WorldKernel: A World Model is the Coupling Kernel of Admissible Possible Worlds
Paper • 2606.10934 • Published
Datasets:
family stringclasses 2
values | id int32 0 15k | P int16 0 30 | L int16 0 15 | q float32 0.01 0.48 | steps int16 0 24 | coupling_w float32 -1 1 ⌀ | width int16 1 16 | chi int16 3 16 | true_off float32 0 1 | empirical_off float32 0 1 | frechet_lo float32 0 0 | frechet_hi float32 0.37 1 | trajectories listlengths 0 40 |
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1
]
},
{
"factual_A": [
1,
0,
0,
0,
0,
0,
1
],
"cf_B": [
1,
0,
0,
... |
route | 43 | 29 | 9 | 0.1976 | 20 | -0.6265 | 8 | 10 | 0.0738 | 0.0706 | 0 | 1 | [
{
"factual_A": [
0,
0,
0,
0,
0,
1,
0,
0,
0,
0,
0,
1,
1,
0,
0,
0,
0,
0,
0,
0
],
"cf_B": [
0,
0,
0,
0,
0,
0,
1,
0,
0,
0,
... |
route | 44 | 10 | 14 | 0.3068 | 23 | -0.3961 | 13 | 15 | 0.1853 | 0.171 | 0 | 1 | [
{
"factual_A": [
0,
0,
1,
0,
0,
1,
1,
0,
0,
1,
0,
0,
0,
0,
1,
0,
0,
1,
0,
0,
1,
1,
0
],
"cf_B": [
1,
0,
0,
1,
1,
0,
0,
... |
route | 45 | 7 | 14 | 0.4396 | 9 | 0.112 | 13 | 15 | 0.5024 | 0.5341 | 0 | 1 | [
{
"factual_A": [
0,
1,
0,
0,
1,
0,
0,
1,
1
],
"cf_B": [
0,
0,
0,
1,
1,
0,
0,
1,
0
]
},
{
"factual_A": [
1,
0,
0,
1,
1,
0,
1,
1,
1
... |
route | 46 | 15 | 7 | 0.1363 | 15 | -0.5006 | 6 | 8 | 0.0681 | 0.0253 | 0 | 1 | [
{
"factual_A": [
1,
1,
0,
0,
0,
0,
1,
0,
0,
1,
1,
0,
0,
0,
0
],
"cf_B": [
0,
0,
0,
0,
0,
0,
0,
0,
1,
0,
0,
1,
0,
0,
0
]
... |
route | 47 | 17 | 11 | 0.3527 | 6 | -0.4387 | 10 | 12 | 0.198 | 0.1647 | 0 | 1 | [
{
"factual_A": [
0,
0,
0,
1,
1,
0
],
"cf_B": [
1,
0,
1,
0,
0,
1
]
},
{
"factual_A": [
0,
0,
1,
0,
0,
1
],
"cf_B": [
1,
0,
0,
1,
0,
0
]
... |
route | 48 | 17 | 12 | 0.092 | 15 | 0.7975 | 11 | 13 | 0.8161 | 0.8 | 0 | 1 | [
{
"factual_A": [
0,
0,
0,
0,
0,
0,
0,
1,
0,
0,
0,
1,
1,
1,
0
],
"cf_B": [
0,
1,
0,
0,
0,
0,
0,
1,
0,
0,
0,
1,
1,
1,
0
]
... |
route | 49 | 26 | 4 | 0.4289 | 14 | 0.3188 | 3 | 5 | 0.611 | 0.6239 | 0 | 1 | [
{
"factual_A": [
0,
0,
1,
0,
1,
0,
0,
0,
0,
0,
1,
0,
0,
0
],
"cf_B": [
0,
0,
1,
0,
1,
0,
0,
0,
0,
0,
0,
0,
1,
0
]
},
{
"fact... |
route | 50 | 22 | 11 | 0.3312 | 12 | 0.9769 | 10 | 12 | 0.9846 | 0.9828 | 0 | 1 | [
{
"factual_A": [
0,
1,
0,
0,
1,
0,
0,
1,
0,
0,
0,
0
],
"cf_B": [
0,
1,
0,
0,
1,
0,
0,
1,
0,
0,
0,
0
]
},
{
"factual_A": [
0,
1,
0,... |
route | 51 | 8 | 7 | 0.3294 | 21 | 0.4351 | 6 | 8 | 0.6212 | 0.5859 | 0 | 1 | [
{
"factual_A": [
0,
0,
1,
1,
0,
1,
1,
0,
0,
0,
1,
0,
0,
0,
0,
1,
0,
0,
0,
1,
1
],
"cf_B": [
0,
0,
0,
1,
0,
0,
0,
1,
0,
... |
route | 52 | 15 | 5 | 0.2052 | 9 | 0.3245 | 4 | 6 | 0.4631 | 0.5556 | 0 | 1 | [
{
"factual_A": [
0,
0,
0,
0,
0,
0,
1,
1,
1
],
"cf_B": [
0,
0,
0,
0,
0,
1,
0,
0,
1
]
},
{
"factual_A": [
0,
0,
0,
0,
0,
0,
0,
1,
0
... |
route | 53 | 25 | 14 | 0.2716 | 17 | 0.9764 | 13 | 15 | 0.9828 | 0.9895 | 0 | 1 | [
{
"factual_A": [
1,
1,
0,
0,
0,
1,
1,
1,
1,
0,
1,
0,
0,
0,
0,
0,
0
],
"cf_B": [
1,
1,
0,
0,
0,
1,
1,
1,
1,
0,
1,
0,
0,
... |
End of preview. Expand in Data Studio
rung3-worldpairs (v2): counterfactual ground truth by construction
30,000 worlds across two families, each carrying a rung-3 (counterfactual) ground truth that is unobservable in any real dataset, plus the marginals-only identified interval and a tractability certificate (width, interaction rank).
Two families
route (15,000): a traveller takes route A or B; each slips with prob q. The
cross-route coupling is injected on a continuous spectrum coupling_w in
[-1, 1] (201 distinct values), so true_off = P(B slips | A slipped) is exact by
construction and empirical_off (from 40 trajectories) tracks it (mean abs err
0.025). Trajectories are retained per row.
ontology (15,000): a hard-core world on a census-calibrated constraint
graph (disjoint sibling cliques + sparse cross edges - the real shape of
declared ontology disjointness), width capped at 16 so every query stays exactly
computable. Here true_off = P(Y_v=1 | Y_u=1) is computed by the kernel (exact
variable elimination on the residual graph), validated against brute-force
enumeration (0 mismatches). Widths span 1-16 (16 classes).
The finding baked into the data
For the ontology family the marginals-only Frechet interval is vacuous (100% of intervals >= 0.5 wide) while the truth is exactly computable from structure: the counterfactual is identifiable from the ontology's shape but not from marginal data. That gap - the off-diagonal being load-bearing - is the whole point.
Columns
family, id, P, L, q, steps, coupling_w, width, chi, true_off, empirical_off, frechet_lo, frechet_hi, trajectories (route only)
Well-calibrated use: a system must cover true_off within [frechet_lo, frechet_hi]
without collapsing the interval; scored e.g. by the Winkler rule. Generated
deterministically by ontoworld/worldpairs_v2.py; companion to WorldKernel
(arXiv:2606.10934). MIT.
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