P
Primordia Co.
Grounded World Models
Paper
PDF
Contents
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Contents
Grounded World Models: Efficient and Verifiable Structural Causal Prediction
1
Introduction
2
The Grounded World Model, Formally
3
Benchmarking the Costs of Grounded Prediction
4
Discussion
5
Conclusion
Acknowledgments
A
Instantiation of Numerical Weather Prediction as a GWM
B
The Returns to Crystallization
C
Explanation-Quality Components and Heuristic Parameter Derivations
D
The Sampling Budget: Latency vs Residual Monte-Carlo Error
E
A Worked Example: GWM vs NWM on One Case
F
Cost-Model Details
G
Proofs
H
On the Internal Representations of Language Models
I
Notation and Parameter Provenance
References
Grounded World Models: Efficient and Verifiable Structural Causal Prediction
Acknowledgments
B
The Returns to Crystallization
Appendix A
Instantiation of Numerical Weather Prediction as a GWM
GWM element
Numerical weather prediction counterpart
Explicit causal mechanism
p
Discretized Navier–Stokes
+
thermodynamics (known physics).
Grounding map
g
(Bayesian conditioning)
Data assimilation: 4D-Var / ensemble Kalman filter over millions of daily observations
(
Kalnay
,
2003
)
.
Predictive distribution (PD)
Ensemble forecast: perturbed initial conditions
+
stochastic physics.
Verified correctness / invariants
Conservation of mass, energy, and momentum enforced by the integrator.
Predictability horizon
Lyapunov limit on forecast lead time
(
Lorenz
,
1963
)
.
Table 1:
Numerical weather prediction realizes the GWM contract element by element—the most mature deployed grounded world model.