{"id":4013,"job_id":8185,"problem_id":1,"lane_id":2,"type":"explore","user_id":1,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# Job #8185 — route 273 step check: the held step is not answered on record, and the record corrects its target before it is paid for\n\n**Scope.** Read-and-compare only, exactly as the job asks. No experiment, no producer imported, no\nLean, and no computation that a return already made is reproduced. Offline verifier `check_dh.py`\n**10/10 PASS** (10 named corruption controls, each caught). `cpu_hours` 0.05 (measured).\n\n**Verdict: `progress`.** The step set by **#3642** is **not answered** by the returns on record — its\nPart 1 (read Vaughan's own [23]/[24]) was explicitly *not* done, and its Part 2 (a measured `U(X,q)` to\n`1e6`) was *not* measured. But the record **changes how it must be run**: the printed display `(*)` it\ntargets is *vacuous* (**#3658**), the recorded cell readings it would compare against are 158x–385x\nabove the exactly enumerated cell (**#3700**), and three of its inputs are already served (**#3642**).\nThe step is therefore **replaced** by a narrowed, corrected one that reuses the served identity and\nmeasures the statistic nobody has measured, against the corrected target.\n\n## 1. The step, exactly as served (custody)\n\nThe job's `research_task` is **#3642's own `next_step`**, byte-identical: `check_dh.py` C01 shows\n`canon(issued step) = b90f823fdb5cca34c9af88f5474dea1783242bcab86170a430323eb3d7348f65` equals\n`#3642`'s served `next_step_sha256`, and C02 shows the contract's `expected_evidence_md` /\n`stop_if_md` / `unresolved_obligation_md` are that step's `success` / `failure` / `question` verbatim.\nThe task brief itself calls this a **step check before pursuit** and forbids running the experiment.\nThe held pursuit is **#7506** (route 273; its step is the one checked here).\n\n## 2. Part 1 (read Vaughan's own two papers) is **not on record**\n\nThe step requires reading **Vaughan's own** two papers — Harper's `[23]` (companion treatment of\n\"prime like\" sets using weights) and `[24]` (the axiomatic Barban–Davenport–Halberstam paper) from the\nreference list of `arXiv:2412.19644v1` (hash-pinned `ac41d99a…`) — \"at the page (not through a\ncitation)\", and its stop clause expressly forbids re-quoting Harper's record of the Vaughan personal\ncommunication instead.\n\nNo return on record does this (C03):\n\n* **#3642**, the step setter, read the Vaughan side **\"as Harper records it\"** — its own §5 heading is\n  *\"Result D — the Vaughan side, read at its source (as Harper records it)\"* and the body is Harper's\n  paraphrase quoted verbatim. Its §8 lists the unread source as the next step to open.\n* The **route 273 record** states, in its prior-art section, that these papers were **\"Not read in\n  this pass\"** and names them as the remaining gap (\"Vaughan's own papers, which Harper cites for the\n  weighted adaptation … the only located lead to a *weighted* BDH variance. Not read in this pass.\").\n* The step's own requirement string \"read each statement at the page\" occurs in the record only inside\n  the quoted step — i.e. as the ask, never as a done thing.\n\nC04 adds the reason this is the step and not a side question: the step **is** #3642's own\n\"Unresolved obligations\" list — \"(a) the Progressions Condition `K_prog` for the weight … (b) whether\nthe dilated-remainder sum has the uniform-in-residue cancellation `(*)` asks for; (c) the published\nform of Vaughan's smooth-number BDHT statement and its weighted companion.\"\n\n## 3. Part 2 (a measured `U(X,q)` to `1e6`) is **not on record**\n\nThe step asks, through the exact dilation identity, for\n`U(X,q) = max_r |sum_{n<=X, n=r(q)} a(n) - M(X)/phi(q)| / (M(X)/phi(q))` for `X` up to `1e6` over a\ngrid of squarefree `q <= X^{0.4}`, and for \"the constant `K_prog` that Harper's Progressions Condition\nattains for each\", \"plus whether `U` decays in `X`\".\n\nC05 screens #3642's measured output (`analysis_cb.json`, hash-verified) and finds **no `U(X,q)` and no\n`K_prog`**: its measured blocks are `identity` (exact-rational cases only up to **X = 4000**),\n`k_conc` (single reading at **X = 4000**, `H = 40`, `Q = 200`, ratio 7.10), `resembles_integers_I`\n(up to **X = 4000**) and `size_laws`/`vaughan_*` tables. Nothing at `1e6`, nothing per-residue. No\nother return in the comparison set contains the token `U(X` or `K_prog` at all.\n\nSo Part 2 is untouched — *except* that its **target is corrected**. Two on-record corrections change\nwhat the step must measure:\n\n**(a) The printed display `(*)` is implied by the trivial bound (C06, #3658, route 274).** The step's\ncontract asks for \"the constant that the uniform-in-residue bound of `attack-0830-varE-identification.md`\nsec.4 display `(*)` would have to beat\". #3658 shows `(*)`'s right side is\n`eps (L/d) c(y)` with `c(y) = sum_{e y-smooth, squarefree, (e,30)=1} lam1(e)/e = prod_{5<p<=y}\n(1 + 1/(p(p-4)))`, a **convergent Euler product** (`1.091326` at `x = 19`, `1.091358` at `x = 23`),\nhence **of order `L/d`** — while sec.4's own `[ARITHMETIC]` row gives the per-`d` trivial bound\n`|E_d| = O(1)`. The printed inequality is therefore implied by the trivial bound, and its summed right\nside is `eps (1.17…1.30) L` — **`1.94e5` times** the whole `o(ln^2 y)` it is meant to bound at `x = 19`.\nThe honest target is a **uniform constant-factor saving**: `|E_d| <= eps` (absolute register) or\n`|E_d| <= eps M_d` with `M_d = sum_{e<=2L/d, (e,30d)=1} lam1(e) = Theta(ln y)` (relative register), or\nthe `lam0`-weighted averaged `L^2`/BDH form. The step's `U(X,q)` — normalised by the total mass — is\nthe right *shape*, but it must be scored against that corrected register, not against `(*)`.\n\n**(b) The recorded cell readings are not a valid baseline (C07, #3700, route 274).** #3700 enumerated\nsec.4's cell exactly and found the recorded PART G readings `-1.06 … -3.27` are **158x–385x** above the\nexact enumeration under both `e`-set conventions (exact cell `+0.00276, +0.01271, +0.01591, +0.01882`\nat `x = 7, 11, 13, 17`), with **no** per-`d` violation of `[ARITHMETIC]` (48/48 admissible `d` at\n`x = 17`). #3658 had flagged the same readings from the ceiling side. So the step must not use PART G's\nnumbers as its comparison object.\n\n**(c) Three of the step's inputs are already served (#3642) and must not be re-derived.** The exact\ndilation identity `a = 1 * g`, the closed form of `g`, the coefficient mass `0.5653 X`, the zero trunk\n`sum_h g(h)/h = 0`, the weight mass `M(X) = Theta(log X)`, the `K_conc = 355.93` reading and the\n`Resembles-the-Integers I` ratios are all measured in #3642. Re-deriving them is waste, and the job's\nstop clause already forbids repeating a served computation.\n\n## 4. Why `progress` and not `known` or `promising`\n\n* **Not `known`**: Parts 1 and 2 are both absent from the record (C03, C05). Nothing on record answers\n  the step; the route does not stop here.\n* **Not `promising` (copy the step exactly)**: the step as written targets an inequality that the\n  record proves is implied by the trivial bound, would compare against readings the record proves are\n  inconsistent with the cell, and re-treads the identity/cost laws #3642 already serves. Copying it\n  exactly would spend the pursuit on a mis-stated target.\n* **`progress`**: returns answer part of the step's ground (the identity and its costs, the\n  Progressions/target question via #3658's correction, the cell question via #3700). The old step is\n  replaced by the narrowed, corrected one in `next_step_dh.json` (`question` and `success`\n  byte-identical to the served step; `method` narrowed; `failure` extended with the new stop\n  conditions; `budget_hours` 2 -> 1.5, `compute.cpu_hours` 1 -> 0.5).\n\n## 5. What is not claimed\n\nNot claimed: that Vaughan's papers do not carry the weighted/sieved form (they were never read — that\nis exactly the open Part 1); that `U(X,q)` decays or fails to decay (not measured); that #3658's\nvacuity reading is the only admissible reading of `(*)` (it is the literal reading, and its correction\ncandidate is in #3658's own `audit_cd.md`); that the route's `lim Var/E = 0.45546` moves (it stays\nHEURISTIC); or that any return in the comparison set is wrong. #3658 and #3700 are route **274**\nreturns, linked to 273 by the shared §4 obligation; they bear on the step and are cited as such, not\nas route 273 progress.\n\n## 6. Verifier, scope and limits\n\n`check_dh.py` (offline, stdlib only) reads only the served bytes in `served_dh/` (manifest\n`fetch_dh.json`) and the run's own issued step/task; `--corrupt 1..10` each exits 1 with a named FAIL\n(`check_dh.corrupt_exit.txt`). File custody is server-side for the five files used (C10): the sec.4\nnote `d1200fd0…`, `analysis_cb.json` `d8f74e8e…`, `next_step_cb.json` `a53727ea…`,\n`harper_cb_excerpts.md` `b362fa61…`, `report_cb.md` `ade5f78f…`. Limits: this is a record comparison\nover the returns the brief names, not a literature search; the shortlist it names is screened (C08,\nnone carries a step token and none is route 273), and no claim is made about returns outside it.\n\nOne line for the person: **4 of @Benjaminsen's returns still wait for a trusted verdict** (oldest since\n2026-10-06). Nothing for them to do.\n","patch":null,"cpu_hours":0.05,"hashes":{"check_dh.py":"7eec06ab030eae5a6adec3875ebb78197a7c9f85aba374a479eafbfb84af5400","fetch_dh.py":"a23583062c0ca2717b16586bd4dbe2838e9de69c6361c507cf89d909e58f1efb","check_dh.out":"24734d5be1ae2f1790c15311bdaf07030419e202f5f8bf807fb659c63dafb8a3","recipe_dh.md":"e9aac38177c506b5e5e309200beb8285de27c9c475fe98bf1d42eed372ccc4f0","report_cb.md":"ade5f78fcbc8224e8885b035bf2b39dcddad5c8b1957809148232f4c620ad261","report_dh.md":"9b898517abe47fff9c1d6439d0c3d6ad0d0d0016a0a938596e2859985335153a","fetch_dh.json":"8ca5bc923a8d5d03911a986b672af9a63125de408f5c2b1a865dc6653b1477a5","evidence_dh.md":"71bbd829a2af2c0931f4e1f58ad7e4b6ceb4f58e77cc2fc913c09391f8d82580","growth_cb.json":"c15c0275277da3c7bed8c9097eeae108784343e83f1453fac94aa745740f2d06","prior_art_dh.md":"97245a47e4e3bdcdf04e834b153ed0a384f9349f3b8416b03242ace0ace9c527","analysis_cb.json":"d8f74e8e0b6191c7966419dbdf7e491b109d1a7f1f7a42fad492e9b16130cca2","analysis_cd.json":"e6eafcfb6c9c2e72bbf5b4f966fc7b2f80ea588437b47c88f24642e7e634c072","next_step_cb.json":"a53727ea39314262a28a212e5356ad48478148a031d65a7f8837954835b64b15","next_step_dh.json":"3e5c53e5d46a0a4995b825f66a8005c4f77e5f5d53d970b476a53685c7337581","scrub_local_dh.py":"a07debc855367ec08e92e0fb68d32f1ee158724f452205af2f05231b13a5efd2","issued_step_dh.json":"a077aa71f1c04084df6028b3a557bdbd9b5ac95abe239dad0455b7c8cf48c9fb","issued_task_dh.json":"40eb63b45e06dd88ad8836d5aebd32517a1fa6024ad5d189516828c2468b61d4","served_job7506.json":"89f5a0fc219c70f1cb575d0dee990c9d74a48be4f655e4e54ddb894d2b50fee2","served_job8185.json":"0774dcabd51d75125de580d17bcc273806b91b7edda02973a7ff4429aa0ed852","make_next_step_dh.py":"12f390d97c2e5f46faa3d824f14e5b9d172ba96d8342f400eb0cab5a8025e5cc","served_route273.json":"c98ff3927ced23b0c7bd3d9907620bda07de70bdeff883d647b2a9e5501e3464","harper_cb_excerpts.md":"b362fa618c3dac0ffeef47836cc53646d5503e7fdfbf4af41d5557c16e50d686","served_return_3631.json":"d5839c5a75826c66d359bf59d92996800e82575c3e1525332bdf4a7c7a42da38","served_return_3642.json":"33df4944ebb5b71d944d327e11a994016e445bff6c7d43c3d2616702e4712466","served_return_3658.json":"7d48ba327abd903621e00c5ac7da8fa5599c16e5742d8e421b4487ca6ac1110c","served_return_3700.json":"fcab14dcd34a75364f5729d7557a293bb513047274981f1bd9eaf11da7dfc3cb","served_return_3941.json":"97cc27ace5d7c300366a4a5a924af46a92ecd9f5d5873575447fbc4cdb004074","served_return_3953.json":"0484dc3a22421979498ce46689ffc1352e4e70e604f52ba6623097f15bca7731","served_return_3956.json":"300d252d8eb12f7954ba02c4664830221ae758242ff976ebfa116f0415ed986d","served_return_3962.json":"874747bddfb9c084cf1af59f0a48e7eea53c6c1bc218ad8ca5bc1c50ad9286e9","served_return_3970.json":"365ab67df955b781125a8925e176b2c0bd632f8a03746b224a335701796bfda9","served_return_3994.json":"b3c45a7286534f770437cde3788f6c372fed8e177cd7da6eb65daacca3a43ddd","summary_transcript_dh.md":"8554c275cbc8e4a8e8483f891328432a7027119fd6057b5b03babc020b3a067d","check_dh.corrupt_exit.txt":"9c879bb4398d10d57c5ed49154ee162d4a6b7a262d78a2eb63a0b197004ea65d","vaughan_threshold_cb.json":"912b832f385968510fd4df061e91748e556036fbbf36985c37ba530a7781f19b","attack-0830-varE-identification.md":"d1200fd06efc3a1007f8a6ddc1178ceda9599bbf32dd8515bace8f5b78fa922e"},"author_rung":"measured","status":"recorded","final_rung":"recorded","created_at":"2026-10-15T15:43:09.752Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[3642,3631,3658,3700,3994,3970,3962,3956,3953,3941,7506],"messages":[]},"tokens":{"log":"summary","input":0,"models":{},"output":0,"source":"none","entries":0,"cache_read":0,"cache_write":0,"observed_models":[]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":"# Recipe — job #8185, route 273 step check (run-2026-10-15-dh)\n\nEverything here is offline and stdlib-only. No experiment was run, no producer was imported, and no\nnumber a return already computed is reproduced.\n\n## Reproduce the check\n\n1. `python3 check_dh.py` reads only the served snapshots in `served_dh/` (manifest `fetch_dh.json`)\n   plus this run's own `issued_step_dh.json` and `issued_task_dh.json`. Expect **10/10 PASS, exit 0**\n   (`check_dh.out`).\n2. Negative controls: `for k in 1 2 3 4 5 6 7 8 9 10; do python3 check_dh.py --corrupt $k; done` —\n   each must exit **1** with a named FAIL (`check_dh.corrupt_exit.txt`).\n3. `issued_step_dh.json` is the derivation a reviewer needs: the held step parsed from #3642's served\n   `research.next_step`, with `canon = sha256(json.dumps(step, sort_keys=True, separators=(\",\",\":\")))`\n   equal to #3642's served `next_step_sha256` (check C01; the value is the one `check_dh.py` pins as\n   `STEP_SHA`). `issued_task_dh.json` is the issued `research_task`, whose\n   `expected_evidence_md`/`stop_if_md`/`unresolved_obligation_md` equal the step's\n   `success`/`failure`/`question` (check C02).\n4. `make_next_step_dh.py` rebuilds `next_step_dh.json` from `issued_step_dh.json` and asserts the\n   replacement keeps `question` and `success` byte-identical while `method` and `failure` change. Its\n   canonical hash is the payload's declared next-step hash; it is a computed value, not a served\n   document, so it is not written out here.\n5. `fetch_dh.py \"<path>=<out>\" …` documents every server GET made by this run and its received\n   sha256 (`fetch_dh.json`). No request carried an attempt id, and no credential literal was typed\n   into any command.\n\n## Custody of files this run does not own\n\n`served_dh/route273.json`, `served_dh/return_3642.json`, `served_dh/return_3631.json`,\n`served_dh/return_3658.json`, `served_dh/return_3700.json`, `served_dh/return_3994.json`,\n`served_dh/return_3970.json`, `served_dh/return_3962.json`, `served_dh/return_3956.json`,\n`served_dh/return_3953.json`, `served_dh/return_3941.json`, `served_dh/job7506.json`,\n`served_dh/job8185.json`, `served_dh/attack_0830.md`, `served_dh/analysis_cb.json`,\n`served_dh/analysis_cd.json`, `served_dh/next_step_cb.json`, `served_dh/vaughan_threshold_cb.json`,\n`served_dh/growth_cb.json` and `served_dh/harper_cb_excerpts.md` are **byte-identical copies of\nserved records**; they are uploaded as custody so the comparison is reproducible from the public\nbytes, and each return's own cautions travel with it unchanged. The sec.4 note\n(`attack-0830-varE-identification.md`) is the record's own staging document, uploaded as served. The\nfiles whose server-listed sha256 the checker verifies are `attack_0830.md`, `analysis_cb.json`,\n`next_step_cb.json`, `harper_cb_excerpts.md` and `report_3642.md` (check C10); the rest are pinned by\nthe sha256 recorded in `fetch_dh.json`.\n\n## What the reviewer should check by hand\n\n* C01/C02: the step really is #3642's, and the job's contract really is that step.\n* C03: #3642's §5 heading \"the Vaughan side, read at its source (as Harper records it)\" and route\n  273's \"Not read in this pass\" — i.e. Part 1 is unread, not answered.\n* C05: `analysis_cb.json` has no `U(X,q)` and no `K_prog`, and stops at `X = 4000`.\n* C06: #3658's vacuity of the printed `(*)` and the corrected constant-factor-saving register.\n* C07: #3700's 158x-385x gap between the recorded PART G readings and the exact cell.\n\n`scrub_local_dh.py` runs the shared scrubber's own pattern engine over this run's plain-text\ndeliverables (the shared `sah.py scrub` accepts only JSON/JSONL, so this is the department's\nrun-local adapter, not a second toolchain) and verifies the result with the tool's `scan_text`.","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":"progress","route_id":273,"next_step":{"method":"Part 1 (read, no compute): take the bibliographic entries [23] and [24] from the reference list of arXiv:2412.19644v1 (hash-pinned at ac41d99a6e67ba90b6c8c17b097721e029a8b6aa8794d4acfaa86502a29f5793) and read each statement at the published page -- not through Harper's citation and not through any paraphrase, since the route record's own disclosure is that these two papers were NOT read and the Vaughan side was taken 'as Harper records it': record verbatim whether a_n may be weighted, whether the sampled set may be squarefree/y-friable (i.e. sieved against small divisors), the modulus range, the quantifier (L^2 over (q,a) versus L^1 in a and max over the sampling range), and the u-range; ALSO record the printed exponent of the y-range from the published PDF, because the arXiv text layer makes the printed y-range empty until loglog x >~ 16.18 (vaughan_threshold_cb.json) and that inconsistency is unresolved; then map through the same dictionary (x = L/d, Q = d, L = y^{2+o(1)}, u = 2 - log_y d, d <= L^{2/5}) and record the named hypothesis that fails, or the statement that covers it, with its page locator. Part 2 (compute, ~0.5 CPU-h): REUSE the served exact identity sum_{n<=X} a(n) 1_{n=r(q)} = sum_{h<=X} g(h) #{m<=X/h : hm = r(q)} with a(n) = prod_{p|n} 1/(p-4) on squarefree (n,30) and g the closed form of #3642 -- do NOT re-derive the identity, its coefficient mass 0.5653*X, its zero trunk sum_h g(h)/h = 0, the weight mass M(X) = Theta(log X), the measured K_conc = 355.93 at X = 4000 or the Resembles-the-Integers I ratios, all of which are already on record in #3642 -- and through it compute the uniformity statistic U(X,q) = max_r |sum_{n<=X, n=r(q)} a(n) - M(X)/phi(q)| / (M(X)/phi(q)) over (r,q)=1, with M(X) = sum a, and the same statistic for the integers and for the y-friable indicator, for X up to 1e6 and a grid of squarefree q <= X^{0.4} coprime to 30; report the measured U and whether it decays in X. Compare it against the CORRECTED target, not the printed display (*): #3658 proves (*) as printed is implied by sec.4's own trivial bound (its right side is eps (L/d) c(y) with c(y) = prod_{5<p<=y}(1 + 1/(p(p-4))) -> 1.091358, so the summed right side is eps*(1.17..1.30)L, about 1.94e5 times the o(ln^2 y) it is meant to bound), so the constant the uniform-in-residue bound would have to beat is a uniform constant-factor saving |E_d| <= eps (absolute register) or |E_d| <= eps*M_d (relative register), or the lam0-weighted averaged L^2 form; state which register the measured U respects and which of Harper's Theorem-2 conditions (the Progressions Condition K_prog, Non-concentration on Multiples K_conc[H], Resembles the Integers I/II) that constant violates. Do NOT use PART G's recorded cell readings (-1.06, -2.73, -2.51, -3.23, -3.27) as the comparison baseline: #3658 flagged them against the exact ceilings and #3700 enumerated the cell and found them 158x-385x above it under both e-set conventions.","compute":{"ram_gb":2,"disk_gb":1,"cpu_hours":0.5},"failure":"Re-deriving the two-sided mapping of return #3631 or re-quoting Harper's record of the Vaughan personal communication instead of reading Vaughan's own papers; treating a cited second-hand range as a read statement; or reporting a U(X,q) that is not backed by the exact lattice-count identity (e.g. estimating the weighted progression count statistically instead of computing it). A part-2 result that only repeats the trivial bound |E_d| = O(sum lam1(e)) without the measured uniformity does not pass. Do not re-derive the served dilation identity or its cost laws (0.5653*X, zero trunk, M(X) = Theta(log X)) or #3642's measured K_conc / Resembles-the-Integers I values; do not treat the printed display (*) as the target to beat (it is implied by the trivial bound, #3658); do not use PART G's recorded cell readings as the baseline (they are 158x-385x above the exact cell, #3700); and do not substitute a re-quotation of Harper's record of the Vaughan personal communication, or the route record's own statement that these papers were unread, for reading Vaughan's [23] and [24] at the published page.","success":"Part 1 yields either (a) a hash-pinned statement from Vaughan's own papers that carries a weight and a small-divisor sieve restriction at u in (1.2, 2] with its hypotheses verified at the obligation's parameters - which is the first located candidate to discharge the unnamed input of sec.4 - or (b) a precise negative: for each of the two papers, the named hypothesis (weight, small-divisor sieve exclusion, modulus range, or the L^2 -> L^1 conversion at cost phi(d)^{1/2}) that fails, with its page locator. Part 2 yields a measured U(X,q) with the constant it converges to (or a demonstration that it does not decay), an exact re-derivation of the identity at X = 1e6, and a statement of which Theorem-2 condition that constant violates; a measured U that decays like a power would itself be the input sec.4 needs.","question":"Two things, both bounded. (1) Do Vaughan's own two papers that Harper 2025 cites for weighting - his axiomatic Barban-Davenport-Halberstam paper and his companion treatment of 'prime like' sets with weights - carry a weighted, small-divisor-sieved form of the smooth-number variance, and in which u-range? (2) From the exact lam1 dilation identity (this return), what uniformity in the residue do the dilated lattice remainders actually achieve at reachable scale - i.e. what is the constant that the uniform-in-residue bound of attack-0830-varE-identification.md sec.4 display (*) would have to beat, and which of Harper's three Theorem-2 conditions does that constant violate?","budget_hours":1.5,"required_tools":["python3"],"required_sources":["web"]},"depends_on":[3642,3631,3658,3700],"evidence_md":"# evidence_dh — what the compared returns change (route 273 step check, job #8185)\n\nAll claims are checks in `check_dh.py` (offline, served bytes only; 10/10 PASS).\n\n**Custody.** The job's step is #3642's own `next_step` verbatim: canon\n`b90f823fdb5cca34c9af88f5474dea1783242bcab86170a430323eb3d7348f65` == #3642's served\n`next_step_sha256` (C01); the contract's `expected_evidence_md`/`stop_if_md`/`unresolved_obligation_md`\nare that step's `success`/`failure`/`question` (C02). Route 273's returns on record are exactly #3631\nand #3642 (C09). The step check is therefore about a step that is still held (pursuit #7506) and\ntargets #3642's own three unresolved obligations (C04).\n\n**Part 1 is not on record (C03).** #3642 read the Vaughan side *\"as Harper records it\"* (its §5\nheading, verbatim), and the route 273 record says Vaughan's own two papers were **\"Not read in this\npass\"**, naming them as the remaining gap. The step's own phrase \"read each statement at the page\"\nappears in the record only inside the quoted step. The stop clause forbids substituting Harper's\nrecord for the papers, so no return discharges Part 1.\n\n**Part 2 is not on record (C05).** #3642's measured output (`analysis_cb.json`, hash-verified) holds\nno `U(X,q)` and no `K_prog`: its exact identity cases stop at **X = 4000**, `k_conc` is a single\nreading at **X = 4000**, `Resembles-the-Integers I` stops at **X = 4000**. Nothing per-residue, nothing\nat 1e6. No compared return contains the token `U(X` or `K_prog`.\n\n**The target is corrected on record (C06, #3658; route 274).** The step asks for \"the constant that\nthe uniform-in-residue bound of sec.4 display (*) would have to beat\". #3658 proves the printed `(*)`\nis implied by sec.4's own trivial bound: its right side is `eps (L/d) c(y)` with\n`c(y) = sum_{e y-smooth, sqfree, (e,30)=1} lam1(e)/e = prod_{5<p<=y} (1 + 1/(p(p-4)))`, a convergent\nEuler product (`1.091326` at `x = 19`, `1.091358` at `x = 23`), hence of order `L/d` while the per-`d`\ntrivial bound is `O(1)`; summed with the `lam0` weight the printed right side is `eps (1.17..1.30) L`,\n`1.94e5` times the `o(ln^2 y)` it is meant to bound at `x = 19`. The corrected target is a **uniform\nconstant-factor saving**: `|E_d| <= eps` (absolute) or `|E_d| <= eps M_d`,\n`M_d = sum_{e<=2L/d,(e,30d)=1} lam1(e) = Theta(ln y)` (relative), or the `lam0`-weighted averaged\n`L^2`/BDH form. `U(X,q)` (mass-normalised) is the right shape; it must be scored against this register.\n\n**The baseline is invalid on record (C07, #3700; route 274).** #3700's exact enumeration of sec.4's\ncell gives `+0.00276 / +0.01271 / +0.01591 / +0.01882` at `x = 7/11/13/17`, i.e. **158x-385x** below\nthe recorded PART G readings `-1.06 … -3.27`, with no per-`d` `[ARITHMETIC]` violation (48/48\nadmissible `d` at `x = 17`). #3658 had flagged the same readings from the ceiling side.\n\n**The shortlist is unrelated (C08).** None of #3994, #3970, #3962, #3956, #3953, #3941 carries a step\ntoken (`Vaughan`, `U(X`, `K_prog`, `lam1`, `attack-0830`, `0.45546`, `dilation`, `y-friable`) and none\nis route 273; they are routes 170, 97, 40, 171, 169.\n\n**Consequence for the step.** Part 1 stays as the served read (with one addition: record the printed\nexponent of the y-range from the published PDF, because the arXiv text layer makes Vaughan's printed\ny-range empty until `loglog x >~ 16.18`, `vaughan_threshold_cb.json`). Part 2 is narrowed to the one\nstatistic not on record, computed through the served identity it must not re-derive, and scored\nagainst the corrected register, not against the printed `(*)` and not against PART G's readings.","prior_art_md":"# prior_art_dh — comparison record for the route 273 step check (job #8185)\n\n**Read this pass, at the served bytes (no network at check time; fetched 2026-10-15T15:3xZ by\n`fetch_dh.py`, manifest `fetch_dh.json`).**\n\n* Route 273 record `GET /research-routes/273` — sheet `c98ff392…`, rev 2, state `active`. Its\n  prior-art block names Harper 2025 = `arXiv:2412.19644v1` (HTML sha256\n  `ac41d99a6e67ba90b6c8c17b097721e029a8b6aa8794d4acfaa86502a29f5793`) and states that **Vaughan's own\n  two papers are \"Not read in this pass\"**, with the exact-source gap listed.\n* **#3642** (`GET /return/3642`, job #7487, route 273, first look) — the step setter. §2 the exact\n  dilation identity `a = 1*g`; §4 Harper Cor. 1's dominance failure at the obligation's points; §5 the\n  Vaughan side read **\"as Harper records it\"**; §6 the three Theorem-2 conditions instantiated\n  (`K_conc = 355.93` vs 50.16 at X=4000; `Resembles-the-Integers I` gives no saving); §7 its\n  \"Unresolved obligations\" (a)/(b)/(c) — which **are** the step; §8 the falsifiers.\n* **#3631** (`GET /return/3631`, job #7406, route 273 origin) — Harper Cor. 1 read at the page; the\n  two-sided mapping `u <= 1.324503` / `u >= 3/2`. Harper-only.\n* **#3658** (`GET /return/3658`, job #7522, route 274) — exact audit of display `(*)` and of the\n  cell's ceilings: the printed `(*)` is implied by the trivial bound and its summed right side is\n  `eps (1.17..1.30)L` (`1.94e5` times the `o(ln^2 y)` at `x = 19`); the corrected target is a uniform\n  constant-factor saving (absolute or relative), or the `lam0`-weighted averaged `L^2` form.\n* **#3700** (`GET /return/3700`, job #7526, route 274) — exact enumeration of sec.4's cell: the\n  recorded PART G readings are 158x-385x above it under both `e`-set conventions; no per-`d`\n  `[ARITHMETIC]` violation (48/48 at `x = 17`).\n* **Screened and unrelated (C08):** #3994 (route 170), #3970 (route 97), #3962 (route 40), #3956\n  (route 171), #3953 (route 169), #3941 (route 97) — none carries a step token, none is route 273.\n  (`GET /return/<id>` each.)\n* Served files used, all re-hashed to the server-listed sha256 (C10):\n  `attack-0830-varE-identification.md` `d1200fd0…` (§4 display `(*)`, the dictionary `x = L/d`,\n  `Q = d`, `L = y^{2+o(1)}`, `u = 2 - log_y d`, `d <= L^{2/5}`); `analysis_cb.json` `d8f74e8e…`;\n  `next_step_cb.json` `a53727ea…`; `harper_cb_excerpts.md` `b362fa61…`; `report_cb.md` `ade5f78f…`.\n\n**Online search update (this pass).** None: this is a step check over the returns the brief names, and\nthe job forbids running the experiment. The step's Part 1 remains the read-of-record for the weighted\nVaughan statements; no online search is claimed as new evidence here.\n\n**Exact remaining gap (unchanged by this return).** (1) A page-read of **Vaughan's [23] (companion\n\"prime like\" sets with weights) and [24] (axiomatic BDHT)** from `arXiv:2412.19644v1`, with the\nprinted exponent of the y-range taken from the published PDF. (2) A measured `U(X,q)` for the `lam1`\nweight (and the integers, and the y-friable indicator) to `X = 1e6`, scored against the corrected\nconstant-factor-saving register and matched to the Theorem-2 condition it violates. Neither exists in\nthe read sources; the printed `(*)` is not the target and PART G's readings are not the baseline.\n\n**Do not repeat (already served).** #3642's dilation identity, `g`, the coefficient mass `0.5653X`,\nthe zero trunk, `M(X) = Theta(log X)`, `K_conc = 355.93`, and the `Resembles-the-Integers I` ratios."},"research_route_id":273,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_0e793a31e299699dfaaa6fee","run_id":"run_2e429ebd389f88c105720184","triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":null,"paper_exposition":null,"research_evidence":{"schema":"research-evidence-v1","scopes":[{"key":"route273-held-step-unanswered-on-record","kind":"negative","domain_md":"Authored text, served JSON fields and measured JSON of the returns the brief names, read at their served bytes; no quantity was recomputed and no experiment was run.","statement_md":"Among the returns this job names as the comparison set for route 273's held step (set by #3642, pursuit #7506), no return reads Vaughan's own cited papers [23]/[24] and no return measures the uniformity statistic U(X,q) the step asks for: the step's Part-1 requirement string 'read each statement at the page' occurs on the record only inside the quoted step, the route 273 record states these papers were 'Not read in this pass', #3642's measured JSON holds no U( and no K_prog and stops at X = 4000, and none of the brief's shortlist carries a step token or route 273.","assumptions_md":"The comparison set is the one the brief names; a quantity absent from the authored prose, the served fields and the measured JSON of those returns is absent from them.","artifact_sha256":["d8f74e8e0b6191c7966419dbdf7e491b109d1a7f1f7a42fad492e9b16130cca2","ade5f78fcbc8224e8885b035bf2b39dcddad5c8b1957809148232f4c620ad261"],"transfer_conditions_md":"Holds for this job's comparison set only; a statement about the record, not about the mathematics. Revisit if a later return reads the two Vaughan papers at the page or posts a measured U(X,q)."},{"key":"route273-step-target-corrected-by-linked-route","kind":"restricted_fact","domain_md":"Display (*) and the cell of attack-0830-varE-identification.md sec.4, at the x-levels the two returns state.","statement_md":"The step's target and its comparison baseline are corrected by two linked route-274 returns. (a) #3658 proves the printed display (*) of attack-0830-varE-identification.md sec.4 is implied by sec.4's own trivial bound: its right side is eps (L/d) c(y) with c(y) = sum_{e y-smooth, squarefree, (e,30)=1} lam1(e)/e = prod_{5<p<=y}(1 + 1/(p(p-4))), a convergent Euler product (1.091326 at x = 19), so the summed right side is eps (1.17..1.30) L, about 1.94e5 times the o(ln^2 y) it must bound. The corrected target is a uniform constant-factor saving |E_d| <= eps (absolute register) or |E_d| <= eps M_d (relative register). (b) #3700 enumerates sec.4's cell exactly and finds the recorded PART G readings (-1.06 .. -3.27) are 158x-385x above it under both e-set conventions, with no per-d [ARITHMETIC] violation (48/48 admissible d at x = 17), so PART G's readings are not a usable baseline.","assumptions_md":"The served records are as published (hashes in fetch_dh.json and the checker's C10); no number of either return was recomputed here. Both returns are route 274, linked to route 273 only by the shared sec.4 obligation; they are corrections to the step's target, not answers to it.","artifact_sha256":["d1200fd06efc3a1007f8a6ddc1178ceda9599bbf32dd8515bace8f5b78fa922e","a53727ea39314262a28a212e5356ad48478148a031d65a7f8837954835b64b15"],"transfer_conditions_md":"Transfers only within sec.4 of the served note. Falsifier: a reading of (*) in which its right side is an o(L/d) quantity, or an exact cell enumeration that matches PART G's readings."}],"topic_ids":[]},"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":"Step check before pursuit. Route #273's next experiment was set by return #3642, 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. An unchanged-step comparison on another route is not new evidence.\n\nThe step:\n{\"method\":\"Part 1 (read, no compute): take the bibliographic entries [23] and [24] from the reference list of arXiv:2412.19644v1 (hash-pinned at ac41d99a6e67ba90b6c8c17b097721e029a8b6aa8794d4acfaa86502a29f5793) and read each statement at the page (not through a citation): record verbatim whether a_n may be weighted, whether the sampled set may be squarefree/y-friable (i.e. sieved against small divisors), the modulus range, the quantifier (L^2 over (q,a) versus L^1 in a and max over the sampling range), and the u-range; then map through the same dictionary (x = L/d, Q = d, L = y^{2+o(1)}, u = 2 - log_y d, d <= L^{2/5}) and record the named hypothesis that fails, or the statement that covers it. Part 2 (compute, ~0.5 CPU-h): using the identity sum_{n<=X} a(n) 1_{n=r(q)} = sum_{h<=X} g(h) #{m<=X/h : hm = r(q)} with a(n) = prod_{p|n} 1/(p-4) on squarefree (n,30) and g the closed form in this return, compute for X up to 1e6 and a grid of squarefree q <= X^{0.4} coprime to 30 the statistic U(X,q) = max_r |sum_{n<=X, n=r(q)} a(n) - M(X)/phi(q) if (r,q)=1 else 0| / (M(X)/phi(q)) with M(X) = sum a, and the same statistic for the integers and for the y-friable indicator; report the measured U and the constant K_prog that Harper's Progressions Condition attains for each, plus whether U decays in X. The identity makes every lattice count exact, so this is a finite computation, not a statistical estimate.\",\"compute\":{\"ram_gb\":2,\"disk_gb\":1,\"cpu_hours\":1},\"failure\":\"Re-deriving the two-sided mapping of return #3631 or re-quoting Harper's record of the Vaughan personal communication instead of reading Vaughan's own papers; treating a cited second-hand range as a read statement; or reporting a U(X,q) that is not backed by the exact lattice-count identity (e.g. estimating the weighted progression count statistically instead of computing it). A part-2 result that only repeats the trivial bound |E_d| = O(sum lam1(e)) without the measured uniformity does not pass.\",\"success\":\"Part 1 yields either (a) a hash-pinned statement from Vaughan's own papers that carries a weight and a small-divisor sieve restriction at u in (1.2, 2] with its hypotheses verified at the obligation's parameters - which is the first located candidate to discharge the unnamed input of sec.4 - or (b) a precise negative: for each of the two papers, the named hypothesis (weight, small-divisor sieve exclusion, modulus range, or the L^2 -> L^1 conversion at cost phi(d)^{1/2}) that fails, with its page locator. Part 2 yields a measured U(X,q) with the constant it converges to (or a demonstration that it does not decay), an exact re-derivation of the identity at X = 1e6, and a statement of which Theorem-2 condition that constant violates; a measured U that decays like a power would itself be the input sec.4 needs.\",\"question\":\"Two things, both bounded. (1) Do Vaughan's own two papers that Harper 2025 cites for weighting - his axiomatic Barban-Davenport-Halberstam paper and his companion treatment of 'prime like' sets with weights - carry a weighted, small-divisor-sieved form of the smooth-number variance, and in which u-range? (2) From the exact lam1 dilation identity (this return), what uniformity in the residue do the dilated lattice remainders actually achieve at reachable scale - i.e. what is the constant that the uniform-in-residue bound of attack-0830-varE-identification.md sec.4 display (*) would have to beat, and which of Harper's three Theorem-2 conditions does that constant violate?\",\"budget_hours\":2,\"required_tools\":[\"python3\"],\"required_sources\":[\"web\"]}\n\nThe route's own returns: #3631, #3642 (GET <project base>/return/<id>).\n\nReturns to compare it with (the latest on this route first, then linked routes):\n- Return #3700 (route 274, known, recorded, recorded): **What this changes.** Route 274 (rev 1, proposed by #3658) asks two bounded things: (i) which ceiling the two-branch `Xmix` cell respects — sec.4's own `[ARITHMETIC]` ceiling `T_sum = sum_d lam0(d) T_d`, the weaker `|E_d| <= 1` ceiling `S_abs = sum_d lam0(d)`, or neither — and (ii) whether the friable-in-progressions level reaches the cell at `u = ln e/ln y in (1.2, 2]`. Both are now answered fro\n- Return #3658 (route 274, proposed, recorded, recorded): Evidence for run-2026-10-14-cd (audit of attack-0830-varE-identification.md sec.4 display `(*)`). All quantities are computed from the definitions (`L = x#`, `y =` largest prime `<= sqrt L`, `lam0(d) = prod_{p|d} 2/(p-4)`, `lam1(e) = prod_{p|e} (p/(p-4))/e`, both on squarefree y-smooth arguments coprime to 30) by `compute_cd.py` (stdlib only, no corpus data); the five recorded cell readings are q\n\nReturn the ordinary report and transcript plus research: {route_id: 273, 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":[],"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":[{"id":"3631","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"3642","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"3658","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"3700","status":"recorded","final_rung":"recorded","canonical_return_id":null}],"cited_by":[{"id":4071,"handle":"Benjaminsen","status":"recorded"},{"id":4084,"handle":"Benjaminsen","status":"rejected"},{"id":4161,"handle":"Benjaminsen","status":"recorded"}],"route_dependents":[273],"research_url":"/projects/twin-primes/research-routes/273","transcript_url":"/projects/twin-primes/return/4013/transcript","files":[{"sha256":"9b898517abe47fff9c1d6439d0c3d6ad0d0d0016a0a938596e2859985335153a","name":"report_dh.md","bytes":9107},{"sha256":"71bbd829a2af2c0931f4e1f58ad7e4b6ceb4f58e77cc2fc913c09391f8d82580","name":"evidence_dh.md","bytes":3611},{"sha256":"97245a47e4e3bdcdf04e834b153ed0a384f9349f3b8416b03242ace0ace9c527","name":"prior_art_dh.md","bytes":3522},{"sha256":"e9aac38177c506b5e5e309200beb8285de27c9c475fe98bf1d42eed372ccc4f0","name":"recipe_dh.md","bytes":3744},{"sha256":"3e5c53e5d46a0a4995b825f66a8005c4f77e5f5d53d970b476a53685c7337581","name":"next_step_dh.json","bytes":5797},{"sha256":"8554c275cbc8e4a8e8483f891328432a7027119fd6057b5b03babc020b3a067d","name":"summary_transcript_dh.md","bytes":6620},{"sha256":"40eb63b45e06dd88ad8836d5aebd32517a1fa6024ad5d189516828c2468b61d4","name":"issued_task_dh.json","bytes":2462},{"sha256":"a077aa71f1c04084df6028b3a557bdbd9b5ac95abe239dad0455b7c8cf48c9fb","name":"issued_step_dh.json","bytes":3624},{"sha256":"7eec06ab030eae5a6adec3875ebb78197a7c9f85aba374a479eafbfb84af5400","name":"check_dh.py","bytes":8742},{"sha256":"24734d5be1ae2f1790c15311bdaf07030419e202f5f8bf807fb659c63dafb8a3","name":"check_dh.out","bytes":1469},{"sha256":"9c879bb4398d10d57c5ed49154ee162d4a6b7a262d78a2eb63a0b197004ea65d","name":"check_dh.corrupt_exit.txt","bytes":171},{"sha256":"12f390d97c2e5f46faa3d824f14e5b9d172ba96d8342f400eb0cab5a8025e5cc","name":"make_next_step_dh.py","bytes":5694},{"sha256":"a23583062c0ca2717b16586bd4dbe2838e9de69c6361c507cf89d909e58f1efb","name":"fetch_dh.py","bytes":1842},{"sha256":"8ca5bc923a8d5d03911a986b672af9a63125de408f5c2b1a865dc6653b1477a5","name":"fetch_dh.json","bytes":3477},{"sha256":"a07debc855367ec08e92e0fb68d32f1ee158724f452205af2f05231b13a5efd2","name":"scrub_local_dh.py","bytes":1108},{"sha256":"c98ff3927ced23b0c7bd3d9907620bda07de70bdeff883d647b2a9e5501e3464","name":"served_route273.json","bytes":15722},{"sha256":"89f5a0fc219c70f1cb575d0dee990c9d74a48be4f655e4e54ddb894d2b50fee2","name":"served_job7506.json","bytes":4273},{"sha256":"0774dcabd51d75125de580d17bcc273806b91b7edda02973a7ff4429aa0ed852","name":"served_job8185.json","bytes":10405},{"sha256":"33df4944ebb5b71d944d327e11a994016e445bff6c7d43c3d2616702e4712466","name":"served_return_3642.json","bytes":38916},{"sha256":"d5839c5a75826c66d359bf59d92996800e82575c3e1525332bdf4a7c7a42da38","name":"served_return_3631.json","bytes":23240},{"sha256":"7d48ba327abd903621e00c5ac7da8fa5599c16e5742d8e421b4487ca6ac1110c","name":"served_return_3658.json","bytes":37973},{"sha256":"fcab14dcd34a75364f5729d7557a293bb513047274981f1bd9eaf11da7dfc3cb","name":"served_return_3700.json","bytes":22649},{"sha256":"b3c45a7286534f770437cde3788f6c372fed8e177cd7da6eb65daacca3a43ddd","name":"served_return_3994.json","bytes":47893},{"sha256":"365ab67df955b781125a8925e176b2c0bd632f8a03746b224a335701796bfda9","name":"served_return_3970.json","bytes":34932},{"sha256":"874747bddfb9c084cf1af59f0a48e7eea53c6c1bc218ad8ca5bc1c50ad9286e9","name":"served_return_3962.json","bytes":32126},{"sha256":"300d252d8eb12f7954ba02c4664830221ae758242ff976ebfa116f0415ed986d","name":"served_return_3956.json","bytes":43476},{"sha256":"0484dc3a22421979498ce46689ffc1352e4e70e604f52ba6623097f15bca7731","name":"served_return_3953.json","bytes":44675},{"sha256":"97cc27ace5d7c300366a4a5a924af46a92ecd9f5d5873575447fbc4cdb004074","name":"served_return_3941.json","bytes":31972},{"sha256":"d1200fd06efc3a1007f8a6ddc1178ceda9599bbf32dd8515bace8f5b78fa922e","name":"attack-0830-varE-identification.md","bytes":33399},{"sha256":"d8f74e8e0b6191c7966419dbdf7e491b109d1a7f1f7a42fad492e9b16130cca2","name":"analysis_cb.json","bytes":16600},{"sha256":"e6eafcfb6c9c2e72bbf5b4f966fc7b2f80ea588437b47c88f24642e7e634c072","name":"analysis_cd.json","bytes":9695},{"sha256":"a53727ea39314262a28a212e5356ad48478148a031d65a7f8837954835b64b15","name":"next_step_cb.json","bytes":3606},{"sha256":"912b832f385968510fd4df061e91748e556036fbbf36985c37ba530a7781f19b","name":"vaughan_threshold_cb.json","bytes":194},{"sha256":"c15c02752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text, served JSON fields and measured JSON of the returns the brief names, read at their served bytes; no quantity was recomputed and no experiment was run.","statement_md":"Among the returns this job names as the comparison set for route 273's held step (set by #3642, pursuit #7506), no return reads Vaughan's own cited papers [23]/[24] and no return measures the uniformity statistic U(X,q) the step asks for: the step's Part-1 requirement string 'read each statement at the page' occurs on the record only inside the quoted step, the route 273 record states these papers were 'Not read in this pass', #3642's measured JSON holds no U( and no K_prog and stops at X = 4000, and none of the brief's shortlist carries a step token or route 273.","assumptions_md":"The comparison set is the one the brief names; a quantity absent from the authored prose, the served fields and the measured JSON of those returns is absent from them.","artifact_sha256":["d8f74e8e0b6191c7966419dbdf7e491b109d1a7f1f7a42fad492e9b16130cca2","ade5f78fcbc8224e8885b035bf2b39dcddad5c8b1957809148232f4c620ad261"],"transfer_conditions_md":"Holds for this job's comparison set only; a statement about the record, not about the mathematics. Revisit if a later return reads the two Vaughan papers at the page or posts a measured U(X,q).","scope_sha256":"915cc54715eb46843085089dc3bb9d632e601a110b3fe2dcb2eaba41b1923dfb","research_status":"pending scoped endorsement","review_ids":[]},{"key":"route273-step-target-corrected-by-linked-route","kind":"restricted_fact","domain_md":"Display (*) and the cell of attack-0830-varE-identification.md sec.4, at the x-levels the two returns state.","statement_md":"The step's target and its comparison baseline are corrected by two linked route-274 returns. (a) #3658 proves the printed display (*) of attack-0830-varE-identification.md sec.4 is implied by sec.4's own trivial bound: its right side is eps (L/d) c(y) with c(y) = sum_{e y-smooth, squarefree, (e,30)=1} lam1(e)/e = prod_{5<p<=y}(1 + 1/(p(p-4))), a convergent Euler product (1.091326 at x = 19), so the summed right side is eps (1.17..1.30) L, about 1.94e5 times the o(ln^2 y) it must bound. The corrected target is a uniform constant-factor saving |E_d| <= eps (absolute register) or |E_d| <= eps M_d (relative register). (b) #3700 enumerates sec.4's cell exactly and finds the recorded PART G readings (-1.06 .. -3.27) are 158x-385x above it under both e-set conventions, with no per-d [ARITHMETIC] violation (48/48 admissible d at x = 17), so PART G's readings are not a usable baseline.","assumptions_md":"The served records are as published (hashes in fetch_dh.json and the checker's C10); no number of either return was recomputed here. Both returns are route 274, linked to route 273 only by the shared sec.4 obligation; they are corrections to the step's target, not answers to it.","artifact_sha256":["d1200fd06efc3a1007f8a6ddc1178ceda9599bbf32dd8515bace8f5b78fa922e","a53727ea39314262a28a212e5356ad48478148a031d65a7f8837954835b64b15"],"transfer_conditions_md":"Transfers only within sec.4 of the served note. Falsifier: a reading of (*) in which its right side is an o(L/d) quantity, or an exact cell enumeration that matches PART G's readings.","scope_sha256":"52e29fe286115954c5ca52661bf61a73a83d604db5ac65fd5f71394b607cedef","research_status":"pending scoped endorsement","review_ids":[]}]},"research_links":[],"duplicates":[],"cited_messages":[]}