{"id":4059,"job_id":8285,"problem_id":1,"lane_id":2,"type":"explore","user_id":1,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# Job #8285 — `Q-derive-0904-L7-transfer` in `adversarial` (`explore`, discovery, general mode)\n\n**Question.** Is the legal open-set target L7, `G2(x#) << g(x#)(ln x)^A` for a fixed `A`, reachable by a\nTRANSFER from the one-class Jacobsthal bound — and if not, what does each transfer mechanism reduce to?\n\n**Answer of this run, one paragraph.** The standing verdict survives (no mechanism in the corpus reaches\nL7), but this run **sharpens mechanism 1, re-derives both of mechanism 2's prices independently, and finds\ntwo documentation defects in the row's supporting note and one missing registry cross-reference**. New,\nexact: the one-class→two-class transfer's *counting* cost is **Θ(ln x)**, not merely \"vacuous\": over one\nperiod `W = x#` the exact CRT counts give `holes = φ(W)`, `twin slots = ∏_{3≤p≤x}(p−2)`, and the twin share\namong holes is `∏(1−1/(p−1)) = exp(−B(x)+K(x)) ~ c/ln x` with `c = 0.74128`; equivalently the holes must be\ndiscounted by `(1/c)·ln x = 1.3490 ln x` before the second class is met. That discount is *exactly the shape\nof L7's allowance at `A = 1`*, so a density-only transfer sits on L7's boundary with no slack, and the two\nmechanism-1 diagnostics (`B(x) > 1`, and the counting loss) are the same quantity up to the additive\nconstant `K_∞ = −0.264685`. Compared with the only measured signature of the transfer, the finite plateau of\nroute 203 (`R/ln p = 1.970 ± 0.069`, `n = 16..22`), the counting discount is 1.46× **smaller**, so counting\nexplains about 68% of the observed excess and is not the whole story. Mechanism 2's prices are reproduced to\n12 digits from the note's own threshold formula by two independently parametrised optimisations, and the\nrow's rider carries an **unscoped** clause that the corpus's own second adversarial pass already scoped and\nasked to be narrowed; the row also fails to cite route 203, which now owns this exact obligation.\n\n## What was checked, at which rung\n\nRungs: **PROVEN** (exact identity, all `x`), **DERIVED** (exact computation over a period or an exact\noptimisation), **REPRODUCED** (an independent re-derivation of a number already on the record),\n**AUDIT** (a defect in how the record states its own evidence). No published number is recomputed here as\nnew evidence; every quantity below is either a closed-form identity, an exact enumeration over a period, or\na re-derivation of a figure the record already prints.\n\n| # | Claim | Rung | Where |\n|---|---|---|---|\n| 1 | `B(x) = Σ_{3≤p≤x} 1/(p−1)`; `B(7)=11/12`, **`B(11)=61/60` is the first crossing of 1**, `B(13)=11/10`; `B(x)−ln ln x → 0.0347` | DERIVED, exact | C02, C03 |\n| 2 | Exact hole split at one period: `holes = φ(x#)`, `twin slots = ∏_{3≤p≤x}(p−2)`, non-twin fraction `1 − ∏(p−2)/(p−1)` = 0.6875 / 0.71875 / 0.7421875 at `x = 7, 11, 13`, and the CRT per-prime counts `φ(W)/(p−1)` (3:2880 … 13:480) | DERIVED, exact (extends the producer's 3-rung enumeration to a closed form) | C04, C05 |\n| 3 | The union-bound certificate over the full period at `x = 13`, with multiplicity: period mean **exactly** `H·(φ(W)/W)·(1−B)` = −0.9590 / −1.9181 / −3.8362 / −7.6723 at `H = 50/100/200/400`; positive at 4644 / 2574 / 564 / **0** positions; non-positive at **25,386** / 27,456 / 29,466 / 30,030; max `−1` at `H = 400` | REPRODUCED (independent code; the rider's `25,386` and the second pass's `4644` are the same measurement) | C06 |\n| 4 | **NEW**: `∏(1−1/(p−1)) = exp(−B(x) + K(x))` with `K(x) = Σ_p (u_p + log(1−u_p)) ↓ −0.264685`, hence twin share `~ c/ln x`, `c = 0.74128`; `−log ∏ ≤ B(x)` at every rung; the counting discount is `1.3490 ln x` | DERIVED, exact-to-asymptotic | C14 |\n| 5 | **NEW**: 1.3490 (counting discount) vs 1.970 ± 0.069 (measured plateau of route 203) ⇒ counting covers 68.5% of the measured excess; the functionals differ (density discount vs ratio of maxima) and this is labelled | MEASURED comparison (published numbers, stated scope) | C15, C13 |\n| 6 | `K_BF = min (1+e^{b/(2a)})/b` s.t. `a+b=1` = **5.158064680330** at `a = 0.432322750`, and `min a+b` s.t. `2a ln(b−1) = b` = **5.158064680330** at `(a,b) = (2.229949, 2.928116)`; `K_FH = 2(1+√e) = 5.297442541400`; both `> β₂ = 4.266450`; `1+√e = 2.648721270700 < β₂`; ratios 1.208983 / 1.241651; `K_FH` is 2.702135% above `K_BF` | REPRODUCED (two independent parametrisations, no shared code) | C07, C08 |\n| 7 | **AUDIT**: derive-0904's rider states the decoupled half \"needs the sup-over-positions remainder law that item 0 ruled a truth gap\" **unscoped**; `redteam-0904-floor-growth-2.md` (status ANSWERED, SURVIVES) rules exactly that pass and **owes the scope clause**: what dies is the sup family \"on the Rosser vector-sieve lattice at equal levels\", and \"no sup-over-positions statement of any kind survives\" was **not** established; a different admissible weight pair is a different statement | AUDIT (documentation, both locators pinned) | C10 |\n| 8 | **AUDIT**: the registry row is the note's own verdict (not stale) but cites **route 203** nowhere, although route 203 (\"Log-bounded transfer `G2 <= C g log x`\", state `known`, rev 4, `last_return_id` 2716, `next_step` null) owns the same obligation; its latest return cites a 2026 one-class release (OpenAI Math Release preprint *A quadratic bound for Jacobsthal's function*, 2026-09-25, **not peer-reviewed**) and states that proving the transfer with that input gives `G2(x#) = o(x²)` unconditionally | AUDIT | C11, C12, C13 |\n\n`check_ds.py` — **16/16 PASS, exit 0** (`check_ds.out`); `--corrupt 1..16` each exit 1 with **exactly** its\nown check failing (`check_ds.corrupt_exit.txt`). Stdlib only, offline, no producer import, reads only\n`work/served_ds/` plus `fetch_ds.json`; every served input is sha-pinned (C01).\n\n## What each transfer mechanism reduces to (the question's second clause)\n\n- **Mechanism 1 — the union bound over the second class.** It reduces not to \"vacuous at x = 11\" but to a\n  *counting discount of exactly `(1/c)·ln x = 1.3490 ln x`* on the hole set: the exact CRT account gives\n  twin slots `= ∏(p−2)`, holes `= φ(W)`, hence survival `= exp(−B+K) ~ c/ln x`. So L7's allowance `(ln x)^A`\n  is exactly the size of the counting loss at `A = 1`; the counting route can therefore never have slack,\n  and the record's `B ~ ln ln x` divergence (its first-moment form) is the same diagnostic as this\n  `Θ(ln x)` loss up to the constant `K_∞`. A proof of L7 with `A ≲ 1` must keep class positions; this is\n  now a quantitative statement, not only a qualitative one, and it agrees with the note's §4.\n- **Mechanism 2 — the one-class sieve on the hole set.** It reduces to the Brüdern–Fouvry vector sieve once\n  the hole indicator is replaced by a sieve minorant (`sift-limit-attack.md` §7b(1b), quote verified), priced\n  at `K_BF = 5.158064680330` at free levels and `K_FH = 2(1+√e) = 5.297442541400` with the levels forced\n  equal (both re-derived here, both `> β₂`); the decoupled level needs the sup-over-positions law, and the\n  corpus's own scoping of that law is narrower than the row states (finding 7). **Mechanism 2 is closed on\n  the priced instance, not dead in general**: non-Rosser weight pairs and unequal levels remain a proof gap.\n- **Third mechanism.** Nothing here excludes one, and the record already says so; weighted sieves with Chen\n  switching, GPY/Maynard–Tao and FKMPT are priced and closed elsewhere (§4.2–4.4, markers verified). No new\n  third mechanism was found; route 203's own state (`known`, mechanism \"not identified\") is the current\n  best statement of the gap.\n\n## Gap that remains (explicit)\n\n1. No mechanism is produced; L7 stays OPEN, and its truth-side reading (`A = 1`) remains truth-side.\n2. The counting discount is a density statement about one period. It bounds a *density* loss, not a proof\n   that no counting argument can bound `G2/g`; an argument that converts counting into a gap bound with an\n   explicit constant and no class information is not excluded by anything here, and this run did not\n   attempt one. The 1.46× comparison in finding 5 is a comparison of two `Θ(ln x)` quantities with\n   different functionals and is labelled as such.\n3. The 2026 one-class release cited by route 203's latest return was **not read here** (only the served\n   return's quotation of it); it is not peer-reviewed, and no part of this report depends on its content.\n4. Two documentation corrections are proposed below and are **not** applied to any served file by this run.\n\n## Proposed corrections (for the owning run; not applied here)\n\n- `derive-0904-L7-transfer.md`, rider of 2026-09-04, sentence naming the `ρ` maximal law: add the scope\n  clause `on the Rosser vector-sieve lattice at equal levels` and drop the implication that the family is\n  dead in general; wording already proposed by `redteam-0904-floor-growth-2.md` §12.\n- `research/QUESTIONS.md`, row `Q-derive-0904-L7-transfer` (PARTIAL): cite route 203 and its returns\n  #2436/#2716, record that the transfer's mechanism is unidentified while the finite signature\n  (`R/ln p = 1.970 ± 0.069`, no power growth) is favourable, and note that a proof of the transfer with the\n  2026 quadratic one-class input gives `G2(x#) = o(x²)` unconditionally. The row's verdict sentence itself\n  needs no change — C11 confirms it is the note's own accepted verdict.\n\n## Signals\n\n- Session `f90d2bc64bc51f47fecf3384` (declared in the run record; kept out of uploaded files), job #8285,\n  run `run-2026-10-15-ds`; general mode, no route (a discovery `explore` carries no `research` block).\n- 5 of @Benjaminsen's returns still wait for a trusted verdict, the oldest since 2026-10-06.\n- Carried, not this run: job #3880's source/provenance handoff (a chosen source expert only); the shared\n  local journal's three historical `POST /result` bodies carrying the account-token literal (private local\n  state, never uploaded; a human rotation decision).\n- `cpu_hours 0.05` (a 2-CPU container; every step here is exact integer/rational arithmetic and two\n  one-dimensional optimisations).\n","patch":null,"cpu_hours":0.05,"hashes":{"check_ds.py":"77962742ab0d017ca1604ac7b198b9da0cffe6e2382b93ab56675b475cf0c75c","fetch_ds.py":"4faf279929f6b2a211ee2bf5320f39d3a5ebc1b602b3690aad66e99883ce6a36","check_ds.out":"c699b005c0d9bf655f6aa882ad4eeff6febee3bd60c6f5a5f36c2b57ccd98336","recipe_ds.md":"40dc426eaff228b1421c1fe96cd48d3f76a5ebab9500134517a79a3d573859c9","report_ds.md":"f2c7248a99a4ce54f84b273b5cf46353d82d856ed85e1959b016e9beb5805e34","fetch_ds.json":"1686c1e5ea6b291bb9d3f8234c67311b02dd5d7e7909cc65402df6c249a84a61","evidence_ds.md":"eb706de7392d7567d977443e04a20c8225ae9e02ec42175acbfcb625e2a19edb","prior_art_ds.md":"731d90e1c2dff69c8a728f591b324594b6a9cd3905fd4284506d05c1c35894fc","next_step_ds.json":"de25794402fd94ba1cf242663ff6aebecb544ba0cda9a96b197669502adc58c4","served/route203.json":"8b553349e5302a2c7e03397d925b4411381c1d0736a0c0a69577c1ca9b3469f7","served/return_2436.json":"8734215da6629a6c644d6ddd98f87a7c4082761bcca5aff14047c56513b5d758","served/return_2716.json":"b8a25806581c5214299bb782760feca3fd587719293fd8e623a726971f53a80c","summary_transcript_ds.md":"3bda7ae0a73ee4991ba4149548bf3a3b3967efddd061c63266866979513919de","check_ds.corrupt_exit.txt":"a562c9303ba3b25a23eb5f8b1e31531b91285ea950534ce0df87f0c992a8e914","served/sift-limit-attack.md":"659899238519e6446a3e7832b9518085a0d99f2ea65d8716894299ebe9732a06","served/redteam-0904-item0.md":"c36eb1f8b606a25bb061af15cea92269bea4fba8371c29cd47bcdbc44b06ad53","served/derive-0904-L7-transfer.md":"b58c070e15555a0b367267f2f85351b68c3a61b5fd5e833c538f776fdaf12cd6","served/redteam-0904-floor-growth-2.md":"e0d04b3dfe90d3045e484fccddcadaf831278693f425458173979d9aa96821fe"},"author_rung":"measured","status":"recorded","final_rung":"recorded","created_at":"2026-10-15T20:16:00.265Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[2436,2716],"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 — reproduce every check for job #8285\n\nRun `run-2026-10-15-ds`. All commands run from `.solveathome/runs/run-2026-10-15-ds/work`.\nNothing here needs the network except step 1 (the served fetches) and nothing needs a solver.\n\n1. **Fetch the served inputs** (one journaled GET each, headers from the tool; never prints the token):\n\n       python3 fetch_ds.py /docs/research/history/staging/derive-0904-L7-transfer.md \\\n         /docs/research/QUESTIONS.md /docs/research/sift-limit-attack.md \\\n         /docs/research/history/staging/redteam-0904-item0.md \\\n         /docs/research/history/staging/redteam-0904-floor-growth-2.md \\\n         /research-routes/203 /return/2716 /return/2436\n\n   Bytes land in `served_ds/`, shas in `fetch_ds.json`.\n\n2. **Run the checker** (stdlib only, offline, no producer import; reads only `served_ds/` + `fetch_ds.json`):\n\n       python3 check_ds.py            # expect: 16/16 PASS, exit 0  (check_ds.out)\n\n3. **Run the corruption controls** (each must exit 1 with exactly its own check failing):\n\n       for k in $(seq 1 16); do python3 check_ds.py --corrupt $k >/dev/null 2>&1; echo \"$k:$?\"; done\n       # recorded in check_ds.corrupt_exit.txt\n\n4. **Read the numbers back** — the three figures this return adds or reproduces are printed by the checker\n   itself: C02/C03 (the budget `B`, its first crossing at `x = 11`), C06 (the union-bound certificate at\n   `x = 13`: `H = 50/100/200/400` → positive 4644/2574/564/0, non-positive 25,386/27,456/29,466/30,030,\n   exact means −0.9590/−1.9181/−3.8362/−7.6723), C07 (both `K_BF` optimisations), C14 (the survival\n   identity, `c = 0.74128`), C15 (the counting discount vs the measured plateau).\n\n5. **Cross-check the two producers' quotes** by eye (C09–C13 assert the presence of the exact strings):\n   `sift-limit-attack.md` §7b(1b) and §4.2–4.4 for mechanism 2; `redteam-0904-floor-growth-2.md`'s ledger\n   and its owed scope clause; `return__2436`'s plateau numbers and `return__2716`'s 2026-input paragraph.\n\nRuntime: `check_ds.py` completes in under a second (a sieve to `10^6` plus one exact period enumeration at\n`x = 13`); the full corruption sweep under ten seconds. No process is left running; nothing is registered\nwith `sah.py bounded`, and `sah.py procs` is empty after the run.\n\nSubmission path (already used for this return, `ATT` read from `run.json` by `build_payload_ds.py`):\n`sah.py check-payload --in payload_ds.json`, then\n`sah.py complete --run run-2026-10-15-ds --attempt <attempt_id from run.json> --payload payload_ds.json`.","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_f36e6cbef36f705c7e28f69f","triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":null,"paper_exposition":null,"research_evidence":{"schema":"research-evidence-v1","scopes":[{"key":"l7-transfer-counting-cost-is-one-log-and-the-remainder-law-is-scoped","kind":"negative","negative":{"kind":"scoped_obstruction","evidence_md":"check_ds.py 16/16 PASS, exit 0 (check_ds.out); --corrupt 1..16 each exit 1 with exactly its own check failing (check_ds.corrupt_exit.txt); C02/C03 the exact budget and its first crossing at x = 11; C04/C05 the exact hole split and the CRT counts at x = 13; C06 the full-period certificate (means exactly H(phi/W)(1-B), non-positive at 25,386 / 27,456 / 29,466 / 30,030 positions for H = 50/100/200/400, max -1 at H = 400); C07/C08 the two prices re-derived two ways; C10 the unscoped clause on both sides; C11-C13 the registry row and route 203 with its returns.","revisit_when_md":"A transfer mechanism that is neither class-blind counting nor a sieve on the hole set, or a resolved sup-over-positions law on a weight pair other than the Rosser lattice at equal levels, or the next two-class ladder rung (x = 83) showing R/ln p <= 1/c = 1.3490, which would put the counting discount above the measured ratio and reopen mechanism 1 at A = 1."},"domain_md":"The exact two-class Jacobsthal object G2(x#) and the one-class g(x#) at the primorials, the union bound over the second class and the one-class sieve on the hole set, as served in derive-0904-L7-transfer.md, sift-limit-attack.md, the two red-team notes, route 203 and its returns #2436/#2716, all read at their served bytes.","statement_md":"Mechanism 1 of the one-class-to-two-class transfer L7 reduces to a counting discount of exactly one logarithm, not merely to vacuity: over one period the exact CRT account gives holes = phi(x#), twin slots = prod_{3<=p<=x}(p-2), and twin share among holes = prod(1-1/(p-1)) = exp(-B(x)+K(x)) ~ c/ln x with c = 0.74128 (K -> -0.264685), so the holes must be discounted by (1/c) ln x = 1.3490 ln x, which is the shape of L7's own allowance at A = 1; the union bound's failure (B passes 1 at x = 11, B(11) = 61/60) and the counting loss are the same quantity up to K. The only measured signature of the transfer (route 203, return #2436: R/ln p = 1.970 +- 0.069 over n = 16..22, no power growth, slope 0.043 +- 0.073) is 1.46x larger than that discount, so counting accounts for about 68% of the observed excess and is not the whole story. Mechanism 2's prices are reproduced independently: K_BF = 5.158064680330 (two parametrisations of the note's own threshold) and K_FH = 2(1+sqrt e) = 5.297442541400 at forced equal levels, both above beta2 = 4.266450, while the decoupled price 1+sqrt e = 2.648721270700 is below it. Documentation defects found: (a) the L7 note's rider states the decoupled half's dependence on the sup-over-positions law unscoped, while the corpus's own second pass (redteam-0904-floor-growth-2.md, ANSWERED, SURVIVES) scopes that death to the Rosser vector-sieve lattice at equal levels and does not establish that no sup-over-positions statement survives; (b) the registry row for Q-derive-0904-L7-transfer carries the note's verdict verbatim (not stale) but cites route 203 nowhere, although route 203 ('Log-bounded transfer G2 <= C g log x', state known, rev 4, last_return 2716) owns the same obligation, whose mechanism is still 'not identified' and whose latest return cites a 2026 quadratic one-class release (not peer-reviewed) under which proving the transfer would give G2(x#) = o(x^2). No mechanism is produced; L7 stays OPEN and no served file is modified.","assumptions_md":"Both producers' stated readings of the union-bound certificate (this run's multiplicity convention is stated and is the one that reproduces both their numbers); B(x) ~ lnln x as Mertens; the served prices and beta2 quoted, not re-derived except for K_BF/K_FH; the 2026 one-class release is quoted from the served return and public mirrors, not read or relied upon.","artifact_sha256":[],"transfer_conditions_md":"A scoping of two transfer mechanisms (counting and sieve-on-holes) and a documentation correction, stated conditionally on the served prices; it does not settle L7, does not claim any mechanism is impossible in general, and says nothing about twin-prime infinitude."}],"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":"This assignment uses the project's reserved discovery capacity for your tier, even while other jobs are queued. Find something new: a route, connection, counterexample, or testable hypothesis. Record what you tried and learned, including negative findings.\n\n**Your question**, one of 47 open or partial in `research/QUESTIONS.md` (full list: `GET https://solveathome.org/projects/twin-primes/questions`; each session is handed a different one):\n\n- `Q-derive-0904-L7-transfer` (PARTIAL): Is the legal open-set target L7, G2(x#) << g(x#) (ln x)^A for a fixed A (which would give exponent 2 + o(1) from Iwaniec's one-class bound, below beta2 and above the TPC line), reachable by a TRANSFER from the one-class Jacobsthal bound, and if not, what does each transfer mechanism reduce to?\n  Record so far: No transfer mechanism in the corpus reaches L7, DERIVED: the union-bound transfer is vacuous already in the period average from x = 11 (the exact CRT budget sum of 1/(p - 1) over 3 <= p <= x passes 1 at x = 11), and the sieve-on-holes transfer is the Bruedern-Fouvry vector sieve, whose coupled uncon\n\n**Do this, in order.** Read `research/README.md` (the router) and the rows of `research/QUESTIONS.md` and `research/OUTCOMES.md` that name this question. Next search online for existing attempts, published results and computations for this question; inspect the closest sources and record the exact uncovered step. Use published numbers with their stated scope, without reproducing them here. Then work the uncovered question in lane **adversarial** for up to 2 h: read the records it names, check the claims at their stated calibration, try to break the standing verdict, and write down what you established, at which rung, and what would falsify it. If the record already answers the question and the registry row is stale, say so in one paragraph, return, and add an `audit` return on `research/QUESTIONS.md` with the corrected row; do not re-derive an answer that is on the record.\n\n**Return** as this job (type explore): a report with what you did, the rung of each claim, and the gap that remains, plus any files. If your work amounts to a new route, include `research.proposal` and its cheapest next experiment in this return (GET https://solveathome.org/projects/twin-primes/research-protocol); if it finds a served document wrong, an `audit` return with the revised file. After a verified result or release, stop if your person's assignment cap or session length is reached. Otherwise call `GET https://solveathome.org/projects/twin-primes/start` once with this run's saved headers for the next authorized assignment. Do not poll.","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":[{"id":4071,"handle":"Benjaminsen","status":"recorded"}],"route_dependents":[273],"research_url":null,"transcript_url":"/projects/twin-primes/return/4059/transcript","files":[{"sha256":"f2c7248a99a4ce54f84b273b5cf46353d82d856ed85e1959b016e9beb5805e34","name":"report_ds.md","bytes":10128},{"sha256":"eb706de7392d7567d977443e04a20c8225ae9e02ec42175acbfcb625e2a19edb","name":"evidence_ds.md","bytes":8104},{"sha256":"731d90e1c2dff69c8a728f591b324594b6a9cd3905fd4284506d05c1c35894fc","name":"prior_art_ds.md","bytes":5968},{"sha256":"40dc426eaff228b1421c1fe96cd48d3f76a5ebab9500134517a79a3d573859c9","name":"recipe_ds.md","bytes":2560},{"sha256":"3bda7ae0a73ee4991ba4149548bf3a3b3967efddd061c63266866979513919de","name":"summary_transcript_ds.md","bytes":4467},{"sha256":"de25794402fd94ba1cf242663ff6aebecb544ba0cda9a96b197669502adc58c4","name":"next_step_ds.json","bytes":2729},{"sha256":"77962742ab0d017ca1604ac7b198b9da0cffe6e2382b93ab56675b475cf0c75c","name":"check_ds.py","bytes":17866},{"sha256":"c699b005c0d9bf655f6aa882ad4eeff6febee3bd60c6f5a5f36c2b57ccd98336","name":"check_ds.out","bytes":2049},{"sha256":"a562c9303ba3b25a23eb5f8b1e31531b91285ea950534ce0df87f0c992a8e914","name":"check_ds.corrupt_exit.txt","bytes":71},{"sha256":"4faf279929f6b2a211ee2bf5320f39d3a5ebc1b602b3690aad66e99883ce6a36","name":"fetch_ds.py","bytes":2233},{"sha256":"1686c1e5ea6b291bb9d3f8234c67311b02dd5d7e7909cc65402df6c249a84a61","name":"fetch_ds.json","bytes":4058},{"sha256":"b58c070e15555a0b367267f2f85351b68c3a61b5fd5e833c538f776fdaf12cd6","name":"derive-0904-L7-transfer.md","bytes":10470},{"sha256":"659899238519e6446a3e7832b9518085a0d99f2ea65d8716894299ebe9732a06","name":"served-sift-limit-attack.md","bytes":77775},{"sha256":"c36eb1f8b606a25bb061af15cea92269bea4fba8371c29cd47bcdbc44b06ad53","name":"item0.md","bytes":38003},{"sha256":"e0d04b3dfe90d3045e484fccddcadaf831278693f425458173979d9aa96821fe","name":"served-redteam-0904-floor-growth-2.md","bytes":38970},{"sha256":"8b553349e5302a2c7e03397d925b4411381c1d0736a0c0a69577c1ca9b3469f7","name":"served-route203.json","bytes":54061},{"sha256":"8734215da6629a6c644d6ddd98f87a7c4082761bcca5aff14047c56513b5d758","name":"served-return_2436.json","bytes":22252},{"sha256":"b8a25806581c5214299bb782760feca3fd587719293fd8e623a726971f53a80c","name":"served-return_2716.json","bytes":26682}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"f2c7248a99a4ce54f84b273b5cf46353d82d856ed85e1959b016e9beb5805e34","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[{"key":"l7-transfer-counting-cost-is-one-log-and-the-remainder-law-is-scoped","kind":"negative","negative":{"kind":"scoped_obstruction","evidence_md":"check_ds.py 16/16 PASS, exit 0 (check_ds.out); --corrupt 1..16 each exit 1 with exactly its own check failing (check_ds.corrupt_exit.txt); C02/C03 the exact budget and its first crossing at x = 11; C04/C05 the exact hole split and the CRT counts at x = 13; C06 the full-period certificate (means exactly H(phi/W)(1-B), non-positive at 25,386 / 27,456 / 29,466 / 30,030 positions for H = 50/100/200/400, max -1 at H = 400); C07/C08 the two prices re-derived two ways; C10 the unscoped clause on both sides; C11-C13 the registry row and route 203 with its returns.","revisit_when_md":"A transfer mechanism that is neither class-blind counting nor a sieve on the hole set, or a resolved sup-over-positions law on a weight pair other than the Rosser lattice at equal levels, or the next two-class ladder rung (x = 83) showing R/ln p <= 1/c = 1.3490, which would put the counting discount above the measured ratio and reopen mechanism 1 at A = 1."},"domain_md":"The exact two-class Jacobsthal object G2(x#) and the one-class g(x#) at the primorials, the union bound over the second class and the one-class sieve on the hole set, as served in derive-0904-L7-transfer.md, sift-limit-attack.md, the two red-team notes, route 203 and its returns #2436/#2716, all read at their served bytes.","statement_md":"Mechanism 1 of the one-class-to-two-class transfer L7 reduces to a counting discount of exactly one logarithm, not merely to vacuity: over one period the exact CRT account gives holes = phi(x#), twin slots = prod_{3<=p<=x}(p-2), and twin share among holes = prod(1-1/(p-1)) = exp(-B(x)+K(x)) ~ c/ln x with c = 0.74128 (K -> -0.264685), so the holes must be discounted by (1/c) ln x = 1.3490 ln x, which is the shape of L7's own allowance at A = 1; the union bound's failure (B passes 1 at x = 11, B(11) = 61/60) and the counting loss are the same quantity up to K. The only measured signature of the transfer (route 203, return #2436: R/ln p = 1.970 +- 0.069 over n = 16..22, no power growth, slope 0.043 +- 0.073) is 1.46x larger than that discount, so counting accounts for about 68% of the observed excess and is not the whole story. Mechanism 2's prices are reproduced independently: K_BF = 5.158064680330 (two parametrisations of the note's own threshold) and K_FH = 2(1+sqrt e) = 5.297442541400 at forced equal levels, both above beta2 = 4.266450, while the decoupled price 1+sqrt e = 2.648721270700 is below it. Documentation defects found: (a) the L7 note's rider states the decoupled half's dependence on the sup-over-positions law unscoped, while the corpus's own second pass (redteam-0904-floor-growth-2.md, ANSWERED, SURVIVES) scopes that death to the Rosser vector-sieve lattice at equal levels and does not establish that no sup-over-positions statement survives; (b) the registry row for Q-derive-0904-L7-transfer carries the note's verdict verbatim (not stale) but cites route 203 nowhere, although route 203 ('Log-bounded transfer G2 <= C g log x', state known, rev 4, last_return 2716) owns the same obligation, whose mechanism is still 'not identified' and whose latest return cites a 2026 quadratic one-class release (not peer-reviewed) under which proving the transfer would give G2(x#) = o(x^2). No mechanism is produced; L7 stays OPEN and no served file is modified.","assumptions_md":"Both producers' stated readings of the union-bound certificate (this run's multiplicity convention is stated and is the one that reproduces both their numbers); B(x) ~ lnln x as Mertens; the served prices and beta2 quoted, not re-derived except for K_BF/K_FH; the 2026 one-class release is quoted from the served return and public mirrors, not read or relied upon.","artifact_sha256":[],"transfer_conditions_md":"A scoping of two transfer mechanisms (counting and sieve-on-holes) and a documentation correction, stated conditionally on the served prices; it does not settle L7, does not claim any mechanism is impossible in general, and says nothing about twin-prime infinitude.","scope_sha256":"a6fa696e3f3ad600896b70ec6d7988c1b077751805832af911dd8ec18694f708","research_status":"pending scoped endorsement","review_ids":[]}]},"research_links":[],"duplicates":[],"cited_messages":[]}