Verified Causal Structures: A Framework for Counterfactual Computation over Empirically Attested Causal Graphs

March 2026 · Michael Schreiber · AetherNet Labs

Causal Inference
Formal Methods
Counterfactual Computation

Abstract. We introduce Verified Causal Structures (VCS): directed acyclic graphs whose nodes carry cryptographic attestations of empirical observation and whose edges carry attested counterfactual interventions. Over a VCS, we prove that the full Pearl causal hierarchy — association, intervention, and counterfactual queries — becomes exactly computable for re-derivable computations, with formal guarantees rooted in the protocol's verification economics. We define Compound Verification Depth (CVD) as the canonical measure of how much independent attestation backs a given causal claim, and show that CVD bounds the reliability of every query in the hierarchy. The framework provides the formal substrate that downstream AetherNet Labs papers (Causal Economics, Computational Interference, the Epistemic Substrate Thesis, Topological Encoding, Negative Knowledge, and Process Topology) build on.

1. Motivation

Standard causal inference assumes the underlying causal graph is given, or recoverable from observational data under strong assumptions. In open multi-agent systems — and especially in AI agent economies — neither holds. We need a structure where causal claims are economically backed and cryptographically attested, not asserted.

2. Definitions

A Verified Causal Structure is a tuple (G, A, E) where G is a DAG of variables, A is a set of attestations (signed observation records), and E is a set of attested intervention edges. Each edge carries provenance: who observed it, what stake backed the observation, and whether any challenge bonds were posted against it.

3. Computability of the Causal Hierarchy

Theorem 1 (Hierarchy Computability). Over a VCS with sufficient CVD, all three layers of Pearl's hierarchy admit exact computation for re-derivable queries. Sketch: attestations close the identifiability gap that would otherwise require unverifiable structural assumptions; CVD provides the soundness threshold.

4. Compound Verification Depth

CVD generalizes notions like replication count and Bayesian posterior weight by encoding the *economic* cost of fabricating a chain of attestations. We prove monotonicity, composability under DAG concatenation, and convergence under repeated independent verification.

5. Implications

VCS is the substrate that makes downstream constructions possible: causal economics emerges from settlement against CVD; computational interference patterns emerge from the DAG's combinatorial structure; the epistemic substrate thesis derives general intelligence requirements from VCS minimality; topological encoding lifts VCS to continuous fields; negative knowledge formalizes failed-trajectory attestations as first-class objects; process topology detects coordinated capture from VCS metadata.

6. Conclusion

VCS provides the missing formal object that turns AI work from unverified output into a measurable, composable causal artifact. The remainder of the AetherNet Labs research program builds directly on this foundation.

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