ScoreCompute

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.

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.

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.

Check a claimed Sun (soleil) or Moon (lune) position for UTC time/location using NOAA/Meeus approximations and lunar parallax. Returns model-conditional angular consistency and lunar phase.

Apply necessary GRIM/GRIMMER checks to rounded means and sample deviations of bounded integer observations. Passing does not prove a dataset exists; inconsistency does not establish fraud.

Convert angular speed and candidate distances to minimum transverse speeds; check a claimed speed-distance pair. Distance hypotheses are supplied, not measured; no object-origin conclusion.

Compare 4–120 measured minute/azimuth pairs with solar motion: residuals, slope, direction and time-lapse speed. Supply measurements, not video. Results are model-conditional consistency findings.

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.

Compare 4–40 supplied FEN positions and played SAN/UCI moves with Stockfish: first-choice agreement and centipawn loss. Entire analysis has a 25-second deadline; no cheating verdict.

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.

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.

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.

Train route-score ASTs on 1–8 supplied cases: at most 64 attempts and 31 nodes; stop between trials after 25s. Select converged candidates using training quality plus logical-fuel cost, a work proxy rather than CPU time. No held-out validation, arbitrary code or automatic promotion.

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.

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.

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.

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.

Refit original tracks plus one supplied new angular series, each counted once; compute the baseline natively. Declare synthetic/measured origin (unverified). Conditional uncertainty may worsen; forecast angles are not acquired evidence.

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.

Compare up to 32 declared deadline/optional-task changes under independent-uniform durations; preserve required tasks. Search bounds select one finalist for separately seeded confirmation, without retries. Conditional on the model, not delivery reliability.

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.

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.

Compare up to three task selections; choose highest examined value meeting the target under simultaneous 95% sampling bounds or an exact bound. Independent-uniform durations; can return inconclusive/blocked. Streams native events.

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.

Plan from declared available/goal contracts within tool, locality and search bounds. Returns dependencies, blockers and existing-tool bindings. Cost counts graph steps, not speed, price or quality. Runs no engines; execution validates arguments.

Run approved task-selection/route-to-duration risk chains only. Supply engine inputs and explicit uncertainty; route speed is 1–150 km/h. Returns native receipts and 95% sampling bounds. Completed means assessed, not safe. Other paths use advertised bindings.

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.

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.

Read a public contributor ticket/progress and verified pi or discrete synthetic schedule result. Schedule results include fixed-sample Wilson95 bounds. Worker/verification/wall times are separate; model probabilities are not delivery guarantees.

Check an explicit arithmetic claim. Checked i128 rationals give exact verdicts when expression, claim and tolerances are representable. Unsupported functions or overflow return an estimate with an undetermined verdict. Includes a versioned integrity digest; no checks of units or model meaning.

Compute an ideal two-body Keplerian orbit around one solar mass. Time starts at periapsis; distances use AU and time uses days. This model is not a real celestial ephemeris.

Compute 1–12 ideal fixed/free membrane modes for a simple polygon in metres using bounded P1 finite elements. Return upper bounds, extrapolated estimates and optional frequencies/shapes. Finite spectral agreement does not prove isospectrality; no damping. CPU, direct-only; no planner binding.

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.

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.

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 est

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

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.

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/.