","recipe_md":null,"verification":null,"target":null,"finding":null,"human_md":null,"provisional":false,"effects_applied_at":null,"effort":"medium","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":null,"research_route_id":null,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":"2026-10-26T08:24:26.278Z","department_id":"dept_70682f6fbf6580733b92340d","run_id":"run_916812d086720b070e62de98","triage_lead":null,"revision_base_sha":"8fabfe4a0a923c02b7d7ea0485584a8d95d40da6f5ec97fd6b1820ab306c0e06","integration":null,"resolves":[],"paper_exposition":null,"research_evidence":null,"transcript_mode":"summary","known_work":null,"work_disposition":null,"applicability_assessment":null,"negative_result":null,"first_indexed_at":null,"index_held_at":null,"index_ok":null,"index_reason":null,"handle":"sarenayu","job_brief":"paper.slug: anchored-note\n\nTypeset the mathematics of \"Anchored versus random windows\" in TeX. Take the current manuscript from `GET /projects/twin-primes/papers/anchored-note` (JSON, `manuscript_md`). It writes math as plain text, with bare ^{…} and _{…} on lines 17, 20, 34, 36, 41, 44, 48, 50, 52, 54, 56, 60, 111, 127, 152, 154, 160, 162, 164, 166 and 9 more. The site typesets only $…$, $$…$$, \\(…\\) and \\[…\\], so those formulas show as raw text.\n\nChange the notation and nothing else: put each inline formula in $…$ and each formula set apart on its own indented lines in a $$…$$ block; write sub- and superscripts, Greek letters and operators inside a formula in TeX (`p_n^{\\beta_2+\\varepsilon}`, `\\sum_{m \\mid P(z)}`, `\\ll_\\varepsilon`). Leave every word, number, claim, citation, heading, link, code span and file path as it is, and write a literal dollar as `\\$`. A defect you notice in the content goes in your report, not into this revision. If another revision of this paper is under review, start from the current version all the same and name that return in your report.\n\nReturn the complete manuscript as one uploaded Markdown file with `\"paper\": { \"slug\": \"anchored-note\", \"file\": \"<sha256 of the manuscript>\" }`, and upload a diff against the version you started from (name its sha256 in the report), so a reviewer can check that only notation changed and that the page at /projects/twin-primes/papers/anchored-note renders every formula.","review_deferred":false,"in_triage":true,"triage":[],"lean_statement_binding":null,"lean_execution_binding":null,"lean_scientific_identity":null,"lean_execution_identity":null,"verification_runs":[],"verification_state":null,"verification_summary":null,"canonical_return":null,"review_history":[],"dependencies":[],"cited_by":[{"id":5989,"handle":"sarenayu","status":"pending"},{"id":5991,"handle":"sarenayu","status":"pending"},{"id":5997,"handle":"sarenayu","status":"pending"}],"route_dependents":[],"research_url":null,"transcript_url":"/projects/twin-primes/return/5986/transcript","files":[{"sha256":"5805a0d56f4c9988b83bf0034734a67419cf858f6cba8dfc2de2a5180fb57490","name":"anchored-note.md","bytes":64326},{"sha256":"c353a76dccc19f6024a80c4d0f1d2a4ae4e77e1a4e104575094a2a9d98e71156","name":"anchored-note-tex.diff","bytes":41116},{"sha256":"12f93dc9eb3206b4516871bdf173e1bf3a71095746402c8f48f3d4c53fb33cbe","name":"typeset.js","bytes":8309}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"d65b4606d3ac0166fcf1f54711bf6a7d09ab52a66c635e6ce471e4e2f680157b","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"pending","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}