ScoreCompute

Survey up to 512 initial orbits in a planar circular Sun–Jupiter model; at most 4 million reserved CPU steps. Return finite-window sensitivity, actual durations, sampled Jacobi drift and explicit stops. Bands do not prove chaos or stability; radial overlap is not an encounter. Direct-only.

Read native contracts, themes, units, assumptions, backends and approved composition families; optional exact theme filter. tools/list discovers direct MCP tools; list_composition_capabilities adds planner bindings.

Read implemented versioned contracts, native capabilities, approved adapters and planning examples. Unsupported unit/model facts expose missing adapters. No engines run; direct tools remain independently callable.

Read contributor availability, offered CPU/GPU resources and verified throughput by workload. Hardware is self-reported; per-GPU VRAM is not pooled. Mixed-workload samples do not measure comparative speed.

Exactly maximize value for up to 32 independent, indivisible tasks within an integer-minute budget. Each task is selected at most once; no prerequisites or shared resources.

Compute geometric golden [-4,+6°] and blue [-6,-4°] windows for one UTC day, 1900–2100. Sunrise at -0.833° is a separate convention. No refraction, terrain or weather. Numerical tolerance is not astronomical accuracy; oracle validation covers reference dates only. Shared solar models are not independent corroboration.

Preview robust scheduling without running engines: validate assumptions/permissions and return up to three candidate budgets (nominal, 10% reserve, 20% reserve), compute limits or blockers. No arbitrary tools or external code.

Fit original tracks, then rank 1–64 supplied future series by local-linear uncertainty and declared cost. Assumes constant velocity, independent new errors and exact stations/clocks. Candidate angles and client baselines are forbidden. Prediction is not an acquired measurement or visibility proof.

Check dimensions, then compare first-order GUM with seeded fixed-sample Monte Carlo for an explicit model of 1–16 inputs. Return uncertainty budgets, coverage intervals and convergence/linearization findings. Conditional on supplied distributions; no affine units. CPU, direct-only; no planner binding.

Order 2–256 points from index 0 using planar or spherical kilometre distances. Exact only after completed Held–Karp search (at most 13 points); otherwise bounded heuristics. Returns every leg and stop reason. No roads or traffic.

Execute a supplied bounded score AST on 2–128 Euclidean-km points with depot 0 and 2-opt. Validates the closed tour; exact=false. No retraining, external effects or promotion. Hashes identify programs, not independent validation.

Bounded deterministic float64 scan of a scalar <= or >= claim over a declared grid of 1–6 variables. Reports numerical witnesses, undefined and uncertain evaluations, and the exact stop reason. A propagated screening guard rejects near-boundary candidates; it is not a certified interval or formal proof. An inconclusive outcome preserves unresolved sampled cells; absence of a witness does not establish the claim over the continuous box.

Screen a supplied trade series for repeated volume at nearly equal prices within a declared time window. Return recycled-volume ratio and cycles; a pattern does not prove wash trading.

Kac's question in reverse: design a polygonal drumhead whose lowest tones play requested frequency ratios (a fifth, a triad, a pentatonic scale), each accepted within ±tolerance_cents. proven_impossible is returned only when proven theorems exclude every ratio combination inside those tolerance windows for a connected uniform membrane with a fixed edge: simple fundamental, f2/f1 ≤ j11/j01 ≈ 1.5933 with equality for the disk (Ashbaugh–Benguria 1992), and Yang's universal inequality minimized exactly over the window box; an exact-target exclusion is reported separately. Otherwise multi-start L-B…

Estimate pi with seeded Monte Carlo and a 95% Wilson interval; up to 5 million samples. CPU or optional CUDA. Other direct scientific engines run on CPU.

Estimate deadline success, mean duration and empirical p95 for up to 32 integer-minute tasks under independent bounded uniform duration variations. Seeded CPU sampling; not a real-world forecast guarantee.

Solve Kuhn poker with CFR+ self-play, measure exploitability with pure best responses and compare the game value with -1/18. Illustrative game theory, not gambling advice.

Refit 1–32 declared hypothetical angular/clock perturbations to challenge reconstruction stability. Explicit hypothetical acknowledgement required. Non-convergence is inconclusive; none_found covers examined cases only. No new observations.

Queue fixed public synthetic pi (CPU/CUDA) or one of three discrete schedule scenarios (CPU only). No private data/custom code. Returns a ticket; poll get_network_job. Coordinator recomputes every accepted shard; no net speedup claim. Jobs may expire.

Locally normalized geometric descriptors of 3–256 planar points: distances, nearest-neighbour isolation, centroid spread, PCA collinearity and histogram. The principal-axis mirror residual is null for isotropic noncoincident covariance, whose axes are undetermined. Rounded fingerprints are descriptive, not proofs of equivalence or method benefit.

Fit position/velocity from 2–4 supplied azimuth/elevation tracks using constant velocity in spherical ECEF and declared angular noise/clocks. Reports fit status and conditional local uncertainty; no object identification or calibrated accuracy.

Verify a structured arithmetic, shadow, ephemeris, statistics or route claim with a bounded native engine. Returns a model-scoped verdict and portable Ed25519 server receipt; never truth, authenticity or fraud certification. Route claims explicitly distinguish optimality from a supplied tour total. Native failures return no scientific verdict. Parameters and examples: /verify and /docs/mcp/.

Check measured shadows using NOAA solar position, a ground-plane homography from 4–16 controls and Monte Carlo uncertainty. Returns conditional consistency, never image authenticity.