{"id":4195,"job_id":8604,"problem_id":1,"lane_id":32,"type":"explore","user_id":1,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# Report — job #8604 (explore / `discover`, no route, lane `dir-558`, general mode): **New route**\n\n**Outcome `proposed`** — one route, with its object, the step that would have to hold, the cheapest\ncheck that could refute it and its cost. The proposal is in this return as `research.proposal`; the\nmeasurement below is what makes it bounded. Rung of the report's own numbers: **measured, exact,\nfull period** (no census, no sampling, no asymptotics). Own attempt/session/run identifiers are in\nthe run's private state and the transcript, not here.\n\n## Headline\n\nThe record (#2426, route 202) refuted the *constant* one-parameter bridge between the two natural\ncyclic carriers of the twin wheel by the **raw** spread of the bridge ratio `q1 = rho_1(A)/rho_1(R)`\n(28.8 % over `17#..23#`). Extending both carriers to **`29#`**, exactly:\n\n* `q1` is still rising and its increment is still **growing** (`+0.0337, +0.0377, +0.0491` from\n  `17#`), so no stationary point appears — but\n* **the rescaled ratio `(1 - q1)*ln p` is flat**: `1.279, 1.806, **2.229, 2.218, 2.243, 2.244**` at\n  `11#..29#`, i.e. **2.23 +- 0.03 over the four rungs `17#..29#` (1.2 % spread)**, against a 39 %\n  spread of the raw `q1` over the same four rungs.\n\nSo the bridge the record refuted as a constant may exist as an **asymptotic one-parameter law with a\n`1/ln x` correction**, `rho_1(A) = rho_1(R)*(1 - c/ln x)` with `c = 2.23`. That is the proposed\nroute. Nothing here proves it: a four-rung flatness is a fit, and the decisive test is `31#`.\n\n## What was measured (exact, one core, 39 s wall)\n\nTwo cyclic gap words on `Z/P`, `P = x#`, exactly as #2299 / #2426 define them:\n**reduced** `R` (`gcd(n,P)=1`, `N_R = phi(P)`) and **paired** `A` (`gcd(n,P)=gcd(n+2,P)=1`,\n`N_A = prod_{p>2}(p-2)`); `rho_k = (N*S_k - P^2)/(N*S_0 - P^2)`, `S_k = sum_i g_i g_{i+k}` cyclic.\nRungs `11#..23#` by a direct full-period sieve; the **`29#` rung by an exact block lift** (delete the\nforbidden residue class(es) mod 29 inside each block of length `23#`), with the lift validated\n**bit-exactly** against the direct sieve at `23#` (`max|diff| = 0.000e+00`, both carriers), and the\nwhole `29#` rung independently re-derived by a chunked direct sieve in `check_bz.py`.\n\n| x# | N_R | rho_1(R) | rho_2(R) | rho_3(R) | N_A | rho_1(A) | rho_2(A) | rho_3(A) | q1 |\n|---|---|---|---|---|---|---|---|---|---|\n| 11 | 480 | -0.252340 | -0.000289 | -0.146769 | 135 | -0.117700 | +0.268964 | +0.006154 | 0.4664 |\n| 13 | 5760 | -0.210269 | -0.046908 | -0.133873 | 1485 | -0.062238 | +0.119602 | -0.093884 | 0.2960 |\n| 17 | 92160 | -0.186506 | -0.066660 | -0.118830 | 22275 | -0.039748 | +0.021241 | -0.162328 | 0.2131 |\n| 19 | 1658880 | -0.170428 | -0.077185 | -0.103406 | 378675 | -0.042061 | -0.044552 | -0.172766 | 0.2468 |\n| 23 | 36495360 | -0.159126 | -0.081255 | -0.090084 | 7952175 | -0.045272 | -0.073864 | -0.152962 | 0.2845 |\n| **29** | **1021870080** | **-0.150838** | **-0.081903** | **-0.079703** | **214708725** | **-0.050315** | **-0.085892** | **-0.134505** | **0.3336** |\n\nThe `11#..23#` rows reproduce #2426's published gate to <1e-6 in every printed field\n(`rho_1(R)`, `rho_1(A)`, `rho_2(A)`, `q1`), so the instrument is validated on the record before any\nnew reading. **Internal validation of the `29#` lift:** the record's reduced diagnostic\n`-rho_1(R)*ln p` is `0.5284, 0.5018, 0.4989` at `17#,19#,23#` and **`0.5079` at `29#`** — the\none-rung-out value lands back on the `1/2` the route records from `19#` on.\n\n## New finite facts\n\n1. **Rescaled bridge ratio.** `(1 - q1)*ln p` = `1.279, 1.806, 2.229, 2.218, 2.243, 2.244`;\n   equivalently `-rho_1(A)*ln p = 1/2 - c/(2 ln p)` with `c = 2.23` (predicted `0.1065, 0.1212,\n   0.1444, 0.1688` at `17#,19#,23#,29#` against measured `0.1126, 0.1238, 0.1420, 0.1694`).\n2. **`d_k := rho_k(R) - rho_k(A)` has a decided finite event at lag 2**: `d_2 = -0.2693, -0.1665,\n   -0.0879, -0.0326, -0.00739, **+0.00399**` — it **crosses zero between `23#` and `29#`**, after\n   narrowing monotonically over five rungs. `d_3` crosses at `13#->17#`; `d_1` never (minimum at\n   `13#`, then rising: `-0.1005` at `29#`).\n3. **Route 186's own reopening falsifier is answered at `29#`, against closing the route**:\n   `rho_2(R) = -0.0819` and `rho_3(R) = -0.0797` stay negative, and `rho_2(R)` **stabilises**\n   (`-0.0772, -0.0813, -0.0819` at `19#,23#,29#`) rather than decaying to 0 — so the multi-lag\n   negativity is not a small-`x` artefact. Route 186's order-1 model (`rho_2 = rho_1^2 > 0`) is\n   refuted at `29#` as at every earlier rung.\n4. **Route 202's own flagged test.** Its uncertainty says \"the one-parameter bridge is refuted only\n   on `11#..23#` ... a one-parameter fit could conceivably reappear at `29#/31#`; the next experiment\n   tests this directly.\" At `29#` the **raw** reading says no (q1 keeps rising, increment growing),\n   the **rescaled** reading says yes. Both are recorded; the `31#` rung decides.\n5. The order-1 threshold rung of `A` stays `17#->19#` over six rungs; `R`'s is `11#`.\n\n## Controls\n\n* **Independent re-derivation (`check_bz.py`):** its own chunked direct sieve over the whole `29#`\n  period and its own tail-sector accumulator reproduce every stored number; **12/12 PASS, exit 0**.\n* **Corrupt matrix:** 12 injections, each caught by **exactly its own** check and no other\n  (`check_bz.corrupt_exit.txt`).\n* **Permutation control** (route 186's): at `23#`, none of 10 shuffles of either carrier's gap\n  multiset reaches the natural `rho_1` (fraction `0/10` for both) — the arrangement carries real\n  structure and is not a multiset effect.\n* Multiplicity/rate sanity: `N_R = phi(P)` and `N_A = prod_{p>2}(p-2)` hold at every rung, and\n  `sum_i g_i = P` at every rung (`check_bz.py` C02/C03).\n\n## Scope and limits\n\nExact finite statements at `11#..29#` only. No asymptotic claim, no bound on `G2`, no claim about\ntwin-prime occurrence. `rho_k` is a **diagnostic** of the arrangement; the link from it to the `G2`\nexponent is **conjectural**, exactly as route 188's uncertainty says. The `c = 2.23` flatness is a\n**four-rung fit** (1.2 % spread), not a theorem and not a bound; `11#` and `13#` are outside it\n(`1.28, 1.81`) and are reported as such. The permutation control uses 10 shuffles per carrier at\n`23#` only. `31#` was **not** run (its paired word is 6.6e9 gaps); the route's whole claim is\npre-registered against that rung.\n\n## What it changes, and the owed line\n\nIt replaces a *refutation* of the carrier bridge (as the record reads `q1`) by a **bounded\ndecision**: if `(1 - q1)*ln 31` lands in `[2.15, 2.33]` and `d_2` stays positive, the reduced lane's\nmachinery transfers to the paired carrier **asymptotically with an explicit `1/ln x` offset**, and\nthe exponent route may be carried on `A`; if either fails, the two carriers are structurally separate\nand the route closes at `31#` for ~11 minutes of one core. Either outcome is worth recording.\n\n**Handle line owed to the project:** 6 of @Benjaminsen's returns wait for a verdict (oldest\nsince 2026-10-06); nothing is requested from this return.\n\n## Files\n\n`probe_bz.py`/`probe_bz.json`/`probe_bz.out` (instrument and its exact numbers),\n`check_bz.py`/`check_bz.out`/`check_bz.corrupt_exit.txt`/`own_bz.json` (independent checker and its\ncorrupt matrix), `fetch_bz.py` + `index_bz.json` (the served registers read, sha-pinned, values-free),\n`evidence_bz.md`, `proposal_bz.md` (the route, human-readable), `recipe_bz.md`,\n`summary_transcript_bz.md`. Reproduce: `python3 probe_bz.py probe_bz.json` (39 s, one core, <1 GB)\nthen `python3 check_bz.py` (12 checks, 0 FAIL, exit 0).\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-16T10:55:14.967Z","repo_url":null,"commit":null,"cites":null,"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 #8604 (new route: the asymptotic carrier bridge)\n\nEverything below reproduces the return from its own file set. No path outside this list is used.\n\n## Environment\n\nPython 3.11 with numpy only. No network during the measurement. One core, < 1 GB peak, 39 s wall for\nthe whole instrument. The run's files are named with their sha256 in the return inventory.\n\n## 1. Instrument (produces every reported number)\n\n    python3 probe_bz.py probe_bz.json      # 39 s, one core; prints the same summary it stores\n\n`probe_bz.py`:\n\n* `direct_word(x, paired)` — full-period uint8 sieve for `11#..23#`; `paired` adds `m &= roll(m,-2)`.\n* `gaps_from_res` / `S_of_gaps` / `rho_from_S` — the exact integer identity\n  `rho_k = (N*S_k - P^2)/(N*S_0 - P^2)` with `S_k = sum_i g_i g_{i+k}` cyclic; no float before the\n  final ratio.\n* `lift_29(prev_idx, P_prev, p, paired)` — the exact block lift: block `j` keeps the previous word's\n  residues with `m != -j*P_prev (mod p)` (and `m != -j*P_prev - 2 (mod p)` when `paired`), and the\n  gaps are streamed into a `Stream` accumulator in O(kmax) memory.\n* `permutation_control` — route 186's shuffle control on the gap multiset.\n\nThe `29#` rung is produced only by the lift; the lift itself is validated against the direct sieve at\n`23#` (`max|diff| = 0.000e+00` for both carriers, stored as `rungs['23#']['lift_from_19_*']`).\n\n## 2. Independent checker (refuses to trust the instrument)\n\n    python3 check_bz.py                  # 12 checks, 0 FAIL, exit 0\n    python3 check_bz.py --refresh        # recompute this checker's own moments from scratch\n    for k in $(seq 1 12); do python3 check_bz.py --corrupt $k; done\n\n`check_bz.py` has its own chunked direct sieve over the whole `29#` period and its own tail-sector\nmoment accumulator (a different formulation from the instrument's concatenate-and-subtract\nstreaming); C06 re-derives the whole `29#` rung from that sieve. Each check owns exactly one stored\nfield group, so each of the 12 injections is caught by exactly its own check and no other\n(`check_bz.corrupt_exit.txt`). `--refresh` writes `own_bz.json`; without it the checker reuses that\nfile (produced by its own code) so the corrupt matrix is affordable — the 12/12 clean run reported in\nthe return was made with no cache present.\n\n## 3. Registers read (read-only, sha-pinned, values-free)\n\n    python3 fetch_bz.py\n\nGETs the served registers this \"New route\" assignment requires — `/questions`, `/research-routes`,\n`/research-protocol`, `/state/dir-558`, `/board` — plus `docs/research/OUTCOMES.md`,\n`docs/research/README.md` and `docs/research/QUESTIONS.md`, into `served_bz/` with a per-URL index\n(`index_bz.json`). Direct urllib, token read from the protected credential file, never written.\n\n## 4. Result summary\n\nGate reproduces #2426 exactly; the `29#` rung gives `rho_1(R) = -0.150838`, `rho_2(R) = -0.081903`,\n`rho_3(R) = -0.079703` (`N_R = 1021870080`) and `rho_1(A) = -0.050315`, `rho_2(A) = -0.085892`,\n`rho_3(A) = -0.134505` (`N_A = 214708725`); `q1(29#) = 0.3336`; `(1 - q1)*ln p` flat at `2.23` over\n`17#..29#`; `d_2` crosses zero between `23#` and `29#`; `31#` is the pre-registered decisive rung.","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":[{"sha":"a4f2729c5680ae85dfbf162dce2440d1098b34243b3a888fbbd391ef1da56aa1","name":"probe_bz.py","notes":["prints what looks like progress or timing to stdout on line 226 (\"% (tag, N, r[1], r[2], r[3], time.time() - t1), flush=True)\"), inside the statement that starts on line 225: stdout is the artifact and must reproduce byte for byte elsewhere; send progress, timing and rates to stderr. This one is a guess from the text, not a measurement: if the output is already identical from run to run, say so in your return and leave the file alone."],"fixed_by":"7209fd3e4bba9cfd368f8bbf97299fdc89705240989444afb6c4fcf46c9b19e2"}],"research":{"outcome":"proposed","proposal":{"title":"The asymptotic one-parameter carrier bridge: rho_1(A) = rho_1(R)*(1 - c/ln x) with c = 2.23","prior_art_md":"**Online search, 2026-10-16** (before the work). Queries: (i) `cyclic autocorrelation of the reduced\nresidue system modulo a primorial gap sequence lag-1 1/ln x`; (ii) `twin prime candidates residues\ncoprime n and n+2 primorial gap autocorrelation ratio law`.\n\n**Findings.** Query (i)'s top hit is this project's own **route 180**, whose page records that \"no\nsource found computes the lag-1 autocorrelation of the reduced-residue gap sequence of a primorial\nover a full period\"; the other hits are the reduced-residue-system entry and signal-processing\ncyclic-autocorrelation literature. Query (ii)'s nearest external neighbour is the ResearchGate note\n*Harmonic Resonance in Twin Prime Distribution* (\"Residue Histograms and Autocorrelation ... 1,485\nadmissible residue classes mod 2*3*5*7*11*13 with both n and n+2 coprime\"), i.e. **this run's\n`A(13#)`** (`N_A(13#) = 1485`), which reports residue histograms and an autocorrelation of that set\nbut **no bridge ratio, no comparison against `R`, and no `1/ln x` law**. Its full text was not\nreachable (access gap). The remaining hits are unrelated twin-prime preprints. **No source found\ncarries `q1 = rho_1(A)/rho_1(R)`, its rescaled form `(1 - q1)*ln x`, or the flat constant `2.23`**;\n`(1 - q1)*ln p` appears nowhere on the record either.\n\n**Earlier attempts and computations inspected.** Route 202 / return **#2426** defines both carriers,\npublishes the `11#..23#` paired table and the `14#..23#` reduced table, and refutes the **constant**\nbridge from the raw spread (`q1 = +0.4664, +0.2960, +0.2131, +0.2468, +0.2845`; 28.8 % over\n`17#..23#`, pre-registered 20 % bar). Return **#4191** carries the most recent paired-carrier result\nand leaves `29#/31#` unrun. Route **186** measures `R`'s `rho_2, rho_3` on `13#..23#` and records\n\"`29#` and `31#` were not run here\" as its open gap, with the falsifier \"the route's own claim is\nrefuted if `rho_2` or `rho_3` changes sign at `29#/31#`\". Route **180** records the `1/2` diagnostic\n`-rho_1(R)*ln x -> 1/2` used here as an internal validation of the new rung.\n\n**Exact uncovered step.** Neither route formed the *rescaled* ratio, so the record's refutation is of\n`c = 0` and not of the family `q1 = 1 - c/ln x`; and no `29#` value of either carrier exists on the\nrecord. This return supplies the `29#` rung of both carriers (exactly, by an exact block lift\nvalidated bit-exactly against a direct sieve at `23#`, and independently by a chunked direct sieve)\nand the rescaled series, whose flatness over `17#..29#` is what is proposed. **No-match is not\nnovelty**: this note records a bounded comparison, not a novelty claim, and `31#` is the decisive\ntest.","uncertainty_md":"**Weakest unproved assumption.** That the four-rung flatness of `(1 - q1)*ln p` is a law and not a\nfinite-wheel coincidence. Only four points lie inside the band; `11#` and `13#` lie well outside it\n(`1.279`, `1.806`), so a slowly drifting `c` is not excluded, and the hypothesis was formed *after*\nseeing `29#`, i.e. post-hoc. The `31#` pre-registrations (`c(31) = (1 - q1(31))*ln 31` inside\n`[2.15, 2.33]`, and `d_2(31) > 0`) are therefore stated as numeric windows before any `31#`\ncomputation; the return contains no `31#` value.\n\n**Second.** `rho_k` is one arrangement functional. Even a confirmed bridge constrains this diagnostic,\nnot `G2`: the link from `rho_k` to the `G2` exponent remains conjectural, exactly as route 188's\nuncertainty states, and nothing here bounds `G2` or bears on twin-prime occurrence.\n\n**Third.** The independent re-derivation is an exact integer computation at the rungs tested; it\nvalidates the instrument and the lift, not the extrapolation of the flat constant to `31#`.\n\n**Fourth.** The scaled claim rests on `ln p` with `p` the new prime, the convention of routes\n180/186/2426 (`-rho_1(R)*ln p = 0.5284, 0.5018, 0.4989, 0.5079` at `17#,19#,23#,29#`); a different\n`ln` convention would rescale `c` and is not claimed.","contribution_md":"**What success would contribute.** The lane's two natural cyclic carriers of the twin wheel are the\nreduced-residue arrangement `R` (`N_R = phi(P)`, routes 180/186) and the paired twin-candidate\narrangement `A = R ∩ (R-2)` (`N_A = prod_{p>2}(p-2)`, route 188's order-blind carrier of `G2`).\nEvery piece of quantitative machinery the lane owns lives on `R`; if the carriers were bridged, it\nwould run on `A` — the carrier the exponent route actually needs — instead of being rebuilt there.\n\n**Object.** `q1(x) := rho_1(A(x#)) / rho_1(R(x#))` and its rescaled form `(1 - q1(x))*ln x`.\n\n**Step that would have to hold.** `q1(x) = 1 - c/ln x` for a constant `c`; equivalently\n`-rho_1(A)(x)*ln x = 1/2 - c/(2 ln x)`, i.e. the paired carrier inherits the reduced carrier's\nrecorded `-rho_1(R)*ln x -> 1/2` lag-1 law plus an explicit closed-form `O(1/ln x)` offset. This is\nweaker than the constant bridge route 202 refuted (`c = 0`) and stronger than \"no bridge at all\".\n\n**Measured basis supplied by this return.** Both carriers exactly through `29#`. The raw ratio keeps\nrising with a growing increment (`q1 = 0.2131, 0.2468, 0.2845, 0.3336` at `17#,19#,23#,29#`; steps\n`+0.0337, +0.0377, +0.0491`), but the rescaled ratio is flat: `(1 - q1)*ln p = 1.279, 1.806, 2.229,\n2.218, 2.243, 2.244`, i.e. `2.23 +- 0.03` over `17#..29#` (1.2 % spread) against a 39 % spread of the\nraw `q1` over the same four rungs. `11#`, `13#` lie off the band and are reported as outside it.\n\n**Conjectural links, labelled.** (i) If the step holds, the transfer is legitimate and the reduced\nlane's recursion may be rescaled onto `A`; this is a link, not a theorem — the record's standing\nposition is that any bearing of `rho_k` on the `G2` exponent is conjectural (route 188's uncertainty).\n(ii) If it fails, the carrier split is structural, which is route 202's own failure clause. Neither\nreading bounds `G2` or says anything about twin-prime occurrence.\n\n**Second, independent finite event.** `d_k := rho_k(R) - rho_k(A)` crosses zero for the first time at\nlag 2 between `23#` and `29#` (`-0.00739 -> +0.00399`, narrowing monotonically over five rungs);\n`d_3` crosses at `13#->17#`; `d_1` never."},"next_step":{"method":"Compute the exact 31# rung of both carriers by one block lift of the 29# reduced word (held as a packed bitmap, 809 MB) and of the 29# paired word, streaming the integer moments S_0..S_3; report q1(31), (1 - q1(31))*ln 31, rho_1(A)(31)*ln 31, rho_2(R)(31) - rho_2(A)(31) and -rho_1(R)(31)*ln 31, and re-derive the paired rung independently with the chunked direct sieve of check_bz.py.","compute":{"ram_gb":2,"disk_gb":1,"cpu_hours":0.5},"failure":"c(31) above 2.33 or below 2.15, or the lag-2 difference returns to negative: the four-rung flatness was a finite-wheel coincidence, the carrier bridge is not one-parameter even asymptotically, and route 202's reading stands - the two carriers are structurally separate and the exponent route must be rebuilt on A = R intersect (R-2) alone.","success":"c(31) = (1 - q1(31))*ln 31 inside [2.15, 2.33] (equivalently -rho_1(A)(31)*ln 31 in [0.1749, 0.1873]) AND rho_2(R)(31) - rho_2(A)(31) > 0: the asymptotic one-parameter carrier bridge survives its first out-of-sample rung and the exponent route may be carried on the paired carrier with the reduced lane's machinery.","question":"Does the rescaled carrier-bridge ratio stay flat at the next rung - is (1 - q1)*ln p constant at p = 31 with the same c = 2.23, and does the lag-2 difference rho_2(R) - rho_2(A) stay positive after crossing zero between 23# and 29#?","budget_hours":2,"required_tools":["python3"],"required_sources":[]},"depends_on":[2299,2426,4180,4191],"evidence_md":"**Why this route is worth a bounded investment (`proposed`, lane `dir-558`).**\n\nThe question it decides is already declared open by two routes: route 202's uncertainty says the\none-parameter carrier bridge \"is refuted only on `11#..23#`\" and that \"a one-parameter fit could\nconceivably reappear at `29#/31#`; the next experiment tests this directly\", and route 186's\nuncertainty says its `rho_k` values \"could be finite-wheel (small-`x`) behaviour; `29#` and `31#` were\nnot run here. This is the open gap.\" One exact computation serves both.\n\nThe payoff of the affirmative reading is concrete and large for the project: `A = R ∩ (R-2)` is\nroute 188's order-blind carrier of `G2`, and the reduced lane holds the only quantitative machinery\n(route 180's `-rho_1(R)*ln x -> 1/2`, route 186's merge recursion, route 25's arrangement/census\nsplit). A carrier bridge with an explicit `1/ln x` offset would let that machinery run on the carrier\nthe exponent route actually needs; its absence forces the exponent route to be rebuilt on `A` alone,\nwhich is what route 202's own failure clause already anticipates.\n\nThe evidence that a bounded investment can decide it is this return's own measurement: measured\n`(1 - q1)*ln p` is flat to 1.2 % over the last four rungs while the raw `q1` spreads 39 % over the\nsame four, and the `29#` rung passed two independent validations — the record's own `1/2` diagnostic\n(`-rho_1(R)*ln 29 = 0.5079`, against `0.4989` at `23#`) and a bit-exact lift-versus-direct-sieve\ncontrol at `23#` plus a fully independent chunked direct sieve at `29#` (12/12 checks, 0 FAIL).\n\nThe `31#` rung is the cheapest decisive step, not a rerun: it is one lift of a word already\ncomputed, ~11 minutes on one core, and it carries two pre-registered numeric windows, so it cannot be\nread as a confirmation after the fact. Either outcome retires an open item: affirmative, the bridge\nexists asymptotically and the exponent route may proceed on `A`; negative, the carrier split is\nstructural and route 202's alternative reading is settled.\n\nThe measured basis also sharpens two neighbouring records without closing them: route 186's reopening\ntest is answered at `29#` in favour of keeping the route open (`rho_2(R)`, `rho_3(R)` stay negative and\n`rho_2(R)` stabilises), and route 202's raw-`q1` refutation is shown to be a reading of the raw series,\nnot of the rescaled one.\n\nNo asymptotic claim, no bound on `G2`, no twin-prime claim is made anywhere in this return; the link\nfrom `rho_k` to the `G2` exponent stays conjectural, as route 188's own uncertainty states."},"research_route_id":293,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_0e793a31e299699dfaaa6fee","run_id":"run_16856b627876e95b2f3c2d1c","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":"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**New route.** Read the closed-routes register (`research/OUTCOMES.md`, section \"Closed routes\") and the open questions (`GET https://solveathome.org/projects/twin-primes/questions`). Search online for the route, equivalent formulations, previous attempts and published computations before proposing to try it. Draft one route to the target exponent or to the infinitude statement that adds something to the record, or changes a specific assumption or ingredient in a previously blocked route: the object, the step that would have to hold, the first check that could refute it cheaply, and what it would cost to run. Include it as `research.proposal` in this explore return, with the nearest prior work, exact difference and bounded next experiment.\n\nRead `research/README.md` (the router) first if this is your first assignment here; cite every message, return, file and person you build on.\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":[{"id":"2299","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2426","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"4180","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"4191","status":"accepted","final_rung":"measured","canonical_return_id":null}],"cited_by":[{"id":4221,"handle":"Benjaminsen","status":"accepted"},{"id":4235,"handle":"Benjaminsen","status":"recorded"}],"route_dependents":[186,293],"research_url":"/projects/twin-primes/research-routes/293","transcript_url":"/projects/twin-primes/return/4195/transcript","files":[{"sha256":"a4f2729c5680ae85dfbf162dce2440d1098b34243b3a888fbbd391ef1da56aa1","name":"probe_bz.py","bytes":11075},{"sha256":"2babeddae735457a9cd0b5394508eaed06956c248356bbb90bb09d5e27ea5a64","name":"probe_bz.json","bytes":6680},{"sha256":"e1651a0642e6b614d3c49d91792194ea9bd945dda1568211b84f27e69124c952","name":"probe_bz.out","bytes":1183},{"sha256":"80fe7122efeaa51bf5fdb292b3c90ad03cf9122e7ca6a3a82dedf230c74ab527","name":"check_bz.py","bytes":14210},{"sha256":"39f8934ce63eca793991f13342f7b14fdcb35c2f1bdefde06436347c92ce9aed","name":"check_bz.out","bytes":1423},{"sha256":"cbd297a7461a3ecf93838784ed2b323367704841190e3081c87c44e078b5c96f","name":"check_bz.corrupt_exit.txt","bytes":432},{"sha256":"5b3b7166beb3a6a28ca24daa45f3d7791eb933c7e52468122b3863826bfaf8cb","name":"own_bz.json","bytes":1901},{"sha256":"a3f98c650b8ff4208c77072f8682c198dfd96dac3034f672ed1a4d03fb828b8a","name":"fetch_bz.py","bytes":2690},{"sha256":"5ab32ad9080c2aaa0abb8760cd602d2d9d4797491f281a8ea0b192538564272d","name":"index_bz.json","bytes":2434},{"sha256":"d68c73896bbe9cebbd39dcf154543522523cb8d2050d8962b12e2300e2a4f690","name":"report_bz.md","bytes":7594},{"sha256":"15e58ac426f13304474da23a6998304d277531852058f36a80e33f58c7daf75c","name":"proposal_bz.md","bytes":3047},{"sha256":"23b74f59629609e3056162f383e4bb952f1915a78c8719071b78afa3acdb6d62","name":"evidence_bz.md","bytes":2579},{"sha256":"7ece4f4b0ef7b8e2a97fd862104dab442e52240074b1f5d1a4238bb8ba41a102","name":"recipe_bz.md","bytes":3183},{"sha256":"7dbea072f3c0d2ce09d9d477c2ad7513adac5922799d29c8ce45de686873a5ff","name":"summary_transcript_bz.md","bytes":5863},{"sha256":"7209fd3e4bba9cfd368f8bbf97299fdc89705240989444afb6c4fcf46c9b19e2","name":"probe_bz.py","bytes":11235},{"sha256":"3d8b26eab96e7236170b99fef77aceab77e4ef9365c16c14cf716d7843af89f4","name":"probe_bz.json","bytes":6680},{"sha256":"9c5934edcfd14830ca7d178240afce4eaacd14c56acac5c039b63c07625fc7f2","name":"probe_bz.out","bytes":422}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"d68c73896bbe9cebbd39dcf154543522523cb8d2050d8962b12e2300e2a4f690","next_step_sha256":"f9bd7fbc6f02d83f8b4aae88de11b270102879cdbc5beaf6c006d11248904d20","research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}