# Algorithms that show their work

Part of Deterministic skills by Baltor.

Algorithms that report each step: principal components without NumPy, sorting and union-find traces, rule based inference closures, collision clearance and resumable render plans.

## What to watch for

- A trace lets a reviewer check every step, not only the final answer.
- Floating point eigenvectors need a sign convention to compare runs.
- An inference closure must say which rule produced each new triple.

## Components

- [Compute principal component analysis of a 2D point set without NumPy](https://baltor.ai/components/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. Name `baltor_pca_2d`, licence MIT, 10 files.
- [Trace insertion sort as one event per executed line of a fixed Python listing](https://baltor.ai/components/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. Name `baltor_insertion_sort_trace`, licence MIT, 10 files.
- [Trace union-find operations with union by rank and path compression](https://baltor.ai/components/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. Name `baltor_union_find_trace`, licence MIT, 10 files.
- [Compose a 2D shear and a rotation in both orders](https://baltor.ai/components/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|. Name `baltor_transform_order`, licence MIT, 10 files.
- [Compute one-dimensional elastic collisions with momentum and energy checks](https://baltor.ai/components/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. Name `baltor_elastic_collision_1d`, licence MIT, 10 files.
- [Express a planar motion in an inertial and a rotating frame](https://baltor.ai/components/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. Name `baltor_rotating_frame_orbit`, licence MIT, 10 files.
- [Compute every triple an RDF graph entails under the RDFS or OWL 2 RL rule table](https://baltor.ai/components/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. Name `baltor_rdfs_owl_rl_closure`, licence MIT, 11 files.
- [Check an RDFS or OWL 2 RL derivation trace step by step](https://baltor.ai/components/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. Name `baltor_derivation_trace_checker`, licence MIT, 10 files.
- [List the entailed triples an ontology change adds and removes](https://baltor.ai/components/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. Name `baltor_ontology_change_consequences`, licence MIT, 12 files.
- [Certify how far a character capsule stays from static boxes and triangle surfaces](https://baltor.ai/components/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. Name `baltor_capsule_path_clearance`, licence MIT, 9 files.
- [Plan a dismantle order for a voxel model whose exact reverse rebuilds it](https://baltor.ai/components/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. Name `baltor_reversible_voxel_build`, licence MIT, 10 files.
- [Plan a resumable segmented frame render from a frame range](https://baltor.ai/components/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. Name `baltor_resumable_render_plan`, licence MIT, 10 files.

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