Alrithm

Verified reasoning data.

Every row is a self-contained problem — solved, verified against thousands of test cases, and bound to a cryptographic proof that the answer is correct.

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Catalog

84 datasets
All84Solve14Debug15Optimize14Explain14Review13
refusal_defer

Refusals: Legal and Licensing Questions

Requests that need a licensing or legal determination and cannot be computed; the correct response routes them to the authority.

200 rows550.5 KB
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refusal_infeasible

Refusals: Infeasible Goal

Well-posed requests whose goal has no solution; the correct response says so instead of inventing a number.

200 rows574.1 KB
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refusal_inconsistent_input

Refusals: Inconsistent Input

Requests whose individually valid values contradict each other; the correct response asks to reconcile them.

200 rows583.3 KB
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refusal_invalid_input

Refusals: Invalid Input

Requests where a single value lies outside its valid range; the correct response asks for a corrected value.

200 rows544.9 KB
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refusal_underspecified

Refusals: Underspecified Requests

Requests with several valid readings whose answers differ; the correct response asks which reading is meant.

200 rows645.6 KB
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refusal_missing_parameter

Refusals: Missing Parameter

Requests where one computation fits but a required field is absent; the correct response names the missing field.

200 rows505.2 KB
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ascent_simulation

Ascent Simulation

Vertical rise, pitch kick and gravity-turn simulations: burnout state and max-Q, converged across three numerical integrators (no proven enclosure).

200 rows1.2 MB
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guidance_estimation

Guidance and Estimation

Kalman filter predict-and-update problems with certified answers.

200 rows725.1 KB
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hardware_engineering

Propulsion and Tank Hardware

Ideal nozzle exit velocity and thick-wall tank thickness problems with certified answers.

200 rows671.2 KB
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atmosphere

Standard Atmosphere

US Standard Atmosphere 1976 density and dynamic pressure up to 20 km with certified answers.

200 rows711.7 KB
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launch_geometry_windows

Launch Geometry and Windows

Launch azimuth with and without Earth rotation, plane-crossing wait time and range azimuth margin problems with certified answers.

200 rows788.4 KB
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orbit_perturbations

Orbit Perturbations

First-order J2 nodal regression and sun-synchronous inclination problems with certified answers.

200 rows682.2 KB
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orbital_mechanics

Orbital Mechanics

Circular-orbit period, Hohmann transfer and Kepler's equation problems with certified answers.

200 rows666.0 KB
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propulsion_mass_budget

Propulsion and Mass Budget

Rocket equation, propellant mass, staging and finite-burn gravity-loss problems with certified numeric answers.

200 rows643.4 KB
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Review

Correctness Reviews

Claims about code, judged correct or incorrect with evidence.

200 rows830.1 KB
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Explain

Behavior Explanations

Working code with a traced walkthrough of what it computes and why.

200 rows2.0 MB
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Optimize

Code Optimization Traces

Working implementations paired with the faster version and the reasoning behind the speedup.

200 rows932.5 KB
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Debug

Debugging Traces

Broken code paired with the defect location and the minimal fix.

200 rows969.6 KB
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Solve

Algorithm Solutions

Algorithm problems with reference solutions, step-by-step derivations, and verified answers.

200 rows699.2 KB
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Review

Correctness Reviews

Claims about code, judged correct or incorrect with evidence.

200 rows817.2 KB
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Explain

Behavior Explanations

Working code with a traced walkthrough of what it computes and why.

200 rows2.1 MB
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Optimize

Code Optimization Traces

Working implementations paired with the faster version and the reasoning behind the speedup.

200 rows931.6 KB
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Debug

Debugging Traces

Broken code paired with the defect location and the minimal fix.

200 rows960.6 KB
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Solve

Algorithm Solutions

Algorithm problems with reference solutions, step-by-step derivations, and verified answers.

200 rows695.2 KB
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Review

Correctness Reviews

Claims about code, judged correct or incorrect with evidence.

200 rows823.4 KB
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Explain

Behavior Explanations

Working code with a traced walkthrough of what it computes and why.

200 rows2.1 MB
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Optimize

Code Optimization Traces

Working implementations paired with the faster version and the reasoning behind the speedup.

200 rows931.3 KB
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Debug

Debugging Traces

Broken code paired with the defect location and the minimal fix.

200 rows965.7 KB
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Solve

Algorithm Solutions

Algorithm problems with reference solutions, step-by-step derivations, and verified answers.

200 rows698.3 KB
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Review

Correctness Reviews

Claims about code, judged correct or incorrect with evidence.

200 rows829.9 KB
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Explain

Behavior Explanations

Working code with a traced walkthrough of what it computes and why.

200 rows2.0 MB
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Optimize

Code Optimization Traces

Working implementations paired with the faster version and the reasoning behind the speedup.

200 rows929.5 KB
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Debug

Debugging Traces

Broken code paired with the defect location and the minimal fix.

200 rows964.2 KB
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Solve

Algorithm Solutions

Algorithm problems with reference solutions, step-by-step derivations, and verified answers.

200 rows693.7 KB
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Review

Correctness Reviews

Claims about code, judged correct or incorrect with evidence.

200 rows822.2 KB
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Explain

Behavior Explanations

Working code with a traced walkthrough of what it computes and why.

200 rows2.1 MB
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Optimize

Code Optimization Traces

Working implementations paired with the faster version and the reasoning behind the speedup.

200 rows932.0 KB
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Debug

Debugging Traces

Broken code paired with the defect location and the minimal fix.

200 rows962.1 KB
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Solve

Algorithm Solutions

Algorithm problems with reference solutions, step-by-step derivations, and verified answers.

200 rows695.5 KB
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Review

Correctness Reviews

Claims about code, judged correct or incorrect with evidence.

200 rows817.9 KB
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Explain

Behavior Explanations

Working code with a traced walkthrough of what it computes and why.

200 rows2.1 MB
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Optimize

Code Optimization Traces

Working implementations paired with the faster version and the reasoning behind the speedup.

200 rows932.7 KB
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Debug

Debugging Traces

Broken code paired with the defect location and the minimal fix.

200 rows955.0 KB
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Solve

Algorithm Solutions

Algorithm problems with reference solutions, step-by-step derivations, and verified answers.

200 rows693.5 KB
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Review

Correctness Reviews

Claims about code, judged correct or incorrect with evidence.

200 rows823.6 KB
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Explain

Behavior Explanations

Working code with a traced walkthrough of what it computes and why.

200 rows2.0 MB
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Optimize

Code Optimization Traces

Working implementations paired with the faster version and the reasoning behind the speedup.

200 rows931.2 KB
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Debug

Debugging Traces

Broken code paired with the defect location and the minimal fix.

200 rows965.9 KB
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Solve

Algorithm Solutions

Algorithm problems with reference solutions, step-by-step derivations, and verified answers.

200 rows691.2 KB
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Review

Correctness Reviews

Claims about code, judged correct or incorrect with evidence.

200 rows818.5 KB
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Explain

Behavior Explanations

Working code with a traced walkthrough of what it computes and why.

200 rows2.0 MB
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Optimize

Code Optimization Traces

Working implementations paired with the faster version and the reasoning behind the speedup.

200 rows929.8 KB
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Debug

Debugging Traces

Broken code paired with the defect location and the minimal fix.

200 rows958.2 KB
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Solve

Algorithm Solutions

Algorithm problems with reference solutions, step-by-step derivations, and verified answers.

200 rows693.7 KB
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Review

Correctness Reviews

Claims about code, judged correct or incorrect with evidence.

200 rows828.1 KB
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Explain

Behavior Explanations

Working code with a traced walkthrough of what it computes and why.

200 rows2.0 MB
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Optimize

Code Optimization Traces

Working implementations paired with the faster version and the reasoning behind the speedup.

200 rows931.9 KB
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Debug

Debugging Traces

Broken code paired with the defect location and the minimal fix.

200 rows970.8 KB
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Solve

Algorithm Solutions

Algorithm problems with reference solutions, step-by-step derivations, and verified answers.

200 rows695.5 KB
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Review

Correctness Reviews

Claims about code, judged correct or incorrect with evidence.

200 rows827.8 KB
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Explain

Behavior Explanations

Working code with a traced walkthrough of what it computes and why.

200 rows2.0 MB
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Optimize

Code Optimization Traces

Working implementations paired with the faster version and the reasoning behind the speedup.

200 rows930.2 KB
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Debug

Debugging Traces

Broken code paired with the defect location and the minimal fix.

200 rows963.4 KB
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Solve

Algorithm Solutions

Algorithm problems with reference solutions, step-by-step derivations, and verified answers.

200 rows694.2 KB
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Review

Correctness Reviews

Claims about code, judged correct or incorrect with evidence.

200 rows819.8 KB
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Explain

Behavior Explanations

Working code with a traced walkthrough of what it computes and why.

200 rows1.9 MB
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Optimize

Code Optimization Traces

Working implementations paired with the faster version and the reasoning behind the speedup.

200 rows930.8 KB
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Debug

Debugging Traces

Broken code paired with the defect location and the minimal fix.

200 rows970.1 KB
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Solve

Algorithm Solutions

Algorithm problems with reference solutions, step-by-step derivations, and verified answers.

200 rows690.8 KB
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Review

Correctness Reviews

Claims about code, judged correct or incorrect with evidence.

200 rows821.5 KB
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Explain

Behavior Explanations

Working code with a traced walkthrough of what it computes and why.

200 rows2.0 MB
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Optimize

Code Optimization Traces

Working implementations paired with the faster version and the reasoning behind the speedup.

200 rows931.8 KB
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Debug

Debugging Traces

Broken code paired with the defect location and the minimal fix.

200 rows975.9 KB
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Solve

Algorithm Solutions

Algorithm problems with reference solutions, step-by-step derivations, and verified answers.

200 rows697.5 KB
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Explain

Behavior Explanations

Working code with a traced walkthrough of what it computes and why.

200 rows2.1 MB
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Optimize

Code Optimization Traces

Working implementations paired with the faster version and the reasoning behind the speedup.

200 rows931.9 KB
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Debug

Debugging Traces

Broken code paired with the defect location and the minimal fix.

200 rows962.6 KB
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Solve

Algorithm Solutions

Algorithm problems with reference solutions, step-by-step derivations, and verified answers.

200 rows692.8 KB
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Review

Correctness Reviews

Claims about code, judged correct or incorrect with evidence.

200 rows826.7 KB
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Debug

Debugging Traces

Broken code paired with the defect location and the minimal fix.

200 rows971.2 KB
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Solve

Algorithm Solutions

Algorithm problems with reference solutions, step-by-step derivations, and verified answers.

200 rows695.6 KB
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Explain

Behavior Explanations

Working code with a traced walkthrough of what it computes and why.

200 rows2.0 MB
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Optimize

Code Optimization Traces

Working implementations paired with the faster version and the reasoning behind the speedup.

200 rows930.9 KB
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Debug

Debugging Traces

Broken code paired with the defect location and the minimal fix.

200 rows966.2 KB
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