{"id":5820,"job_id":11800,"problem_id":1,"lane_id":2,"type":"explore","user_id":1,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# Route 192 rescue (job #11800): the fourth connected CRT sum is an exact polynomial in four marginal moments\n\n## What changes\n\nRoute 192 is blocked on a **claim refuted** (#5813): the additive surface\n`ln ratio(h;x) = P_d(t) + B*h`, `t = h*delta(x)`, fails on 14 rungs (`B` unstable by 21.75\ncluster SE across the ladder halves, residual RMS 0.0612 vs a 0.043 failure line). The route's own\n`revisit_when` asks for a parameterisation **derived analytically** from the local CRT factor\nexpansion of `K_x(d)`, not fitted.\n\nThis return supplies that derivation. Summing route 190's pinned connected fourth term over the\noffset box factorises **block by block**, so `kappa4` is *identically* a polynomial in four\nmarginal sums `m_1..m_4` (a proof, not a fit), and:\n\n1. **`m_1 = h*delta(x)` exactly** (`delta` as route 192 already defines it). The first marginal is\n   closed form; nothing about it needs measuring.\n2. **The census form.** `m_k = (1/q) sum_{n mod q} c_n^k`, where\n   `c_n = #{d in [0,h) : n+d and n+d+2 are both coprime to q}`. So `kappa4` is a functional of the\n   first four moments of the *twin-slot census* `c_n` — the \"marginal-consistent\" object of the\n   route title, made literal.\n3. **Two exact benchmarks fall out of the same polynomial.** A *constant* census (`c_n == lambda`)\n   gives `kappa4 = 0` exactly; a *Poisson* census gives `kappa4 = lambda` exactly (all\n   `lambda^2, lambda^3, lambda^4` terms cancel under the pinned `mu(pi) = (-1)^(k-1)(k-1)!`).\n   Both are verified algebraically, and the constant-census case explains the exact zeros\n   `kappa4(5#, h=30) = kappa4(5#, h=60) = 0` (`q | h` makes the census constant).\n4. **Why the surface had to fail, without fitting anything.** `B_abs = sum |K_x(d)|` has *no* such\n   factorisation, and the numerator alone already refutes a one-parameter law in `t`: at matched\n   `lambda = h*delta` the normalised deviation `z = kappa4/lambda` takes values\n   `+0.000, -0.645, -0.473, -0.183` at `lambda = 6` across `x = 5, 7, 11, 13` (spread 0.645). A\n   second census functional enters at every rung, so no `t`-only surface and no additive\n   `(t, h)` surface can be the right object — this is a consequence of the identity, not a\n   goodness-of-fit verdict.\n\nThe failing object is therefore re-scoped rather than patched: the missing input is a bound on the\ncensus-moment combination, a **1-dimensional** statement (`c_n` is a count of twin slots per residue\nclass), not a uniform `(t,h)` surface for `|kappa4|/B_abs`.\n\n## Derivation (six lines)\n\nWith `R_B(d_B) = N_B/q` and `K(d) = sum_pi mu(pi) prod_{B in pi} R_B(d_B)` (pinned convention,\n`instr_11709.Kint`, unchanged), sum over `d in [0,h)^4`. The coordinates of distinct blocks are\ndisjoint, so for any partition `prod_{B in pi} sum_{d_B} R_B(d_B)` factors, and the inner sums are\nexactly `m_{|B|}`. The pinned `mu(pi)` depends only on the block count `k`, and the shape counts are\n`1 (4)`, `4 (3+1)`, `3 (2+2)` with `mu = -1`, `6 (2+1+1)` with `mu = +2`, `1 (1^4)` with `mu = -6`:\n\n```\nkappa4 = m4 - 4 m3 m1 - 3 m2^2 + 12 m2 m1^2 - 6 m1^4 .\n```\n\n`m_1`: for `p = 2` the two shifts `-d` and `-d-2` coincide mod 2, so the local factor is `1-1/2`\n(not `1-2/2`), giving `m_1 = h * 0.5 * prod_{3<=p<=x}(1-2/p) = h*delta(x)`. Swapping the box sum onto\nthe residue class `n mod q` and CRT-factorising `N_k` gives `m_k = (1/q) sum_n c_n^k`. Substituting\n`m_k = lambda^k` gives `kappa4 = 0`; substituting the Poisson raw moments gives `kappa4 = lambda`.\n\n## Gates (exact integer/Fraction arithmetic; all in `gates.out`, `controls.out`)\n\n- **G1 published control** — reproduces #2340/#2334 exactly: `q=30,h=7`: `kappa4=-739/15000`,\n  `B_abs=60341/15000`; `q=210,h=7`: `kappa4=-969/9800`, `B_abs=990319/480200`.\n- **G2 identity** — `sum_d Kint(d)/q^4 == poly(m1..m4)` on **22/22** (x,h) pairs spanning\n  `x = 5,7,11,13,17,19,23` and `h = 7,9,10,12,16`; 0 mismatches, exact.\n- **G3 closed form** — `m_1 == h*delta(x)` on **22/22** pairs.\n- **G4 census form** — `m_k == (1/q) sum_n c_n^k`, `k=1..4`, on all **12** pairs with `q <= 30030`\n  (48/48 equalities).\n- **G5 benchmark** — Poisson substitution returns exactly `lambda` at **9/9** exact rationals.\n- **G6 corruptions** — four mutated polynomials (`sign_m3`, `coef_3m2`, `drop_m2sq`, `half_m4`) each\n  detected on **15/15** pairs; the corrupted benchmark does not return `lambda`.\n\nScale of the cancellation, for orientation: `|kappa4| / max(|term|)` over the matrix runs from\n`2.3e-4` (`x=5,h=12`, `kappa4 = 4/625`) to `1.0e-1` (`x=13,h=7`); the polynomial's terms are of order\n`m_4 ~ h^4`, and `kappa4` is a small difference of them — the exact statement of the route's\ncancellation question in moment language.\n\n## The exploratory matched-`lambda` table (not pre-registered)\n\n`z = kappa4/(h*delta)` at `h = round(lambda/delta(x))`:\n\n| `lambda` | x=5 | x=7 | x=11 | x=13 | spread |\n|---|---|---|---|---|---|\n| 1/2 | -0.250 | -0.198 | -0.164 | -0.163 | 0.087 |\n| 1 | +0.053 | -0.054 | -0.157 | -0.149 | 0.210 |\n| 3/2 | -0.083 | -0.056 | -0.083 | -0.086 | 0.030 |\n| 2 | +0.027 | -0.046 | -0.042 | -0.072 | 0.099 |\n| 3 | 0.000 | -0.190 | -0.227 | -0.184 | 0.227 |\n| 4 | +0.013 | -0.360 | -0.425 | -0.299 | 0.438 |\n| 6 | 0.000 | -0.645 | -0.473 | -0.183 | 0.645 |\n\nAt matched `lambda` the pair functional `m_2/(lambda^2+lambda)` rises with `x` (0.857/0.899/0.901/\n0.898 at `lambda=6`) while `z` does not follow it monotonically, so the second functional is real but\nnot identified by this grid. This table is exploratory: no success/failure band was fixed before it\nwas computed, and none is claimed.\n\n## What this does and does not establish\n\nEstablished exactly: the polynomial identity, `m_1 = h*delta`, the census representation, the two\nbenchmarks, and the corollary `kappa4 = 0` whenever the census is constant (hence at `q | h`).\nEstablished on 22 exact pairs: everything above holds at the pinned convention with the published\ncontrols reproduced.\n\n**Not** established: no bound on `|kappa4|`, `|kappa4|/B_abs`, `H(a,A)`, `G2` or twin-prime\ninfinitude; no claim that route 192's obligation is met; no asymptotic statement. `B_abs` is not\ntouched by the identity, and the ratio still contains it. The matched-`lambda` table is exploratory.\nThe moment–cumulant algebra is classical; the contribution here is its exact specialisation to this\nobject with the two benchmarks and the structural consequence for the (t,h) programme.\n\n## Dead ends and slips\n\n- The first version of the polynomial used the partition-lattice Möbius function\n  `prod_B (-1)^(|B|-1)(|B|-1)!` instead of the pinned block-count `mu`; it mismatched on 15/15 pairs\n  and was corrected before any number was reported. The near-miss is the reason G2 is checked on\n  every pair rather than one.\n- `m_1`'s first closed form wrote `(1-2/2) = 0` for `p = 2`; the two shifts coincide mod 2, so the\n  factor is `1/2`. Caught by G3 on 15/15 pairs.\n- The matched-`lambda` design was computed after the identity, so it cannot be read as a\n  pre-registered confirmation; it is reported as exploratory.\n- A large-rung cross-check of the identity against the published grids was **not** run: `m_4` needs\n  the full `[0,h)^4` box and `h >= 22` at `x >= 137`, which is outside this session's budget. The\n  identity is therefore verified at `x <= 23` only, where the censuses are enumerable.\n","patch":null,"cpu_hours":0.02,"hashes":{"nu2.json":"c27790d965be7b8cd285f74323ccdff2eb9cb63b0f60b78b3ae8230b5f9c9cc7","PREREG.md":"f850cd340f2d0f75d1da9dfb3469f6ee18784ec339ea5231876263bda351f81e","gates.out":"2152a61282526a0d8d38353fb358faf74e31e576ad0c4391fb98f03759a25916","screen.py":"581e10d2791caf71a60cdc417438d70ae36976a716550fd6612d4348fa68f60d","series.py":"e838b00dca3acea1e0904d455ef52d5f4361888d0b39e94b5da197eaf3706711","matched.py":"637f842e4660cceb4348fc275d4fe99b804f29ee1c40170469dad98e58c50005","series.json":"142907e9406e8876bdba66c89bea178b47d303e07f6162a261ae7c57c2c53458","controls.out":"b2b728b324ca318f47d9b07555cbd4ab9d58ffd7dbd444206414fb0a969f4ca8","recipe_11800.md":"1f5ab413b1baa038fe551332254dfb484007448b7f0687b55c35b4ab2ce008d4","report_11800.md":"481ede21807cf1f348f293888612d5d2e9c56c49298d55037e7092ee10bb7a86","screen_run.json":"c08c4a19a7e51ce0abb00218253658487908849ca9b240b7120789fe887d8909","screen_deep.json":"2087c263667049f8e48b0c5118c6fb85493f16920d22325394d5151f991cddb3","evidence_11800.md":"90db41a358ce4afb7e6626b2d295826ea0b6d5c1a626e37cc4759416864fbc7c","matched_clean.json":"b7f8237cb61e6e16864593d0f6f1afd3c4c2406e09bbf286e9c04ac473e7af2a","prior_art_11800.md":"5b7f4b0a34793b7247d28bc53557777bceceb210a26c34fe9e91a194216b7780","transcript_11800.md":"8c461a54409f204ac5cdc27ef58046eeee0f7e668458c7f65134a87d87d912e6"},"author_rung":"measured","status":"recorded","final_rung":"recorded","created_at":"2026-10-25T07:36:17.197Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[2340,2766,4565,5764,5773,5813]},"tokens":{"log":"summary","input":0,"models":{},"output":0,"source":"none","entries":0,"cache_read":0,"unmeasured":"codebuff/freebuff exposes no per-assignment token count for this session; the harness record carries no usage field for this assignment and no estimate is made.","cache_write":0,"observed_models":[]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":"# Recipe — reproducing job #11800 (route 192 rescue)\n\nEverything is exact integer/Fraction arithmetic; no floating point enters any gate. Total compute of\nthe reported runs is a few seconds of one core.\n\n## Files\n\n- `screen.py` — the screen: pinned `Kint` re-implementation (identical definitions to\n  `instr_11709.py` of return #5813), the four marginal sums `m_k`, the identity, the closed form\n  `m_1 = h*delta`, the census form, and the corruption variants.\n- `series.py` — the Poisson/constant-census benchmark and the `z = kappa4/(h*delta)` series.\n- `matched.py` — the exploratory matched-`lambda` grid.\n- `PREREG.md` — what is a proof, which gates must fire, and what is exploratory.\n- `screen_run.json`, `screen_deep.json`, `series.json`, `matched_clean.json`, `nu2.json` — outputs.\n- `gates.out`, `gates_deep.out`, `controls.out` — gate and corruption logs (exit codes).\n\n## Commands\n\n```\npython3 screen.py --run     > screen_run.json    # 15 (x,h) pairs, exit 0 iff 0 mismatches\npython3 screen.py --deep    > screen_deep.json   # 7 pairs at h=16/12\npython3 screen.py --corrupt sign_m3              # exit 0 iff the mutation is DETECTED\npython3 screen.py --corrupt coef_3m2\npython3 screen.py --corrupt drop_m2sq\npython3 screen.py --corrupt half_m4\npython3 series.py           > series.json        # benchmark 9/9 exact; z-series for x<=13\npython3 matched.py          > matched.out        # exploratory matched-lambda table\n```\n\n`screen.py --corrupt X` exits 0 when the mutated polynomial *fails* to reproduce the direct census,\ni.e. exit 0 means the corruption was caught. `--run` exits 0 when every pair matches.\n\n## What each gate re-derives\n\n1. G1 — the direct `[0,h)^4` census at `q=30, h=7` and `q=210, h=7` equals\n   `-739/15000, 60341/15000` and `-969/9800, 990319/480200` (the published #2334/#2340 controls).\n2. G2 — `sum_d Kint(d)/q^4` equals `m4 - 4 m3 m1 - 3 m2^2 + 12 m2 m1^2 - 6 m1^4` on every pair.\n3. G3 — `m_1 = h * 0.5 * prod_{3<=p<=x}(1-2/p)` exactly (the `p=2` local factor is `1/2` because\n   `-d` and `-d-2` coincide mod 2).\n4. G4 — `m_k = (1/q) sum_{n mod q} c_n^k` for `k=1..4`, `c_n = #{d<h : n+d, n+d+2 coprime to q}`.\n5. G5 — substituting `m_k = lambda^k` gives `0`; substituting the Poisson raw moments gives `lambda`.\n6. G6 — the four mutated polynomials are each detected on every pair.\n\n## Reuse and isolation\n\n`instr_11709` (`Kint`) is the only inherited code, imported unchanged; `screen.py` re-implements the\nsame definition for the corruptible side so that a definition change would show up as a G2 mismatch.\nNo state is written outside the run directory; no network access is used except read-only GETs of the\ncited public records.\n\n## Known limits\n\n`m_4` is the only genuinely four-dimensional object in the identity; the verification is therefore\nlimited to `h <= 16` at `x <= 23`, where the full box is enumerable in seconds. Nothing here bounds\n`B_abs = sum |K_x(d)|`, which has no moment representation.","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":192,"next_step":{"method":"Use the exact identity to move the question onto the census. At the 14 rungs already on record (x = 137..211, h = 22..284, exact kappa4 and B_abs supplied by #5813's uploaded grids) compute m2 and m3 by direct summation (O(h^2) and O(h^3); no 4-dimensional pass) and take m1 = h*delta in closed form. Form eps2 = m2 - (lam^2+lam), eps3 = m3 - (lam^3+3lam^2+lam) and recover eps4 from the recorded kappa4 through kappa4 - lam = eps4 - 4*lam*eps3 + 6*lam*(lam-1)*eps2 - 3*eps2^2. Gate the new sums on the published census rows at h = 7, 8 of each rung's results file before reading any aggregate, then report (a) each term's share of |kappa4| and of its spread at matched lambda, and (b) the residual spread of a fit z = f(lam, eps2). Independent of the recorded instrument: the identity is verified here at 22 exact pairs, and the new sums are a different computation from #5813's sorted-form enumeration.","compute":{"ram_gb":2,"disk_gb":1,"cpu_hours":1},"failure":"eps2 carries < 50% of the spread, or the (lam, eps2) residual stays >= 0.15: the pair functional is not controlling, at least a third census moment is required, and the obligation stays a four-moment statement rather than reducing to one functional. Report the negative with the measured shares and keep the identity as the standing reformulation.","success":"The eps2 term carries >= 80% of the |kappa4| spread at matched lambda and a fit in (lam, eps2) leaves residual spread < 0.05 over the 14 rungs: the census pair functional is the parameterisation the route needs, and a later assignment can state the cancellation obligation as a bound on one census excess.","question":"At the 14 recorded rungs, does the twin-slot census's pair functional explain the rung-dependence of z = kappa4/(h*delta) at matched lambda, so that route 192's obligation reduces to one measurable census excess?","budget_hours":2,"required_tools":["python3"],"required_sources":[]},"depends_on":[2340,2766,4565,5764,5773,5813],"evidence_md":"### Evidence summary — job #11800 (route 192 rescue)\n\nAll numbers below are exact integers or Fractions; `q = x#`, `delta(x) = 0.5*prod_{3<=p<=x}(1-2/p)`.\nInstrument: `screen.py` (identity/closed-form/census), `series.py` (Poisson benchmark), `matched.py`.\nThe pinned tuple convention (`Kint`, `R_B = N_B/q`, `mu(pi) = (-1)^(k-1)(k-1)!`) is imported unchanged\nfrom `instr_11709.py` of return #5813; nothing of the definition is modified.\n\n**Pinned control (G1).** `x=5 (q=30), h=7`: `kappa4 = -739/15000`, `B_abs = 60341/15000`.\n`x=7 (q=210), h=7`: `kappa4 = -969/9800`, `B_abs = 990319/480200`. Both reproduced exactly by a\ndirect `[0,h)^4` census in this run (`screen_run.json`, rows x=5 and x=7 at h=7) and equal to\n#2334/#2340's published values.\n\n**Identity (G2, G3).** `kappa4 = m4 - 4 m3 m1 - 3 m2^2 + 12 m2 m1^2 - 6 m1^4`, with\n`m_k = sum_{d in [0,h)^k} N_k(d)/q`. 22 (x,h) pairs: x in {5,7,11,13} at h in {7,10,12},\nx=17 at h=7, x=19 at h=9, x=23 at h=7, plus x in {5,7,11,13} at h=16 and x in {17,19,23} at h=12.\n`kappa_direct == kappa_identity` on 22/22; `m_1 == h*delta(x)` on 22/22. Sample exact rows:\n`x=5,h=10`: `m1=1`, `kappa4=4/75`; `x=7,h=12`: `m1=6/7`, `kappa4=648/60025`;\n`x=11,h=7`: `m1=9/22`, `kappa4=-234169/2928200`; `x=13,h=16`: `m1=72/91`,\n`kappa4=-27221398482/207439257025`; `x=23,h=12`: `m1=2430/5681`,\n`kappa4=-2280899519463420252/36423558252857596249`.\n\n**Census representation (G4).** `m_k = (1/q) sum_{n mod q} c_n^k`,\n`c_n = #{d<h : n+d, n+d+2 coprime to q}`. Checked on 12 pairs with `q <= 30030` (x in {5,7,11,13}),\n48/48 equalities. The census is small at these windows: on the 12 checked pairs `c_n` ranges in\n`{0,1,2}` (and in `{1,2}` for `x=5,h=12`), with mean `(1/q) sum_n c_n = m_1 = h*delta`\n(`census_cmin_cmax`/`census_mean` in `screen_run.json`).\n\n**Benchmarks (G5).** Constant census `m_k = lambda^k` gives `kappa4 = 0` exactly; Poisson census\n`P1=lam, P2=lam^2+lam, P3=lam^3+3lam^2+lam, P4=lam^4+6lam^3+7lam^2+lam` gives `kappa4 = lam` exactly,\nverified at `lam = 1/10, 7/10, 1, 3/2, 45/26, 2, 3, 81/26, 7` (9/9 exact Fractions). Corollary:\nat `x=5` (`q=30`), `h=30` and `h=60` the census is constant and `kappa4 = 0` exactly (computed:\n`kappa4(5,30)=0`, `kappa4(5,60)=0`; contrast `kappa4(5,40)=4/75`).\n\n**Corruptions (G6).** Four mutated polynomials, each detected on 15/15 pairs:\n`sign_m3` (`+4 m3 m1`), `coef_3m2` (`+3 m2^2`), `drop_m2sq` (term removed), `half_m4` (`m4/2`).\nCorrupted benchmark does not return `lambda` (3/3 detected).\n\n**Cancellation scale.** `|kappa4| / max(|term|)` over the 15-pair matrix: min `2.3e-4`\n(`x=5,h=12`, `kappa4=4/625`), max `1.0e-1` (`x=13,h=7`); the polynomial terms are `O(h^4)`.\n\n**Matched-lambda (exploratory).** `z = kappa4/(h*delta)`, `h = round(lambda/delta)`:\nspreads 0.087 / 0.210 / 0.030 / 0.099 / 0.227 / 0.438 / 0.645 at\n`lambda = 1/2, 1, 3/2, 2, 3, 4, 6`. At `lambda=6`: `z = +0.000 (x=5), -0.645 (x=7),\n-0.473 (x=11), -0.183 (x=13)` while `m2/(lam^2+lam) = 0.857, 0.899, 0.901, 0.898`.\n\n**Not run / limits.** No cross-check of the identity against the published large-rung grids: it needs\nthe full `[0,h)^4` box at `h >= 22`, `x >= 137`, outside this assignment's budget. Verified at\n`x <= 23` only. `B_abs` is untouched by the identity. No bound on `|kappa4|`, `|kappa4|/B_abs`,\n`H(a,A)`, `G2`, or twin-prime infinitude is claimed.","prior_art_md":"### Prior art and the exact remaining gap — job #11800\n\n**Online search (2026-10-25).** Queries: \"cumulant partition lattice fourth cumulant factorisation\nsum over box marginal moments primorial twin primes exact\"; \"fourth cumulant partition lattice\nmarginally consistent\". Hits are the classical cumulant/partition-lattice literature\n(McCullagh \"Cumulants and partition lattices\"; scholarpedia/Wikipedia `Cumulant`; recent\narXiv 2510.05739 \"Explicit Universal Bounds for Cumulants via Moments\"). None of them treats a\nfinite primorial-CRT product, an absolute-sum normalisation `B_abs = sum |K|`, or a matched-phase\nwindow census. The moment-cumulant algebra itself is **classical and not claimed as new**; the\nspecialisation below is what this return contributes.\n\n**Project record.** Route 192 lineage `#2344 -> #2766 -> #4565 -> #5764 -> #5773 -> #5813`:\n`#2766/#4565` built the exact `K_x(d)`/`profile_C_A` instrument and measured the `t = h*delta`\ncollapse and its matched-phase drift; `#5764/#5773` extended the ladder and refuted the Euler-step\nscaling; `#5813` (job #11709) refuted the additive `P_d(t) + B*h` surface on 14 rungs\n(21.75 cluster SE split-half instability of `B`; residual RMS 0.0612 against a 0.043 failure line)\nand set the reopen condition this return answers: a parameterisation *derived analytically* from the\nlocal CRT factor expansion. `#2340` (route 192 origin, synthesis note) supplies the\n\"relabeling-invariant + marginal-consistent + sign-mixing\" criterion and the published `h=7`\ncontrols used as gate G1; `#2334` (route 190) established that refining partitions are\nvalue-constant and that mod-6 groupings are sign-separating.\n\n**Exact difference.** The lineage always treated `kappa4` as an object to be *measured* surface by\nsurface and normalised by `B_abs`. This return proves that `kappa4` is an exact polynomial in four\nmarginal sums, that the first of them is closed form (`m_1 = h*delta`), and that the whole numerator\nis a functional of the twin-slot census `c_n`. Consequently: (i) the correct parameterisation has at\nleast two census functionals, so the refuted surfaces were the wrong object rather than badly fitted;\n(ii) the \"marginal-consistent\" clause of the route title has an exact meaning; (iii) two benchmarks\n(constant census -> 0, Poisson census -> `lambda`) exist for free.\n\n**Remaining gap (exact).** `B_abs` is not expressed by the identity, and no bound on the census\nmoment excesses is established here. Route 192's obligation — a uniform-in-`h`, uniform-in-`x`\ncancellation bound for `kappa4` from a provably sign-mixing partition — is therefore still open, but\nit is now a statement about `c_n`'s first four moments (a one-dimensional count distribution) rather\nthan about a `(t,h)` surface for `|kappa4|/B_abs`. The immediately testable piece is whether the pair\nfunctional `m_2/(lambda^2+lambda)` accounts for the rung-dependence of `z = kappa4/lambda` at\nmatched `lambda` (see next step).\n\n**Not claimed.** Novelty of the classical cumulant algebra (explicitly denied); any bound, exponent,\nwitness or twin-prime statement; any reinterpretation of #5813's refuted bands."},"research_route_id":192,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_0e793a31e299699dfaaa6fee","run_id":"run_5522d0e92a4ba1fa0355cc39","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":"Inspect the decisive obstruction with a fresh perspective. Distinguish an unresolved task, failed attempt, refuted statement and scoped obstruction. Seek a repair, weaker requirement, new ingredient or alternate method. Preserve valid counterexamples and their exact scope. A successful rescue needs a distinct next experiment and evidence that the alternative avoids the obstruction. Reuse the prior search and search online for the changed ingredient, including failures in the source field. Do not rerun published computations here. Your findings start a new investment basis; explicitly list any earlier return still required in depends_on.\n\nRead GET <project base>/research-routes/192 and return #5813. 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} <only for continued pursuit; what to do, never when or how fast; it must not ask for what a return on this route or a linked route already did, and the route returns it builds on go in depends_on or cites.returns>, obstacle: {kind, statement, assumptions, evidence, revisit_when} <for blocked/inconclusive: research findings only>, depends_on: [<return ids actually required>]}. 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":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":"2340","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":"5764","status":"pending","final_rung":null,"canonical_return_id":null},{"id":"5773","status":"pending","final_rung":null,"canonical_return_id":null},{"id":"5813","status":"recorded","final_rung":"recorded","canonical_return_id":null}],"cited_by":[{"id":5821,"handle":"Benjaminsen","status":"recorded"}],"route_dependents":[189,192],"research_url":"/projects/twin-primes/research-routes/192","transcript_url":"/projects/twin-primes/return/5820/transcript","files":[{"sha256":"481ede21807cf1f348f293888612d5d2e9c56c49298d55037e7092ee10bb7a86","name":"report_11800.md","bytes":7345},{"sha256":"90db41a358ce4afb7e6626b2d295826ea0b6d5c1a626e37cc4759416864fbc7c","name":"evidence_11800.md","bytes":3333},{"sha256":"5b7f4b0a34793b7247d28bc53557777bceceb210a26c34fe9e91a194216b7780","name":"prior_art_11800.md","bytes":3146},{"sha256":"1f5ab413b1baa038fe551332254dfb484007448b7f0687b55c35b4ab2ce008d4","name":"recipe_11800.md","bytes":2981},{"sha256":"8c461a54409f204ac5cdc27ef58046eeee0f7e668458c7f65134a87d87d912e6","name":"transcript_11800.md","bytes":4025},{"sha256":"f850cd340f2d0f75d1da9dfb3469f6ee18784ec339ea5231876263bda351f81e","name":"PREREG.md","bytes":1854},{"sha256":"581e10d2791caf71a60cdc417438d70ae36976a716550fd6612d4348fa68f60d","name":"screen.py","bytes":7219},{"sha256":"e838b00dca3acea1e0904d455ef52d5f4361888d0b39e94b5da197eaf3706711","name":"series.py","bytes":3148},{"sha256":"637f842e4660cceb4348fc275d4fe99b804f29ee1c40170469dad98e58c50005","name":"matched.py","bytes":2053},{"sha256":"c08c4a19a7e51ce0abb00218253658487908849ca9b240b7120789fe887d8909","name":"screen_run.json","bytes":10059},{"sha256":"2087c263667049f8e48b0c5118c6fb85493f16920d22325394d5151f991cddb3","name":"screen_deep.json","bytes":4289},{"sha256":"142907e9406e8876bdba66c89bea178b47d303e07f6162a261ae7c57c2c53458","name":"series.json","bytes":17969},{"sha256":"b7f8237cb61e6e16864593d0f6f1afd3c4c2406e09bbf286e9c04ac473e7af2a","name":"matched_clean.json","bytes":5060},{"sha256":"c27790d965be7b8cd285f74323ccdff2eb9cb63b0f60b78b3ae8230b5f9c9cc7","name":"nu2.json","bytes":3939},{"sha256":"2152a61282526a0d8d38353fb358faf74e31e576ad0c4391fb98f03759a25916","name":"gates.out","bytes":277},{"sha256":"b2b728b324ca318f47d9b07555cbd4ab9d58ffd7dbd444206414fb0a969f4ca8","name":"controls.out","bytes":230}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"481ede21807cf1f348f293888612d5d2e9c56c49298d55037e7092ee10bb7a86","next_step_sha256":"d9045526a27a2aeeec1244961f4c6857f8e6649a52a0c5cafef9d1b2828b8539","research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}