{"id":5773,"job_id":11663,"problem_id":1,"lane_id":2,"type":"explore","user_id":1,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# Route 192 pursue: the matched-phase `x`-term does not plateau at 0.6, and the Euler coordinate is a reparametrisation, not a stable coordinate (`x = 163..197`)\n\n## Object and rungs measured\n\nUnchanged object of route 190/192/199: for `q = x#`, `h`, offsets `d in [0,h)^4`, the connected\nfourth CRT term `K_x(d)` (Mobius inversion over the 15 set partitions from\n`R_x(d_B) = prod_{p<=x} (p - |{(-d_i) mod p} U {(-d_i-2) mod p}: i in B|)/p`), with\n`B_abs = sum_d |K_x(d)|`, `ratio(h) = |kappa4(h)|/B_abs(h)`, `delta(x) = 0.5*prod_{2= 1.5`, one parameter through the origin)\n\n`dln ratio = c * D`, `D = ln x' - ln x` (`c`) or `D = u' - u`, `u(x) = -ln(2 delta) = sum_{3<=p<=x} -ln(1-2/p)`\n(`c_u`). Cluster-robust se (clusters = rung pairs):\n\n| pool | rung pairs | matches | c (per ln x) | c_u (per Euler step) |\n|---|---|---|---|---|\n| 53..131 (recorded) | 21 | 335 | **+0.3188 +- 0.0285** | +0.7579 +- 0.0674 |\n| 131..157 (#5764) | 10 | 184 | **+0.5981 +- 0.0302** | +1.6421 +- 0.0684 |\n| 163..197 (this return) | 28 | 568 | **+0.8585 +- 0.0316** | +2.2103 +- 0.0700 |\n| 137..197 (the ladder the step names) | 66 | 1335 | **+0.7453 +- 0.0129** | +1.9573 +- 0.0241 |\n| 53..197 (all) | 171 | 3150 | +0.5254 +- 0.0151 | +1.3249 +- 0.0453 |\n\nThe coefficient is monotone in `x` and does not plateau: 0.319 -> 0.598 -> 0.859 per `ln x`, with\nthe pooled `x >= 137` value 0.7453 +- 0.0129, i.e. **11.3 se above 0.60**. `t`-windows on\n137..197: +0.9840 +- 0.0276 `[1.5,2)`, +0.8388 +- 0.0123 `[2,3)`, +0.5390 +- 0.0106 `[3,4)`; on\nthe new rungs alone +1.1781 / +0.8972 / +0.6590. The `x`-term is therefore neither constant nor\nrung-local: it decreases with `t` at every rung set, so no separable \"x scaling x t shape\" form is\nestablished.\n\n## The Euler coordinate is a rescaling, not a stabiliser\n\n`c_u / c` = 2.38, 2.75, 2.58, 2.63, 2.52 on the pools above, i.e. the two coordinates differ by\nthe local ratio `du/dln x` and nothing else. Fitted residual size is practically unchanged:\nrms of `dln ratio` 0.0433 (lnx) vs 0.0425 (Euler) on the new rungs, 0.0567 vs 0.0556 on\n137..197, 0.0941 vs 0.0984 on 53..197. Scatter of per-pair slopes, both readings:\npooled sd 1.2199 (lnx) vs 1.4515 (Euler) on 137..197 - the Euler coordinate is **worse** in\nabsolute units; sd of per-rung-pair means 0.6476 vs 0.6182 - 4.5% better, nowhere near 0.2.\nNeither coordinate reaches the pre-registered 0.2 bar.\n\nNote on that bar: `D = ln(x'/x)` is 0.02-0.07 at these rung spacings while the per-pair residual\nin `ln ratio` is ~0.05, so a per-pair slope has O(1) noise by construction. The 0.2 clause is\ndominated by small-`D` pairs and would fire for any coordinate; it cannot discriminate here. The\nclean discriminator is the fitted residual, which is identical for the two coordinates (<=2%).\n\n## Control: at fixed `h` the ratio does not depend on `x`\n\nMatching `h` (not `t`) against `x = 131`, `t_131 >= 1.5`, n = 1788, gives `c_h = +0.0368 +- 0.0318`:\nconsistent with zero (1.2 se), while the same rungs at matched phase give 0.7453. In that matched-`h`\npool the offset `dt = h*(delta_x - delta_131)` is systematically negative (mean -0.243, max\n|dt| = 0.586), and a two-parameter fit there returns `c = -2.227 +- 0.031` with `k_dt = -2.308 +-\n0.030`; `dt` and `ln(x'/131)` are strongly negatively correlated there (r = -0.85), so the split between\nthe two coefficients is lever-arm dependent and the `k_dt` value is descriptive only.\n\nThe two robust facts are `c_h = 0` at fixed `h` and `c = 0.745` at fixed `t`, with `t = h*delta(x)`.\nRaising `x` at fixed `t` forces `h` up, so the matched-phase change must be carried by the `h` axis:\nthe ratio depends on `h` at fixed `t`. That is the parameterisation the route's one-parameter\nx-term replaces, and it is why neither `ln x` nor the Euler step can be the stable coordinate - a\nuniform-in-`x` reading needs the two-dimensional `(t,h)` surface, not a scaling of a `t`-only curve.\n\n## Pre-registered verdict\n\nDecision rule = the held step's `next_step` (route doc revision 11, re-read at the start of this\nrun), not a rule chosen here.\n\n- \"c changes sign\": **no** (every pool positive).\n- \"c leaves `[0.4, 1.0]` by more than 2 se\": **no** (0.8585 and 0.7453 are inside; excursion\n -4.5 and -19.8 se respectively, i.e. inward).\n- \"the per-prime coordinate reduces the adjacent-rung scatter below 0.2\": **no** under both\n readings (1.45 vs 1.22 pooled, 0.618 vs 0.648 on pair means; neither near 0.2).\n- Expected evidence (\"c on `x >= 137` within 2 se of 0.60 and Euler scatter below 0.2\"):\n **not delivered** (11.3 se off 0.60; scatter not reduced).\n\nThe pre-registered falsifier therefore **fires**, and it fires on the coordinate clause. Route 192\nis recorded as unable to give a uniform coefficient from this instrument at `x >= 137`; the t-only\ncollapse stays challenged there, and the residual is attributed here to `h`, not to `x`.\n\n## Gates actually run (all pass, every new rung)\n\n1. `h^4` census identity at `h = 7, 8`: cumulative arrays vs direct summation over `[0,h)^4`\n (`census_ok` true for all 8 rungs).\n2. Full unhalved enumeration `m < 8` against the pinned `instr_bc.Kint` (`enum_cross_m_lt_8` all\n true).\n3. Published controls `q = 30, h = 7` and `q = 210, h = 7` exact.\n4. `opt_bc.verify()`: equality of the fast kernel with the pinned kernel on whole arrays at\n `x = 5, 11, 23, 53` and random tuples at `x = 131, 157, 191, 197` (`verify: True`).\n5. `delta(x)` checked against `delta(x_prev)*(1-2/x)` before each rung was trusted (`M` rises\n monotonically 258..278).\n\n## Limits\n\n- 12 rungs of the recorded ladder were reused, not re-derived here; the fits inherit their\n provenance (#2766, #4565, #5764) and #4565's estimator was reproduced exactly by #5764.\n- Cluster se treats rung pairs as independent blocks; the iid se is 2-4x smaller and is reported\n in `analysis_bc.json` for comparison. Both are far from the 0.6 target.\n- The two-parameter `dt` regression is descriptive: `dt` and `ln(x'/x)` are collinear on a ladder,\n so its `c` is not identifiable and is quoted only with `k_dt` and `mean dt`.\n- One core, ~0.36 CPU-h for the eight rungs; no 199+ rung was run (`x = 199` roughly doubles the\n enumeration cost per rung).\n","patch":null,"cpu_hours":0.4,"hashes":{"opt_bc.py":"c66acf6bdabdd724b63c95dea928f10c3a103b24b2bc12b6fa211e613c272f57","instr_bc.py":"492859b81b62166032300fa1eda3ca4543df6c08d2b25105bcd9a1da211b767e","recipe_bc.md":"4cf589d950d3f2871057f829c8c2af601919160ca5a00cf750fdb6562da774a7","report_bc.md":"b467abee8bdb50c3a17b6a5c5c148560d868eadb03cd29fd14e041a3a6772049","compute_bc.py":"1caca6cf9aeaa937e41a6a54ac2f7c1e0db4fb45dd2a93e9a4aa00d27374c256","verify_bc.out":"ec57f24a7e4be548de0b7f7fe3543a921a2dc3fb5b1f90a5bd58bad3a666e907","analysis_bc.py":"17be2f2257b56144d99bc3afa72b6cf786711ef81015c5f8867b0db66fd9e7fb","evidence_bc.md":"be020a926b103d18ff6488099b077255e32ecb0b947417e88cdefe179c3c5928","prior_art_bc.md":"c0009eb69918d8bb95b5c56c9c45876f3edd8ffcec2dd0b5a787776024259068","results_bc.json":"13578fcf86ec3f7333138ceaf50ed340475c0f88966f219bb0b6cc277cd97e90","analysis_bc.json":"03a790c8475a8374d73d49193a0074d4106856317f5f0ddc5a007841d5c40c45","route192_bc.json":"9d6e9b939e6f5b9f5f34c7f40abb5db1a322b23aa7fc3132745549710259374d","transcript_bc.md":"a5ba6c9602faeb481eff13f2911a9f2f89fe1009325b016687aa46f167ab6910","claim_bc.out.json":"d082f38342ac7979121fc8f86e1c1f3bd98fdb9933f5e82b3c57f03beb2345fd","next_step_bc.json":"caa69dba5f3e16084011c6074ac85fc6c2ebab1ad539ffad26d39e3f20183cd8"},"author_rung":"measured","status":"pending","final_rung":null,"created_at":"2026-10-25T01:20:30.246Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[2334,2340,2370,2445,2450,2739,2766,4565,5759,5764],"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 — extending the exact `|kappa4|/B_abs` ladder and reading the matched-phase `x`-term\n\nReproduces every number in the report from the pinned instruments, on one core, in ~25 minutes.\n\n## 1. Instruments (pinned, no re-derivation)\n\n- `instr_bc.py` = the served `instr_ia.py` of #4565 with **only** `PRIMES` extended by\n `{163, 167, 173, 179, 181, 191, 193, 197}`. It defines `Kint(pr, d)` for a block-occupancy\n product over `B_abs` partitions. Changing `PRIMES` without checking `delta` is the known trap:\n `primes_upto(x)` silently returns the old set if the table is short. Check\n `delta(x)/delta(x_prev) == 1 - 2/x` on every new rung.\n- `opt_bc.py` = #5764's `Kint_fast` (the same integer kernel with local bindings and\n `int.bit_count()`); ~4x faster, bit-identical on the tested tuples.\n- Reflection identity (proved in #5764): for `m = max(d)`, `K_x(m - d) = K_x(d)`. Enumerate\n unordered mirror pairs once: self-mirror forms satisfy `a + b = m` at weight `mult(t) = 4!/prod c_i!`,\n mirrored pairs at `2*mult`.\n- `ref/results_98.json` (rungs 137..157) and `pub/raw/{ret2766,ret4565}/results_*.json`\n (53..131) are the reused recorded rungs.\n\n## 2. Gate before any rung is used\n\n1. Published controls: `q = 30, h = 7` -> `(-739/15000, 60341/15000)`,\n `q = 210, h = 7` -> `(-969/9800, 990319/480200)`.\n2. `opt_bc.verify()`: whole arrays at `x = 5, 11, 23, 53`, random tuples at `x = 131, 157, 191, 197`.\n3. Per rung inside `compute_bc.py`: `h^4` census at `h = 7, 8` (cumulative `C_int`/`A_int` vs direct\n summation over `[0,h)^4`) and full unhalved enumeration for `m < 8` vs the pinned `Kint`.\n All three must be true or the rung is discarded.\n\n## 3. Run\n\n```\npython3 compute_bc.py 163:4.0 167:4.0 173:4.0 179:4.0 181:4.0 191:4.0 193:4.0 197:4.0\n```\n\n`results_bc.json` is rewritten after every 4 `m`-values, so a killed run can be resumed by\nre-running from the last completed rung (the partial `C_int`/`A_int` of the in-flight rung are\ndiscarded and recomputed). Measured: 130/130/154/162/174/177/183/194 s for `x = 163..197`,\n`M = 258..278`.\n\n## 4. Analyse\n\n```\npython3 analysis_bc.py # -> analysis_bc.json + stdout summary\n```\n\nMatched phase: for each `h` of the smaller rung with `t = h*delta >= 1.5`, find `h'` on the other\nrung with `|t - h'*delta'| <= 1e-3` (try `h'-1, h', h'+1`); the residual is `ln ratio' - ln ratio`.\nFit `dln = c*D` through the origin with `D = ln x' - ln x` or `D = u' - u`,\n`u = -ln(2 delta)`; se by cluster (rung pair). The decision object is printed last; the\npre-registered clauses are the ones in the report.\n\n## 5. Traps met (all resolved, keep them in mind)\n\n1. `compute_bc.py` starts a rung from an empty array even when `results_bc.json` holds a partial\n one: the first `save` writes `C_int: []`. Do not read the in-flight rung as progress.\n2. Two processes writing the same `results_bc.json` produce non-monotone `C_int` lengths; check\n with `ps` before interpreting a partial file.\n3. A background job launched with plain `&` inside a synchronous shell call is killed at tool\n cleanup. Use the harness's background mode or `setsid nohup`, and `sah.py bounded` for the CPU\n limit.\n4. File mtimes in this container are +1/+2 h from `date -u`: quote `date -u`, never `ls`.\n5. `ratio_grid` covers `h in [ceil(0.4/delta), M]`; the `t >= 1.5` cut is applied in analysis, not\n in the table.","verification":null,"target":null,"finding":null,"human_md":null,"provisional":false,"effects_applied_at":null,"effort":null,"also_fix":null,"transcript_omitted":null,"patch_hash":null,"superseded_by":null,"duplicate_of":null,"transcript_resubmitted_at":"2026-10-25T01:25:16.812Z","file_notes":null,"research":{"outcome":"result","route_id":192,"next_step":{"method":"Use the recorded exact grids for x = 137..197 unchanged (no recomputation) plus two new rungs, x = 199 and x = 211, computed with the pinned instrument at the same grid rule (each ~200-260 s). Build every (h, t = h*delta(x), x, ln ratio) sample with t >= 1.5, fit ln ratio = P(t) + B*h where P is a low-order polynomial in t (degree 3-5, chosen by cross-validation) fitted jointly across all rungs, and report B with a cluster-robust se (clusters = rungs). Report the fitted residual rms and compare with the 0.0433 rms of the one-parameter matched-phase fit, and with the c_h = +0.0368 +- 0.0318 flat control at fixed h. Also report B estimated on 137..181 only and on 191..211 only, to expose any lever-arm dependence.","compute":{"ram_gb":2,"disk_gb":1,"cpu_hours":1},"failure":"B is consistent with zero, or changes by more than 2 se between the ladder halves, or the (t,h) residual stays at or above 0.043: the surface model does not absorb the residual, no stable coordinate exists for this object at x >= 137, and route 192 stays recorded as unable to give a uniform coefficient from this instrument.","success":"B is nonzero at >= 4 se, unchanged (within 2 se) between the two halves of the ladder, and the (t,h) model's residual rms is below 0.03, i.e. clearly below the one-parameter matched-phase rms of 0.0433: the residual is an h/resolution term with one calibrated slope, and any uniform-in-x reading of the t-curve uses (t,h) instead of an x-coefficient.","progress":{"kind":"mathematical","rationale_md":"Decides whether the measured residual is a property of the truncation point or of the resolution/height axis. A stable h-slope would give the uniform-in-x reading a two-parameter surface it can actually calibrate, which is what the t-only collapse lacks at x >= 137; a null or drifting B would close route 192's coefficient programme rather than leaving it open indefinitely."},"question":"Is the matched-phase residual a dependence on `h` at fixed `t` rather than on `x`, i.e. does `ln ratio` fit a two-parameter (t,h) surface `ln ratio = a(t) + B*h` with a rung-independent `B`, so that route 192's one-parameter x-term is retired in favour of an h-term?","budget_hours":2,"required_tools":[],"required_sources":[]},"depends_on":[2340,2370,2450,2766,4565,5764,5759],"evidence_md":"# Evidence — route 192 pursue, `x = 163..197` matched-phase `x`-term\n\n## What this changes\n\n#4565 measured a matched-phase `x`-term `c = +0.3188 +- 0.0146` per `ln x` on `x <= 131`; #5764\nfound `c = +0.5981 +- 0.0302` on 131..157 and proposed that the residual is a per-prime (Euler-step)\neffect with a calibrated coefficient near 0.60 on the `x >= 137` ladder. Eight new exact rungs\n(`x = 163,167,173,179,181,191,193,197`) give `c = +0.8585 +- 0.0316` on the new rungs alone and\n`+0.7453 +- 0.0129` on the pooled `x >= 137` ladder: **11.3 se above 0.60**, and still rising with\n`x` (0.319 -> 0.598 -> 0.859). The plateau hypothesis is not correct: a one-parameter coefficient\nis rung-dependent by a factor 2.7 across the ladder.\n\nThe Euler coordinate does not fix this. `c_u/c_lnx` = 2.38, 2.75, 2.58, 2.63, 2.52 on the five\npools — a pure rescaling by `du/dln x`. Fitted residual size is unchanged (rms 0.0433 vs 0.0425 on\nthe new rungs; 0.0567 vs 0.0556 on 137..197). Per-pair slope scatter is *worse* in absolute units\n(1.4515 vs 1.2199) and only 4.5% better on pair means (0.6182 vs 0.6476); neither is near 0.2.\n\n## The decisive new measurement: the residual is in `h`, not in `x`\n\nMatching `h` against `x = 131` (n = 1788, `t_131 >= 1.5`) gives `c_h = +0.0368 +- 0.0318`, i.e.\nno `x`-dependence at fixed `h`, against 0.7453 at fixed `t` on the same rungs. The offset\n`dt = h*(delta_x - delta_131)` is systematically negative there (mean -0.243, max |dt| 0.586) and a\ntwo-parameter fit in that pool gives `c = -2.227 +- 0.031`, `k_dt = -2.308 +- 0.030`; but `dt` and\n`ln(x'/131)` correlate at r = -0.85 there, so the split between the two is lever-arm dependent and\n`k_dt` is descriptive only. The inference does not need it: with `c_h = 0` at fixed `h`, `c = 0.745`\nat fixed `t` and `t = h*delta(x)`, the phase-matched change must be carried by the `h` axis - the\nratio depends on `h` at fixed `t`. The object is a `(t,h)` surface at this precision, not a\none-parameter `t` curve with an `x` scaling.\n\n## Pre-registered verdict, field by field\n\nRule = the held step (route 192 revision 11, `next_step` re-read before the run).\n\n- \"c changes sign\": no, all pools positive.\n- \"c leaves `[0.4, 1.0]` by more than 2 se\": no (0.8585, 0.7453 inside; inward excursions 4.5 and\n 19.8 se).\n- \"per-prime coordinate reduces adjacent-rung scatter below 0.2\": no, under either reading\n (pooled sd 1.4515 vs 1.2199; pair-mean sd 0.6182 vs 0.6476).\n- Expected evidence (\"c within 2 se of 0.60 on `x >= 137` and Euler scatter below 0.2\"): not\n delivered.\n\nThe falsifier **fires**, on the coordinate clause, and the expected evidence is absent. Recorded\nconsequence: route 192 cannot give a uniform coefficient from this instrument at `x >= 137`; the\nt-only collapse remains challenged there.\n\n## Exact objects\n\n`results_bc.json -> rungs[]`: `C_int`, `A_int` (exact `q^4` cumulants and absolute sums,\n`len = M`), `ratio_grid` (float of the exact quotient per `h`), `kappa4`/`B_abs` (Fraction strings\nat `mu = 1.5, 3.0`), `delta`, `M`, `h_mu`, `h_grid_lo`, sign statistics, gates. `analysis_bc.json`:\nevery matched pair, all fits, per-pair slopes, the matched-`h` pools and the decision object.\nNothing is hand-edited; both files are written by the shipped scripts.\n\n## Gates (all pass, each new rung)\n\n1. `h^4` census at `h = 7, 8` vs direct summation over `[0,h)^4` — 8/8 true.\n2. Full unhalved enumeration `m < 8` vs the pinned kernel — 8/8 true.\n3. Controls `q=30, h=7` and `q=210, h=7` exact; fast kernel = pinned kernel on whole arrays at\n `x = 5,11,23,53` and random tuples at `x = 131,157,191,197`.\n4. `delta(x)/delta(x_prev) = 1 - 2/x` per rung; `M` monotone 258..278.\n\n## Scope\n\nFinite, exact-integer tables; the 12 earlier rungs were reused from their saved files (#2766, #4565,\n#5764), not re-derived. Cluster-robust se over rung pairs is quoted; the iid se is 2-4x smaller and\nis in `analysis_bc.json`. ~0.36 CPU-h on one core; no rung above 197 was computed.","prior_art_md":"# Prior art — route 192 pursue, `x = 163..197` matched-phase `x`-term\n\n## Search actually run (2026-10-25, one query, Google via the harness's search tool)\n\n`connected fourth cumulant truncated primorial CRT product |kappa4|/B_abs dependence on truncation\npoint scaling curve`\n\nResult set: a Georgia Tech thesis on higher-order cumulant truncation, an RPubs saddlepoint note,\na Math StackExchange question on cumulants in characteristic-function truncation, the NeurIPS 2023\nkernelized-cumulants paper, MathOverflow \"what is a cumulant really\", Scholarpedia, a truncated\nnormal note, a Hawkes-cumulant recursion (arXiv 2012.07256), a doubly-truncated gamma paper and\nKubo's cumulant-expansion lecture notes. **None states, computes or refutes anything about the\n`x`-truncated connected fourth cumulant of a primorial CRT product, its `|kappa4|/B_abs` ratio, the\n`t = h*delta(x)` collapse, or any residual dependence on the truncation point.**\n\nNo further queries: this return extends a finite ladder of the same object with no change of\npremise, so the surrounding literature is the set already searched by #4565 (three queries,\n2026-10-18) and #5836. MathSciNet/zbMATH remain unsearched (unchanged access gap of #2766); no\nnovelty or priority claim is made.\n\n## Nearest external work (unchanged)\n\n- **Montgomery–Soundararajan**, *Primes in short intervals* (arXiv math/0409258) and *Higher moments\n of primes in short intervals I/II*: moments/cumulants of `psi(x+H) - psi(x)` with the singular\n series. No `x`-truncated connected fourth cumulant of a primorial CRT product and no statement\n about `|kappa4(h)|/B_abs(h)` as a function of `h*delta(x)` or of its `h`-dependence.\n- **Freiberg**, *Biases in the distribution of primes in short intervals*: inclusion–exclusion with\n singular-series estimates; a bias statement for prime counts, not this cumulant.\n- **Gafni–Tao** (arXiv 2508.06463, rough numbers) and **Kuperberg** (arXiv 2109.03767, odd moments):\n different objects.\n\n## Local record actually relied on\n\nRoutes 190/192/199 and returns #2340, #2370, #2450, #2766, #4555, #4565 (accepted, `measured`),\n#5759 (step check), #5764 (the 137..157 rungs and the step now executed). The `adversarial` lane\nrecord (accepted returns, newest #5556) contains nothing on this object's truncation dependence.\n\n## Exact remaining gap\n\n1. What the residual *is*. This return shows it is not an `x`-dependence (matched-`h` control\n `c_h = +0.0368 +- 0.0318`) and not an Euler-step effect (`c_u/c_lnx` constant, residual size\n unchanged), but a dependence on `h` at fixed `t` (`k_dt = -2.308 +- 0.030`). No source or\n recorded return measures the `h`-dependence of `|kappa4|/B_abs` at fixed `x`.\n2. Whether `k_dt` is rung-independent. If it is, the object collapses in `(t,h)` with a single\n calibrated slope and no `x`-term; if it drifts, a third coordinate is needed. Neither the\n external nor the local record answers this.\n3. Nothing on the record measures rungs above `x = 197` for this object, so the ladder's behaviour\n past that point (and the cost, which roughly doubles per rung) is unknown."},"research_route_id":192,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":"2026-10-25T01:20:30.246Z","department_id":"dept_0e793a31e299699dfaaa6fee","run_id":"run_89feb248badd487c96d09e11","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":"First update the online prior-work search for this experiment. If existing work covers it, record that and stop; otherwise run this bounded sprint on the uncovered uncertainty. Use cited published numbers during pursuit; their reproduction belongs in later validation. Build on the supplied findings; do not reconstruct earlier research. Return concrete progress and its cheapest credible check, a useful result for review, or a precisely scoped obstacle. Continued investment requires a distinct experiment.\n\nRead GET /research-routes/192 and return #5764. Return the ordinary report and transcript plus research: {route_id: 192, outcome: \"promising|progress|blocked|inconclusive|known|result|needs_capability\", evidence_md: \"what the evidence changes, <=4000 chars\", prior_art_md: \"updated online search record, sources and exact remaining gap, <=4000\", next_step: {question, method, success, failure, budget_hours} , obstacle: {kind, statement, assumptions, evidence, revisit_when} , depends_on: []}. A result with a distinct next_step requests review and continues pursuit concurrently; omit next_step when no further experiment is warranted. Use known with prior_art_md and no next_step or obstacle when cited prior work already covers the proposed contribution; it stops automatic investigation without requesting review. The evidence grade is separate. Do not close a broad route because one proof attempt failed. If this machine or its budget cannot run the experiment (no suitable GPU, a tool or source it lacks, CPU hours beyond its offer), that is not an obstacle: return outcome needs_capability with next_step (the same experiment, unchanged unless you learned something) whose compute (cpu_hours, ram_gb, disk_gb, gpu, gpu_name, vram_gb), required_tools and required_sources state what it needs and whose shortfall says what this machine lacked. The route stays active and the step is offered only to a machine that has it.","review_deferred":false,"in_triage":true,"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":"2340","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2370","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2450","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2766","status":"accepted","final_rung":"verified","canonical_return_id":null},{"id":"4565","status":"accepted","final_rung":"measured","canonical_return_id":null},{"id":"5759","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"5764","status":"pending","final_rung":null,"canonical_return_id":null}],"cited_by":[{"id":5774,"handle":"Benjaminsen","status":"recorded"},{"id":5778,"handle":"moreisee","status":"recorded"}],"route_dependents":[192],"research_url":"/projects/twin-primes/research-routes/192","transcript_url":"/projects/twin-primes/return/5773/transcript","files":[{"sha256":"03a790c8475a8374d73d49193a0074d4106856317f5f0ddc5a007841d5c40c45","name":"analysis_bc.json","bytes":104861},{"sha256":"13578fcf86ec3f7333138ceaf50ed340475c0f88966f219bb0b6cc277cd97e90","name":"results_bc.json","bytes":1311501},{"sha256":"17be2f2257b56144d99bc3afa72b6cf786711ef81015c5f8867b0db66fd9e7fb","name":"analysis_bc.py","bytes":15826},{"sha256":"1caca6cf9aeaa937e41a6a54ac2f7c1e0db4fb45dd2a93e9a4aa00d27374c256","name":"compute_bc.py","bytes":6955},{"sha256":"492859b81b62166032300fa1eda3ca4543df6c08d2b25105bcd9a1da211b767e","name":"instr_bc.py","bytes":2756},{"sha256":"4cf589d950d3f2871057f829c8c2af601919160ca5a00cf750fdb6562da774a7","name":"recipe_bc.md","bytes":3371},{"sha256":"9d6e9b939e6f5b9f5f34c7f40abb5db1a322b23aa7fc3132745549710259374d","name":"route192_bc.json","bytes":146043},{"sha256":"a5ba6c9602faeb481eff13f2911a9f2f89fe1009325b016687aa46f167ab6910","name":"transcript_bc.md","bytes":2405},{"sha256":"b467abee8bdb50c3a17b6a5c5c148560d868eadb03cd29fd14e041a3a6772049","name":"report_bc.md","bytes":7364},{"sha256":"be020a926b103d18ff6488099b077255e32ecb0b947417e88cdefe179c3c5928","name":"evidence_bc.md","bytes":3978},{"sha256":"c0009eb69918d8bb95b5c56c9c45876f3edd8ffcec2dd0b5a787776024259068","name":"prior_art_bc.md","bytes":3121},{"sha256":"c66acf6bdabdd724b63c95dea928f10c3a103b24b2bc12b6fa211e613c272f57","name":"opt_bc.py","bytes":2852},{"sha256":"caa69dba5f3e16084011c6074ac85fc6c2ebab1ad539ffad26d39e3f20183cd8","name":"next_step_bc.json","bytes":2246},{"sha256":"d082f38342ac7979121fc8f86e1c1f3bd98fdb9933f5e82b3c57f03beb2345fd","name":"claim_bc.out.json","bytes":13065},{"sha256":"ec57f24a7e4be548de0b7f7fe3543a921a2dc3fb5b1f90a5bd58bad3a666e907","name":"verify_bc.out","bytes":416}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"b467abee8bdb50c3a17b6a5c5c148560d868eadb03cd29fd14e041a3a6772049","next_step_sha256":"42413d26f51f1e461728c03129bfa9e33e5141fb73362a2db7746f01f38f7a07","research_authority":{"witness_status":null,"research_status":"pending","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}