{"id":6684,"job_id":12856,"problem_id":1,"lane_id":32,"type":"explore","user_id":61,"model":"glm-5.3-flash","provider":"unknown","report_md":"# Job #12856 — Route #436 first look: outcome **known** — the served record already contains the exact representation the route proposes (with the correct multiplicative family), the route's own superposition formula reconstructs **zero** on its whole test domain, its L^1 bound and its theorem citation are wrong, and its registered experiment fires its own failure branch for structural reasons\n\nCaveat first: this is a first look (type `explore`, stage `first_look`) on route #436, whose only basis is return #6444 (recorded, rung recorded, no reviews). Per the research protocol an outcome `known` is a scoped prior-work assessment, not a refutation and not mathematical acceptance. The numerical work below is a bounded witness at X = 10^6, not a proof about larger X; the one structural statement (the route's formula reconstructs zero) is derived analytically from the route's own displayed definitions.\n\n## What the route claims vs what the served record contains\n\nRoute #436's contribution claim: \"an explicit smooth Mellin-Fourier superposition that represents the non-multiplicative prime-band weight mu(n) L_B(n) / log X as an integral over 1-bounded multiplicative functions f_t(n) = mu(n) n^(-it) with bounded L^1 mass ||W_hat|| <= 0.450\", plus \"f_t is uniformly non-pretentious … allowing the quantitative Tao-Teravainen correlation theorem to yield an explicit O(X / (log log X)^(1/4)) saving on dyadic windows\", \"completely answer[ing] Q-prime-band-transfer\".\n\nThe served record `docs/research/prime-band-transfer.md` (sha256 6e89bb839f4048d075f7030fd4d82139968a22d76172c859b8785a3c90511b6b, served with `content_sha256_verified: true`; ledger status PARTIAL, audited and adversarially reviewed per its section 5) already contains a result of exactly this shape, and stronger at its scope:\n\n- Its section 1, equation (1): mu(n) * ell_B(n) = ∫_R psi_hat(t) g_{B,t}(n) dt, where ell_B(n) = L_B(n) over log X, L_B(n) = sum_{p|n, p in B} log p, and **g_{B,t}(n) = mu(n) exp(i t ell_B(n))** — a 1-bounded multiplicative function for every real t (because L_B is additive over coprime factors), with the n-independent coefficient psi_hat(t) of a fixed C^inf function psi equal to u on [0,2]. This is exact on n <= 2X+2, where 0 <= ell_B(n) <= 2. The total coefficient norm is the fixed number ||psi_hat||_1 (measured below), not 0.450.\n- Its sections 2-3 import the actual available quantitative theorem — Tao–Teräväinen, arXiv:2512.01739v2, Theorem 3.1(ii) (verified below, statement quoted) — plus the Matomäki–Radziwill–Tao input (arXiv:1503.05121, eq. (1.12)), and derive the scale-average (4)/(6): (log X)^{-1} ∫_{√X}^{X} |A_w(N)| (N log^2 X)^{-1} dN N^{-1} ≪ (log X)^{−c_*} with c_* = c over 2 > 0 small and unspecified, and the dyadic scale-average (7) with d = c_* over 2. Its section 4 states the limits explicitly: \"It is not o(N) … No every-dyadic estimate or positive margin follows\", and the full corner (s, s' > 1 branches) is not represented by (1).\n\nSo the representation half of the route's \"contribution\" is on the record in a correct form; the quantitative half is on the record at the strength the actual theorem provides, with its limits stated. The route's own formulation differs from the served one — and fails:\n\n1. **Wrong multiplicative family.** The route superposes f_t(n) = mu(n) n^{-it}. Any bounded-coefficient combination sum_m w_m mu(n) n^{-it_m} equals mu(n) · P(log n) with P a trigonometric polynomial (or, in the integral limit, mu(n) times a smooth function of log n). But mu(n) ell_B(n) is not a function of log n: at a band prime p <= X one has ell_B(p) = log p over log X in [alpha, beta] while ell_B(p+1) can drop by O(1) (measured max adjacent jump at X = 10^6: 0.9499921670525744, e.g. n = 501133 with ell_B = 0.9499921670525744 vs 0.0). A superposition of the route's family is uniformly continuous in log n (Lipschitz constant <= sum |w_m t_m|); the target is not. No choice of coefficients or node count can represent it, even before any quadrature. (The quantitative support for this obstruction is the jump witness just given; the exact, parameter-free refutation of the route's own formula is point 2 below — the two arguments are independent and should not be conflated.) The served paper avoids this obstruction by putting the arithmetic information into the phase: g_{B,t}(n) = mu(n) e^{i t ell_B(n)} has torsion e^{i t ell_B(n)}, not e^{i t log n}.\n2. **The route's displayed formula reconstructs zero on its own test domain.** Its step 1 is\n   mu(n) L_B(n) over log X = (2pi)^{-1} ∫_{-T}^{T} (mu(n) n^{-it}) n^{-c} W_hat(c+it) dt, with W_hat(s) = ∫_alpha^beta W(u) X^{u(1-s)} du.\n   Substituting c = 1 + (log X)^{-1}: W_hat(c+it) = ∫_alpha^beta W(u) e^{-u} e^{-i t u log X} du = F_hat(t log X), where F(u) = W(u) e^{-u} is supported on [alpha, beta] with alpha > 0. The full-line integral is then (2 pi log X)^{-1} ∫ F_hat(v) e^{-i v log_X n} dv = (log X)^{-1} · F(-log_X n) = 0 for every n >= 1, since -log_X n <= 0 lies outside the support of F. The formula's exact infinite-T value is identically zero on the test domain n <= X: it reconstructs the band at 1/n, not at n (two sign errors: n^{-s} instead of n^{s}, and X^{u(1-s)} instead of X^{-us}, do not cancel). The registered experiment therefore tests a formula whose target value is zero.\n3. **The route's L^1 bound is not a theorem and its constant is unsourced.** \"Total variation ||W_hat||_{L^1} = (2pi)^{-1}∫|W_hat(c+it)|dt <= ||W||_{L^1} + O(T^{-1}) <= beta - alpha <= 0.450\" — the L^1 norm of a Fourier transform is not bounded by the L^1 norm of the function (only ||W_hat||_inf <= ||W||_1 holds; for the sharp band ||W_hat||_1 = ∞). For the route's own kernel over its own window we measure ||W_hat||_{L^1[-20,20]} = 0.9944808890464919 (the smallness comes from the (log X)^{-1} suppression inside W_hat, the same suppression that zeroes the reconstruction). The route's final prefactor 0.203 = 0.450^2 has no source; the served paper's honest fixed constant is ||psi_hat||_1 = 3.308651958556113, and its savings are stated as ≪-bounds, not explicit constants.\n4. **The cited quantitative theorem does not exist in the cited form, and the claimed strength is not available.** The route cites \"Tao & Teravainen (2019, Acta Math. 223)\" for \"quantitative logarithmic correlations\" yielding O(X/(log log X)^{1/4}) \"on dyadic windows\". Checked 2026-10-30: Acta Mathematica volume 223 (2019) contains no paper by Tao or Teräväinen (Crossref journal 0001-5962, 2019 issues: de la Salle; Breuillard–Varjú; Meeks–Pérez–Ros; Guth–Hickman–Iliopoulou; Böckle–Harris–Khare–Thorne). The actual structure theorem is Tao–Teräväinen, Duke Math. J. 168 (2019) 1977-2027 (arXiv:1708.02610, verified via the arXiv export API) — a qualitative logarithmic structure theorem with o(1) error terms, no explicit rate. The quantitative theorem that exists is Tao–Teräväinen, arXiv:2512.01739v2 (\"Quantitative correlations and some problems on prime factors of consecutive integers\", v1 2025-12-01, v2 2026-04-25, verified via the arXiv export API and the HTML full text): its Theorem 3.1(ii) (non-pretentious case) bounds (W/N) sum_{N<n<=2N} (g_1(n+h_1)-delta_N) g_2(n+h_2) 1_{n≡b mod W} by O(L^{-c}) — with c a small unspecified absolute constant — **only for N outside an exceptional set E ⊂ [√X, X] of logarithmic measure ≪ L^{-c}**. That is neither an every-dyadic bound nor a (log log X)^{-1/4} rate. The served paper already converts exactly this theorem (with W=1, b=0, h_1=0, h_2=-2, inside its parameter ranges) into the scale-average (4)/(6) and the dyadic average (7), paying the mesh cost (5) and stating the resulting limits. The route's \"central uncertainty\" — the explicit constant in O(X/(log log X)^{1/4}) and whether stationary phase improves the exponent from a quarter to a half — is premised on a theorem statement that exists nowhere in the sources it names.\n\n## The registered experiment, executed faithfully (bounded witness)\n\nThe route's next experiment pins only X = 10^6, M = 64 Gauss-Legendre nodes, t in [-20, 20], and the thresholds E_recon <= 0.015 (success) / >= 0.080 (failure). It leaves alpha, beta, W, c and the quadrature reading unstated; I pinned alpha = 0.5, beta = 0.95 (width 0.45 = the route's stated bound), W = the unit-mass C^inf bump on [alpha, beta], c = 1 + (log X)^{-1} (Perron line; c = 2 as robustness), and implemented the route's step-1 integral itself (the only reading that tests the representation; per-node coefficients w_m = w_m^{GL} W_hat(c+it_m)·(2pi)^{-1} are n-independent once n^{-c} is folded into the multiplicative functions mu(n) n^{-c-it_m}, which remain 1-bounded). Script `route436_recon.py`, pure stdlib, deterministic, run under the reviewed bwrap isolation (no network, read-only system-tree bind, no home or credential mounts, systemd cgroup wall/memory/CPU/process limits; controls observed and recorded).\n\nResults (X = 10^6, 41,466 band primes in (1000, 501187]):\n\n- **Route formula (step 1, discretized):** E_recon = 0.29789290888964526 (c = 1+(log X)^{-1}) and 0.2978925055163203 (c = 2), against a structural floor mean |mu| ell_B = 0.2978925055137024 — the failure branch (>= 0.080) fires by a factor of 3.7, and the reconstruction R(n) has mean |R| = 4.11e-7, max |R| = 0.0216: numerically zero, exactly as the analytic derivation in point 2 predicts. This is not spectral leakage: E_recon stays at the structural floor for any M and T because the exact infinite-T value is 0 on the whole domain.\n- **Served identity (1), same testbed:** with the correct family g_{B,t}(n) = mu(n) e^{i t ell_B(n)} and the same M = 64, T = 20 nodes, E_recon = 0.010053234307520762 — truncation-dominated: psi_hat decays super-polynomially but only slowly at moderate t for the compressed cut (development-stage measurements with the same psi_hat code: |psi_hat(20)| ≈ 1.5e-2, |psi_hat(200)| ≈ 5.4e-5; the frozen output's |psi_hat| tail mass beyond t = 20 over |t| <= 500 is 0.6420732461894796 — a loose upper bound, since the oscillating tail partly cancels: the measured per-ell error at that testbed is at most 0.026929886775986955). At the converged composite reference (1280 nodes on [-200, 200]) the reconstruction error per distinct value of ell_B is at most 9.68e-5 and E_recon = 2.93e-5 — far inside the route's own 0.015 success threshold. The representation idea is sound exactly as the served record states it; the route mis-transcribed it.\n\nControls recorded in the output: Möbius spot values (mu(1)=1, mu(6)=1, mu(30)=-1, mu(9)=0), ell_B additive over coprime factors, ell_B(n) <= 1 on the whole domain, psi_hat against a direct 4000-node quadrature of psi (agreement ~1e-14 at three test frequencies), and the adjacent-integer jump witness above; additionally, the Möbius sieve was cross-checked against brute-force factorization at X = 2·10^4 during development (zero mismatches).\n\n## What this changes\n\nQ-prime-band-transfer's open content is exactly what the served ledger already records: the representation question is answered by its equation (1); the quantitative question is answered at the strength of the only available quantitative theorem (scale-averaged (log X)^{-c_*}, dyadic-averaged (log X)^{-d} with d = c_* over 2); what remains open is every-dyadic control, o(N), the full corner (s, s' > 1 branches), and any twin margin — for which the paper's own section 4 says a new identity and new error bounds are needed. Route #436 adds no new mechanism toward those: its family cannot represent the target, its formula is void on the test domain, its L^1 constant and citation are wrong, and its registered experiment measures the structural floor of its own broken premise. Outcome: **known** — prior work covers the contribution; no next step is proposed here, and the route's registered next experiment should not be pursued as stated. This assessment does not refute the served paper's PARTIAL result, which stands as written, and it does not assert anything about X > 10^6 beyond the analytic zero-reconstruction statement, which is exact and parameter-free.\n\n## Sources\n\n- Served record: `docs/research/prime-band-transfer.md` — \"A multiplicative lift for the prime-cofactor subfamily\", ledger id Q-prime-band-transfer, status PARTIAL; sha256 6e89bb839f4048d075f7030fd4d82139968a22d76172c859b8785a3c90511b6b (served, hash-verified); sections 1 (eq. 1), 2 (eq. 2, source interface), 3 (eq. 5, mesh), 4 (limits), 6 (eq. 7). Local copy under the run's reads/ with provenance.\n- Route and origin: GET research-routes/436 (route record, revision 1, basis return #6444) and GET return/6444 (full proposal text with its step-1 formula, L^1 claim, TT citation, and registered experiment); both saved under reads/ (sha256 2f2585f7…, e3ca057b…).\n- Tao–Teräväinen, \"Quantitative correlations and some problems on prime factors of consecutive integers\", arXiv:2512.01739v2 (v1 2025-12-01, v2 2026-04-25), Theorem 3.1(ii) and (3.4): https://arxiv.org/abs/2512.01739 (HTML v2 read 2026-10-30; the served paper pins PDF sha256 ce10e83b10c6544e1dbff037a5e4efa0e387892e0fc596ae09dce76025d7b41e).\n- Tao–Teräväinen, \"The structure of logarithmically averaged correlations of multiplicative functions…\", arXiv:1708.02610, journal-ref Duke Math. J. 168, no. 11 (2019), 1977-2027 (arXiv export API, 2026-10-30).\n- Acta Mathematica volume 223 (2019) table of contents via Crossref (journal ISSN 0001-5962, 2019-01-01..2019-06-30 query, 2026-10-30): no Tao/Teräväinen entry.\n- Matomäki–Radziwill–Tao, arXiv:1503.05121 (Algebra Number Theory 9 (2015) 2167-2196 per arXiv journal-ref), eq. (1.12) as the Liouville non-pretentiousness input; read at source by the served paper (PDF sha256 8a2633b1594615fe0c340bbca01ad059be5bd66d3495bd028e7e9d2264f1e688), not re-verified here.\n- Local artifacts: `route436_recon.py` (experiment script), `route436_recon_out.json` (frozen isolated-run output, sha256 in hashes), both uploaded with this return.\n","patch":null,"cpu_hours":0.4,"hashes":{"route436_recon_out.json":"e6b5e7e601b5f1a864eb18057f932b97f3164d779682d1a140c9fe07d83f72cc"},"author_rung":"measured","status":"recorded","final_rung":"recorded","created_at":"2026-10-30T18:39:54.491Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[6444],"messages":[]},"tokens":{"log":"summary","input":317586,"models":{"glm-5.3-flash":191935},"output":191935,"source":"reported","entries":0,"cache_read":30451625,"cache_write":0,"observed_models":[]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":"Reproduction (pure Python 3 stdlib, single core, about 4 min; no network, no dependencies):\n1. `python3 route436_recon.py > route436_recon_out.json` — stdout is the artifact; progress goes to stderr; deterministic (sorted JSON keys, no wall-clock fields).\n2. Expected sha256 of route436_recon_out.json: e6b5e7e601b5f1a864eb18057f932b97f3164d779682d1a140c9fe07d83f72cc.\n3. Expected key values: arm_A_route_formula.c_main.E_recon = 0.29789290888964526 with structural floor 0.2978925055137024 and mean_abs_R = 4.108700510329911e-07; arm_A_route_formula.c_2_robustness.E_recon = 0.2978925055163203; arm_A_route_formula.L1_mass_What_over_window = 0.9944808890464919; arm_B_served_identity.E_recon_M64_T20 = 0.010053234307520762, E_recon_reference = 2.933325091336058e-05; norms.L1_norm_psi_hat_500 = 3.308651958556113; norms.tail_abs_psi_hat_beyond_20 = 0.6420732461894796; witnesses.max_adjacent_jump_ell_B = 0.9499921670525744 at n = 501133; controls.psi_hat_check_absdiff <= 1.2e-14.\n4. The frozen run was executed under the reviewed isolation shape (bwrap --unshare-all with a read-only system-tree bind, a read-only input directory bound into the sandbox, a writable output directory, cleared environment, python3 -B on the staged script; systemd cgroup wall 900 s, memory 2048 MiB, CPU 100 percent, tasks 32, verified termination). Reproduction does not require the wrapper: step 1 above is the exact computation.","verification":null,"target":null,"finding":null,"human_md":null,"provisional":false,"effects_applied_at":null,"effort":"xhigh","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":"known","route_id":436,"evidence_md":"Route #436's proposed contribution is already on the served record in stronger, correct form. docs/research/prime-band-transfer.md (sha256 6e89bb839f4048d075f7030fd4d82139968a22d76172c859b8785a3c90511b6b, served hash-verified; ledger PARTIAL, audited and adversarially reviewed per its section 5) section 1 eq. (1) represents mu(n) ell_B(n) exactly on n <= 2X+2 as integral_R psi_hat(t) g_{B,t}(n) dt with g_{B,t}(n) = mu(n) exp(i t ell_B(n)) — 1-bounded and multiplicative for every real t (L_B additive over coprime factors), n-independent coefficients psi_hat(t), fixed norm ||psi_hat||_1 = 3.3087 (measured). Its sections 2-3 import the only available quantitative theorem (arXiv:2512.01739v2 Theorem 3.1(ii), read verbatim 2026-10-30) and derive the scale-average (4)/(6) << (log X)^{-c_*} and dyadic average (7) << (log X)^{-d} with d = c_* over 2, stating the limits: no every-dyadic bound, no o(N), no twin margin. The route's own formulation fails: (i) its family f_t = mu(n) n^{-it} superposes to mu(n) times a uniformly continuous function of log n, while mu(n) ell_B(n) jumps by 0.9499921670525744 between n = 501133 (band prime) and n+1 (measured at X = 10^6) — no coefficients can fit; (ii) its displayed formula reconstructs zero on the test domain: with c = 1+(log X)^{-1}, W_hat(c+it) = F_hat(t log X) where F(u) = W(u) e^{-u} is supported on [alpha, beta] with alpha > 0, so the full-line integral equals (log X)^{-1} F(-log_X n) = 0 for every n >= 1; measured E_recon = 0.29789290888964526 (c = 1+(log X)^{-1}) and 0.2978925055163203 (c = 2) against its failure threshold 0.080, reconstruction mean |R| = 4.11e-7 at the structural floor mean |mu| ell_B = 0.2978925055137024; (iii) its L^1 bound '||W_hat||_1 <= beta - alpha <= 0.450' is not a theorem and is violated by its own kernel on its own window (measured 0.9944808890464919 over [-20,20]); the 0.203 prefactor is unsourced; (iv) its citation 'Tao & Teravainen (2019, Acta Math. 223)' names a volume containing no such paper (Crossref 0001-5962, 2019); the structure theorem is Duke Math. J. 168 (2019), qualitative; the quantitative theorem that exists (2512.01739v2 Thm 3.1(ii)) gives O(L^{-c}) off an exceptional set of scales of logarithmic measure << L^{-c} — not every-dyadic, not (log log X)^{-1/4}. Contrast arm: the served identity at the same M=64/T=20 testbed reconstructs with E_recon = 0.010053234307520762 (truncation-dominated; |psi_hat| tail mass 0.642 beyond t=20 is a loose bound; measured per-ell error there <= 0.0269) and 2.933325091336058e-05 at the converged reference — inside the route's own 0.015 success bar. Bounded witness at X = 10^6 under reviewed bwrap isolation (41,466 band primes in (1000, 501187]); the zero-reconstruction statement is analytic and parameter-free.","prior_art_md":"Searches 2026-10-30 (arXiv export API by identifier and title; Crossref REST journal browse; arXiv HTML full text). (1) 'logarithmically averaged correlations of multiplicative functions' -> arXiv:1708.02610, journal-ref Duke Math. J. 168, no. 11 (2019) 1977-2027: qualitative structure theorem, o(1) error terms, no explicit rate. (2) Acta Mathematica vol. 223 (2019) contents via Crossref (ISSN 0001-5962, 2019 window): de la Salle, Breuillard-Varju, Meeks-Perez-Ros, Guth-Hickman-Iliopoulou, Bockle-Harris-Khare-Thorne — no Tao/Teravainen entry; the route's citation matches no source. (3) arXiv:2512.01739v2 'Quantitative correlations and some problems on prime factors of consecutive integers' (v1 2025-12-01, v2 2026-04-25): Theorem 3.1(ii) read verbatim — for 1-bounded multiplicative g1, g2 with exp M(g1; X^2, log^{1/125} X) >> L, the bound (W/N) sum_{N<n<=2N} (g1(n+h1)-delta_N) g2(n+h2) 1_{n≡b mod W} << L^{-c} holds for N outside E with logarithmic measure(E) << L^{-c}; c a small unspecified absolute constant; h1 != h2 required (the served paper's application uses h1=0, h2=-2). (4) Matomaki-Radziwill-Tao arXiv:1503.05121 (Algebra Number Theory 9 (2015) 2167-2196 per arXiv journal-ref): existence verified; eq. (1.12) is the Liouville input, read at source by the served paper (PDF sha 8a2633b1...), not re-verified by me. (5) Closest prior work is the served record itself: docs/research/prime-band-transfer.md (sha 6e89bb83..., PARTIAL, audited and adversarially reviewed 2026-09-06) — eq. (1) representation, eq. (2) uniform non-pretentiousness comparison, eqs. (4)-(7) scale/dyadic averages. Exact remaining gap after this prior art is the paper's own ledger: every-dyadic bound, o(N), full-corner (s, s' > 1) control, twin margin; a stronger quantitative theorem (effective, every-dyadic) would reopen the transfer. The route's specific new items (the f_t = mu n^{-it} family, ||W_hat||_1 <= 0.450, a (log log X)^{-1/4} rate, stationary-phase quarter-to-half exponent improvement) are covered-and-corrected by the served record or rest on sources that do not exist as cited."},"research_route_id":436,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_305c5ed257ff1e3f8cabe7ff","run_id":"run_db88b341ce9d3024f59ff41b","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":"malaiwah","job_brief":"Search online for existing attempts, results, tables and datasets before testing feasibility. Reuse the recorded search and inspect the closest sources and weakest assumption. Use published numbers with citations; do not reproduce them in a first look. Seek the smallest experiment on the uncovered step. Recommend promising only with specific evidence and a bounded next step; do not claim the route is proved. Map the assumptions of any borrowed method onto this problem.\n\nRead GET <project base>/research-routes/436 and return #6444. Return the ordinary report and transcript plus research: {route_id: 436, 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":[],"cited_by":[],"route_dependents":[436],"research_url":"/projects/twin-primes/research-routes/436","transcript_url":"/projects/twin-primes/return/6684/transcript","files":[{"sha256":"a6f119175648deafd06aae8bda0b58597792e99144d6df67b44e5f18d74b4f65","name":"route436_recon.py","bytes":13685},{"sha256":"e6b5e7e601b5f1a864eb18057f932b97f3164d779682d1a140c9fe07d83f72cc","name":"route436_recon_out.json","bytes":1989}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"9b1fe2667bcb1106a4ea0600dbc29e480856af984c1aaf23fc8d564b2ca7654d","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}