Algorithms that show their work

Components

1. Compute principal component analysis of a 2D point set without NumPy

   baltor_pca_2d

   Compute principal component analysis of a 2D point set without NumPy: mean, covariance, eigenvalues and unit eigenvectors, principal angle, explained variance, scores and first-component reconstruction, with decomposition self-checks.

   Command

   python3 -B scripts/tool.py < examples/example.input.json

   Input fields

   points, normalization, include_projections

   SkillMIT10 files, 35.6 KBreads files, runs commands

2. Trace insertion sort as one event per executed line of a fixed Python listing

   baltor_insertion_sort_trace

   Trace insertion sort as one event per executed line of a fixed Python listing with array snapshots, highlight indices and comparison, shift and write counters checked against inversion identities, plus a sourced note on insertion sort inside introsort.

   Command

   python3 -B scripts/tool.py < examples/example.input.json

   Input fields

   values

   SkillMIT10 files, 42.9 KBreads files, runs commands

3. Trace union-find operations with union by rank and path compression

   baltor_union_find_trace

   Trace union, find and connected operations on a disjoint-set forest with union by rank or size and path compression, recording parent arrays and ranks before and after every operation, the paths followed, the nodes compressed and the roots linked.

   Command

   python3 -B scripts/tool.py < examples/example.input.json

   Input fields

   elements, union_rule, compression, operations

   SkillMIT10 files, 45.9 KBreads files, runs commands

4. Compose a 2D shear and a rotation in both orders

   baltor_transform_order

   Compose a 2D shear and a rotation in both orders and report where each point lands under each order, the intermediate positions for animation and the distance between the results, checked against the closed form |k sin(theta)| |p|.

   Command

   python3 -B scripts/tool.py < examples/example.input.json

   Input fields

   shear, rotation, points, tolerance

   SkillMIT10 files, 35.1 KBreads files, runs commands

5. Compute one-dimensional elastic collisions with momentum and energy checks

   baltor_elastic_collision_1d

   Compute post-collision velocities of one-dimensional elastic collisions with momentum and energy checks, and run an event-driven simulation with optional reflecting walls that returns every collision, sampled positions and conservation checks.

   Command

   python3 -B scripts/tool.py < examples/example.input.json

   Test

   python3 -B -m unittest discover -s verification -p 'test_*.py' -v

   SkillMIT10 files, 48.3 KBreads files, runs commands

6. Express a planar motion in an inertial and a rotating frame

   baltor_rotating_frame_orbit

   Express one planar motion (circular orbit, Kepler ellipse or straight line) in an inertial frame and a constantly rotating frame as sampled positions and velocities, with distance, round-trip, velocity and Kepler self-checks, labeled as an illustrative kinematic model.

   Command

   python3 -B scripts/tool.py < examples/example.input.json

   Input fields

   motion, frame, samples, tolerance

   SkillMIT10 files, 46.1 KBreads files, runs commands

7. Compute every triple an RDF graph entails under the RDFS or OWL 2 RL rule table

   baltor_rdfs_owl_rl_closure

   Compute every triple an RDF graph entails under the RDFS or OWL 2 RL rule table, with one checkable derivation per derived triple.

   Command

   python3 -B scripts/tool.py < examples/example.input.json

   Input fields

   version, profile, format, document, max_closure_triples, include_derivations

   SkillMIT11 files, 54.1 KBreads files, runs commands

8. Check an RDFS or OWL 2 RL derivation trace step by step

   baltor_derivation_trace_checker

   Check a derivation trace of RDFS or OWL 2 RL inferences step by step without trusting the reasoner that wrote it, in JSON or the two-file certificate format.

   Command

   python3 -B scripts/tool.py < examples/example.input.json

   Test

   python3 -B -m unittest discover -s verification -p 'test_*.py' -v

   SkillMIT10 files, 29.5 KBreads files, runs commands

9. List the entailed triples an ontology change adds and removes

   baltor_ontology_change_consequences

   List the entailed triples an ontology change adds and removes, each with an independently checked trace, bound to the digests of the graph before and after.

   Command

   python3 -B scripts/tool.py < examples/example.input.json

   Input fields

   version, profile, format, document, base_digest, added, removed, max_listed and 1 more

   SkillMIT12 files, 73.9 KBreads files, runs commands

10. Certify how far a character capsule stays from static boxes and triangle surfaces

    baltor_capsule_path_clearance

    Certify how far a character capsule stays from static boxes and triangle surfaces at keyframes and continuously along piecewise-linear keyframed motion, returning a proven lower bound, or the time, clearance and nearest obstacle of a violation, or an unresolved interval.

    Command

    python3 -B scripts/tool.py < examples/example.input.json

    Input fields

    units, capsule, keyframes, obstacles, margin_m, max_depth, max_queries

    SkillMIT9 files, 85.9 KBreads files, runs commands

11. Plan a dismantle order for a voxel model whose exact reverse rebuilds it

    baltor_reversible_voxel_build

    Plan a dismantle order for a voxel model whose exact reverse rebuilds it with every block supported when placed, and check supplied dismantle and rebuild orders for missing blocks, wrong reversal and unsupported placements.

    Command

    python3 -B scripts/tool.py < examples/example.input.json

    Test

    python3 -B -m unittest discover -s verification -p 'test_*.py' -v

    SkillMIT10 files, 41.1 KBreads files, runs commands

12. Plan a resumable segmented frame render from a frame range

    baltor_resumable_render_plan

    Plan a resumable segmented frame render from a frame range, a measured per-frame time and a checkpoint folder listing, reporting finished and remaining frames, a resume queue and a linear time estimate while refusing overlapping, out-of-range or re-rendering claims.

    Command

    python3 -B scripts/tool.py < examples/example.input.json

    Input fields

    frame_start, frame_end, segment_frames, measured_seconds_per_frame, parallel_workers, min_complete_bytes, frame_file, checkpoint_listing and 1 more

    SkillMIT10 files, 51.4 KBreads files, runs commands