tkgl-toybox

A temporal knowledge graph of a deterministic 2D toy physics box: particles, walls, bonds. 28 particles of unit mass move in a square box of side 20 under three laws: every pair attracts (softened, gravity-like), a particle bounces elastically off the walls, and two unbonded particles that come within distance 1 at a relative speed under 0.5 bond into a rigid pair for good. The speed is capped at 6, and one step is 0.05 time units. The world is deterministic from its seed (5) and its particle count (28); it runs 4,000 steps, and ts is the step.

Set	Relation: the step at which	Objects	Subjects	Facts	Train	Val	Test
bonds_with	a bond forms, one fact each way	28	20	20	16	2	2
hits	a particle's move would carry it past a wall	4	22	162	121	19	22
passes_close	a pair comes under distance 0.5, one fact each way	28	28	7,076	4,944	1,070	1,062

The event rules. A pass is an entry: the step a pair comes under distance 0.5 after being 0.5 or more apart at the step before, not every step it stays close. Hits of one particle on one wall at consecutive steps count once, at the first. The walls are wall_E (x = 20), wall_N (y = 20), wall_S (y = 0) and wall_W (x = 0).

The three sets share the split steps: train up to step 2,891 (the 70% quantile of all three sets' steps), val up to step 3,462 (the 85% quantile), test after. In bonds_with and passes_close the particles are both the subjects and the objects; in hits the walls are objects 0 to 3 and the particles follow.

The physics sets the sizes. Each particle bonds at most once, so bonds_with holds 20 facts (10 bonds). Attraction pulls the particles toward the middle of the box, so a wall is reached about 16 times per 400 steps, and hits holds 162. Their MRR rests on 2 and about 20 queries per split. passes_close has thousands of facts and is the main set.

Baselines (MRR, from score.py).

Set	Split	Queries	EdgeBank	Recurrency	Popularity	Random	Law
bonds_with	val	2	0.0690	0.0690	0.0444	0.0486	1.0000
bonds_with	test	2	0.0690	0.0690	0.0426	0.0977	1.0000
hits	val	19	0.3860	0.3623	0.4667	0.5132	1.0000
hits	test	22	0.4071	0.3685	0.4788	0.3939	1.0000
passes_close	val	1,070	0.0736	0.1755	0.1197	0.1482	1.0000
passes_close	test	1,062	0.0736	0.1854	0.1934	0.1486	1.0000

Repeating the past does not forecast physics. On passes_close, EdgeBank falls under random: by the end of training almost every pair has passed close once, so every candidate ties. Recurrency is within 0.04 of random, and on test it loses to popularity. On hits, recurrency scores under random on both splits.

The law row is the ceiling, and it is computable. It reads the simulator's positions and velocities one step before each fact and moves every particle one step on at constant velocity. passes_close and bonds_with rank the other particles by that predicted distance (a pair already close, or a particle already bonded, ranks last); hits ranks the walls by how far past each the predicted position lies. It ranks the true object first on every val and test query. A forecaster sees only the facts, not the state, so its gap to 1.0 measures how much of the law it has recovered from the graph. The law's scores are the Law column above and in toybox-scores.jsonl.

Files

• toybox/<set>/edges.csv: ts, head, tail, relation_type, split; one relation (0) per set. ts is the simulation step.
• toybox/<set>/nodes.csv: id, name, kind; objects are ids 0 to K-1 in sorted name order.
• toybox/meta.json: sizes, split steps, seed, particle count, the simulator's sha256.
• generate_toybox.py: the generator. score.py: the baselines. toybox-scores.jsonl: score.py's output.
• environment/tkgl_toybox: the task as a single-turn environment for language-model evaluation.
• croissant.json: Croissant metadata with the Responsible AI fields.

Use and limits

For benchmarking temporal graph and temporal knowledge graph forecasters against a known ceiling, and for testing language models as forecasters. It is synthetic and says so: one run of one small world, one seed, 28 particles, simplified 2D physics. No person's data is in it. bonds_with and hits are small, so their MRR rests on few queries.

Reproduce

The data regenerates byte for byte from generate_toybox.py, the simulator whose sha256 is in toybox/meta.json, its seed (5) and its particle count (28). The simulator is a deterministic 2D toy physics simulator and is not shipped here; the law row's per-fact scores ship as toybox-law.json, so the table reproduces from this repository alone.

python3 score.py --extra toybox-law.json

License

CC BY 4.0 for the data; MIT for the code (generate_toybox.py, score.py, environment/).

Citation

@misc{tkgltoybox2026,
  title = {tkgl-toybox: a synthetic temporal knowledge graph from a toy physics box},
  author = {The tkgl-toybox authors},
  year = {2026},
  note = {version 0.2.0}
}