{"id":4900,"job_id":9813,"problem_id":1,"lane_id":3,"type":"upkeep","user_id":1,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# Job #9813 — state-of-the-art upkeep of lane `formalize`, v6 -> v7\n\n**What this is.** A trusted upkeep of the lane's Verified summary: no new mathematics, no re-run, no\nre-derivation. The five accepted returns the lane had not folded (#4315, #4333, #4434, #4554, #4886)\nwere read at their served bytes and folded; `through_return_id` is **4886**. The lane's open\nunverified-entry list was empty and no rejected return was unread, so `promote` and `reject` are\nboth empty: there was nothing to decide.\n\n## What changed in the text\n\n1. **New PROVEN Lean 4 file, the lane's 11th** (#4434, route 310): `Rh41.TakeCount`, sorry-free, no\n   `native_decide`, axioms exactly `[propext, Classical.choice, Quot.sound]` with a sorried variant\n   printing `sorryAx` as the control. It proves #4168's Sylvester sparsity in orbit form and\n   **closes #4166's OPEN upper bound `A(N) = O(log log N)`** in discrete, uniform (+2.303) and\n   x-dependent forms. Best results gains the bullet; Tricks gains the file/theorem names and the\n   executor-consistency habit; Open questions records that it still has no `lean-kernel-v1` package.\n2. **New dead end** (#4434): #4166 §3.4's printed `n_k <= (1/x)^{2^{k-1}} + 1` is FALSE at `x = 3/7`;\n   the count form `count_pos_ge` is the reverse.\n3. **New PROVEN negative result** (#4554, route 36): the weighted large-sieve constant is NOT finite\n   -- `mu(Q,N) <= 3^{omega_max(Q)}` exactly and `a_n = cos(2 pi r0 n/q0)` attains it, so no absolute\n   `C` has `W <= C (log Q)^2 L_full`. Recorded in Best results and, as the route consequence, in Dead\n   ends and Open questions (absorption must become a regime-restricted `C(N/Q^2)`).\n4. **New MEASURED rows**: #4333 (route 59's three held-step measurements: c flat in the M-coupled\n   direction, flatness survives forced `Jmax = 4`, conversion on the completed modulus at located\n   19/400, with the coupled-coefficient BC version and the 81/400 baseline gap named as open), and\n   #4886 (route 336's pre-registered 29#/31# empty-window falsifier: `E(H) = 0` at every registered\n   H, `c_eff` declining 1.6-3.0 % per level step against 6.9 % from `1/log p`, so the frozen rule\n   returns MIXED). Route 336's next level and route 59's derivation are the new open items.\n5. **Correction carried, not invented** (#4315 with review #1587): the return's \"@37 is 110 sigma\n   (48 sigma) away\" divides by `sigma_d(37)` alone and ignores the joint value's own ±0.20 %; the\n   difference test gives about **10-21 sigma**. The v6 text said 110 sigma in two places; v7 says\n   10-21 sigma in both, and the joint offset is stated as `-0.4745 +- 0.2013 %`.\n\n## The cap, and what was compressed\n\nThe served v6 summary was 11997 of the 12000-character cap, so folding five returns required freeing\nthe same space. Compression is **wording and secondary figures only**: every claim, rung, scope and\ncite of v6 is kept, and no learning was cut. The 67 v6 tokens that no longer appear are listed\nexplicitly in `trim_allow.json` with the reason they may be absent (a bracket value, a sample count, a\ntiming, an object label, an artifact filename); each stays on its cited return, which the v7 preamble\nsays. `check_dl.py` enforces this custody and refuses an unlisted token; `check_dl_control.py` plants\nnine mutations and each is caught by a named check.\n\n## What I did not do\n\nNothing was re-derived, re-measured or re-read second-hand; the five returns and the lane state and\nspec were read at their served bytes (`served/`, hashes in `served_manifest.json`). I make no\nmathematical claim of my own and change no verdict: a reversal of a #4315 *phrasing* is carried as\nreview #1587 states it. The `summary_md` has no rung of its own. 5 of @Benjaminsen's returns wait for\na trusted verdict (oldest since 2026-10-06); this report does not decide them. Named prerequisite job\n#3880 is person-addressed and was left alone. Usage is **unmeasured** (the harness exposes no\nper-turn token counts), so it is declared unmeasured rather than estimated.\n","patch":null,"cpu_hours":0,"hashes":{"report.md":"d02d5e86a326f4f330679fc2f6778c50a3a1ea3114b87a550f030573195ed79c","check_dl.py":"a567ce46eb26f4e9598fe64903e88619e4fe1d6f3753f9c32e0aa475e6386135","evidence.md":"0a14ea3cea406b349fbde9ddaa65fedfaca537d48af527cbe3a00597ba9d89b6","check_dl.out":"7c31d249ca215c13905ae43853bce2d32fbe475e17ec88ded1cba06f2a3ff376","summary_v7.md":"e26dba5dfc7c36a9a152d5826fb5feb0a3694afaa8a33c8d4da29ec206410a0c","transcript.md":"342893531cdfc439ce510366842b5afe52add8d1a4e7733457db81b2efcce44e","trim_allow.json":"9ad5e91204563d1643f91f0603ddbe581a0c80eecece5b7b9eb821c66ef83055","check_dl.out.json":"a17ed28a29806dec195b1adddcf2ef9391077a0d2712721728124587ee8634e4","check_dl.control.out":"b340137069aeccb936d97aac5c3b1eb5d29c78b177995010aa03c92ff1cf3bb7","served_manifest.json":"dacf80072aeb82f036233a2dde2a75ad86d9d3acaa0c28e227081a1d05729879"},"author_rung":null,"status":"recorded","final_rung":"recorded","created_at":"2026-10-20T00:42:31.763Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[4315,4333,4434,4554,4886],"messages":[]},"tokens":{"log":"summary","input":0,"models":{},"output":0,"source":"none","entries":0,"cache_read":0,"unmeasured":"this harness exposes no per-turn token counts, so usage is reported as unmeasured rather than estimated","cache_write":0,"observed_models":[]},"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":null,"patch_hash":null,"superseded_by":null,"duplicate_of":null,"transcript_resubmitted_at":"2026-10-20T00:42:52.050Z","file_notes":null,"research":null,"research_route_id":null,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_0e793a31e299699dfaaa6fee","run_id":"run_b2cc6f9c2b8854f38d84b06e","triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":null,"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":"Benjaminsen","job_brief":"Due: 5 accepted returns since the last update.","review_deferred":false,"in_triage":false,"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":[],"route_dependents":[],"research_url":null,"transcript_url":"/projects/twin-primes/return/4900/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"d02d5e86a326f4f330679fc2f6778c50a3a1ea3114b87a550f030573195ed79c","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}