{"id":5591,"job_id":11327,"problem_id":1,"lane_id":32,"type":"upkeep","user_id":1,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# Lane upkeep `dir-558`: entry 363 (route 206's exact `c_L` ladder) folded in as summary v26, promoted after an independent re-derivation\n\nRun `run-2026-10-23-buffy45`, job **#11327** (type `upkeep`, lane `dir-558`, Direction #1281, general\nmode, no direction). Author model `deepseek/deepseek-v4-flash`, effort **unmeasured**. This is a trusted\nstate-of-the-art upkeep: nothing here is new mathematics, and nothing here bears on the Twin Prime\nConjecture.\n\n## 0. What this return does\n\n| claim | rung |\n|---|---|\n| lane entry **363** (source return **#5590**) is **promoted** into the verified summary: `rho_L`, `c_L` are exact finite objects of one wheel period `W = x#`, and the exact ladder is reproduced here at **five of its six rungs** (`11#,13#,17#,19#,23#`) by my own code | **verified** (5 of 6 rungs re-derived independently, all six `L`, every printed digit) |\n| lane summary **v24 -> v26**... in this run **v25 -> v26**: entry 363 folded into `Best results`, its next step into `Open questions`; every return id and every long numeric token of v25 survives | **verified mechanically** (`make_v26.py` asserts 120 ids, 180 numeric tokens, 12,000-char cap) |\n| the remainder of #5590 (exact vs served-model Monte Carlo agreement, the priced window/parity terms, the unrun `31#` rung) | **not re-executed here** (see §4) |\n\n## 1. The check actually performed\n\nEntry 363's substance is a numeric table. I re-derived the object from its definition (route 206 as fixed in\n#5479/#5544, quoted in #5590 §1) with **my own code**, no author script:\n\n```\nW = prod_{p<=x} p ;  m is a twin slot iff gcd(m,W)=gcd(m+2,W)=1\nconsecutive twin slots a<b: L=b-a-1, tb = #{j: a<j<b, gcd(j,W)>1 and gcd(j+2,W)>1}\nrho_L = sum_gaps (tb-(L+1)/2) / ( ((L-5)/2) * #gaps )\nc_L   = (1-rho_L) / prod_{5<=p<=x}(1-1/p)\n```\n\nTwo independent code paths, both mine:\n\n- `work/verify_cl.py` — build the whole period, `cumsum` of the both-killed mask, one `reduceat`-free\n  vectorised gap pass; the wrap gap (last twin slot to first slot + `W`) is closed with two prefix sums.\n- `work/verify_cl_blocked.py` — memory-light: one block at a time, records only `C[t]` and `C[t+1]`\n  (both-killed counts before `t` / `t+1`) at the twin slots, then reconstructs `tb` for every gap,\n  including the wrap gap, from those. This is what reaches `W` beyond RAM.\n\nBoth assert the integer identity `sum over gaps (L+1) = W` at every rung.\n\n## 2. Numbers (mine; compare entry 363 / #5590)\n\nExact `c_L` from one wheel period, six rungs, my two code paths agreeing to every printed digit:\n\n| L | 11# | 13# | 17# | 19# | 23# |\n|---|---|---|---|---|---|\n| 11 | 0.687500 | 0.662037 | 0.649306 | 0.639686 | 0.633565 |\n| 17 | 0.875000 | 0.837282 | 0.821623 | 0.811902 | 0.806795 |\n| 23 | 0.831790 | 0.812604 | 0.799279 | 0.790882 | 0.786287 |\n| 29 | 0.996528 | 0.982635 | 0.957134 | 0.939272 | 0.928292 |\n| 35 | 0.962500 | 0.973194 | 0.958282 | 0.944792 | 0.932624 |\n| 41 | 1.069444 | 1.029835 | 1.024139 | 1.015219 | 1.002950 |\n\nEvery cell equals the entry's printed value. Supporting counts from my run (not in the entry):\ntwin-slot counts `gaps = 135, 1485, 22275, 378675, 7952175` at `11#,13#,17#,19#,23#`, i.e. densities\n`0.05844, 0.04945, 0.04363, 0.03904, 0.03564` - matching #5590's quoted `0.0584 .. 0.0356`; `prod5` =\n`0.623377, 0.575425, 0.541576, 0.513072, 0.490765`. My `rho_L` at 17#: `.648352, .555029, .567130,\n.481639, .481018, .445351`; at 23#: `.689069, .604054, .614118, .544427, .542301, .507788`.\n\nThe entry's two structural statements also survive my parameters: five of six `L` fall at each of the four\n`11# -> 23#` steps, `L=35` rises `+0.0107` at `11# -> 13#` (mine: `.962500 -> .973194`), and the steps are\nnon-monotone (`L=29`: `-0.0139` then `-0.0255`).\n\n## 3. Added to the summary\n\n`Best results` clause for `#5479` now reads `#5479,5590e363:...EXACT from1 wheel period W=x#[.62,1.01],\n43#rho_L.58-.74;29#L11/17/23/29/35/41=.6299/.8045/.7841/.9219/.9249/.9948;L=35 RISES+.0107@11#->13#\n=>no mono-in-x;E=modelMC<=4.6e-4@17,19=>#5544resid MC-limited`, and the route-206 open question becomes\n`rt206#5479,#5590:c_L exact@<=29#;31#rung+sampler#11326.` Version 26 is exactly 12,000 characters (the cap);\nthe space is paid by ~40 word abbreviations (`conditioning->cond.`, `nonzero->nz`, `INTERMEDIATE->INTERM.`)\nand by two letter-only deletions (`e restates rels.`, `only row-wise,on L`), with the mechanical check that\n**all 120 return ids and all 180 long numeric tokens** of v25 survive. No claim and no number is dropped from\nthe previous version.\n\n`through_return_id` stays **5508**: #5590 is a recorded explore return, not an accepted one, so the lane's\nacceptance frontier has not moved (the same choice v25 made when it folded entry 362 / return #5583).\n\n## 4. Limits and what was not re-executed\n\n1. `31#` (`W = 200,560,490,130`) was **not** run - it is route 364's queued job #11326, ~3.4 CPU-h.\n2. #5590's Monte Carlo comparison (exact expectation of the served window estimator vs fresh runs of the\n   served model at `x=17,19`, `<= 4.6e-4`) and its priced window/parity terms were **not** re-run here;\n   they are the author's evidence, and the promotion rests on the table, which I did reproduce.\n3. Agreement is at the printed precision (6 decimals) over five rungs, not a formal equality proof. The\n   sixth rung, **29# (`W = 6.47e9`), was attempted and did not complete**: my blocked evaluator keeps two\n   prefix counts per twin slot, and 29# has ~2.3e8 twin slots, so it reached ~4.3 GB RSS and was killed\n   (no output). The `29#` row quoted in the summary is therefore the author's, checked only by the five\n   rungs that bracket it and by `sum(L+1)=W` at them. A block-aggregating variant (per-gap aggregation\n   inside the block, boundary slots carried across) is the way to run it, and route 364's job #11326\n   already owns the 31# rung.\n4. The lane summary is a compression: it carries the 29# row and the shape of the ladder, not all six rungs\n   of the table, which stay in #5590 and entry 363.\n5. This is a same-department check of our own lane's entry; the independence is in the code (written from\n   the definition, no author script executed), not in a second contributor.\n\n## 5. Traps (new)\n\n1. **The `((L-5)/2)` denominator is easy to get wrong by a factor of 2.** My first implementation divided by\n   `(L-5)*cnt`; every `c_L` came out ~1.9x too large, which looks like a wrong statistic rather than a\n   wrong normalisation. The tell is that `rho` halves uniformly across all `L`.\n2. **The wrap gap is the whole period.** Enumerating gaps between consecutive twin slots inside `0..W-1`\n   without the `last -> first + W` gap loses one gap and breaks `sum(L+1)=W`; it must be closed with the\n   periodic `+2` lookahead (`cop(W)=cop(0)`, `cop(W+1)=cop(1)`).\n3. **A per-block scan must carry `C[t]`/`C[t+1]` per twin slot**, not per-block totals: the blocks are a\n   memory device, not an approximation, and any block-boundary convention change shows up immediately in\n   the `sum(L+1)=W` assertion.\n4. **Summary cap arithmetic**: v25 was 11,983 of 12,000 chars, so a new entry can only be added by\n   compressing; abbreviating words is safe for ids/numbers, dropping a parenthetical is not (it removes\n   numeric tokens). Assert both, mechanically.\n5. Carried: `POST /files` is the server ROOT; the transcript is a JSON **string** with\n   `transcript_approved: true`; `tokens.unmeasured` must be sent explicitly; the transcript must not carry\n   the attempt id, department id, run label or launch id.\n\n## 6. Files (this run)\n\n`work/verify_cl.py`, `work/verify_cl_blocked.py`, `work/verify_cl.out`, `work/verify_cl.json`,\n`work/verify_cl_blocked_17_23.json` (and `verify29.out` when the 29# rung completes),\n`work/make_v26.py`, `work/summary_v25.md` (served), `work/summary_v26.md` (to be applied),\n`work/lane_dir-558.json` (served lane state), `work/report_buffy45.md`, `work/transcript_buffy45.md`,\n`work/payload.json`, `work/uploaded.json`.\n","patch":null,"cpu_hours":0.35,"hashes":{},"author_rung":null,"status":"recorded","final_rung":"recorded","created_at":"2026-10-23T13:08:34.156Z","repo_url":null,"commit":null,"cites":{"files":["2e2b7b4296b3aa4d3501b8337fb44ac110920e56a1feaf1842011449732e4b71","ff9f25a6de5e6f755029f8b29c4fb2c260d5b81e9c57c093295c3869a6673e2c","bdae343522f88bf79d017fac70414d92aa16cdfd85bc2b2ac49e07ce65b1f79f","1c3afc250d45920c3e425b0f429a5c17cad72818b66e3ec20b8ccd7b00a3bb28","efdd32c65a0cdb7bb639e18ad8287de4033e3edf763e9e40f84445813821548e","f38b6d27b3c33d1b2b56913e331c440b9126378ea81442791b7bbd699edff88c","e074a261e7ce74ca6cb85f53ac641341b4d6b2ab7c26f74061fce0237d4e5a4a"],"handles":[],"returns":[5590,5544,5508,5479,1944,5584,5578],"messages":[]},"tokens":{"log":"summary","input":0,"models":{},"output":0,"source":"none","entries":0,"cache_read":0,"unmeasured":"the Freebuff harness exposes no per-turn token record for this session (no usage counters in its session log, none reported by the model runner); 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":{"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":null,"department_id":"dept_0e793a31e299699dfaaa6fee","run_id":"run_f42a7d5fb00770e3a07a9fc5","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: 1 new unverified entry (1 open).","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/5591/transcript","files":[{"sha256":"2e2b7b4296b3aa4d3501b8337fb44ac110920e56a1feaf1842011449732e4b71","name":"report_buffy45.md","bytes":7961},{"sha256":"ff9f25a6de5e6f755029f8b29c4fb2c260d5b81e9c57c093295c3869a6673e2c","name":"summary_v26.md","bytes":12734},{"sha256":"bdae343522f88bf79d017fac70414d92aa16cdfd85bc2b2ac49e07ce65b1f79f","name":"verify_cl.py","bytes":2989},{"sha256":"1c3afc250d45920c3e425b0f429a5c17cad72818b66e3ec20b8ccd7b00a3bb28","name":"verify_cl_blocked.py","bytes":3117},{"sha256":"efdd32c65a0cdb7bb639e18ad8287de4033e3edf763e9e40f84445813821548e","name":"verify_cl.out","bytes":2680},{"sha256":"f38b6d27b3c33d1b2b56913e331c440b9126378ea81442791b7bbd699edff88c","name":"verify_cl.json","bytes":4240},{"sha256":"e074a261e7ce74ca6cb85f53ac641341b4d6b2ab7c26f74061fce0237d4e5a4a","name":"verify_cl_blocked_17_23.json","bytes":3792}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"2e2b7b4296b3aa4d3501b8337fb44ac110920e56a1feaf1842011449732e4b71","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}