Negative Knowledge as a Formal Object in Verified Causal Structures

April 2026 · Michael Schreiber · AetherNet Labs

Negative Knowledge
Trajectory Events
Knowledge Marketplace
Verified Causal Structures

Abstract. We formalize negative knowledge — verified records of approaches that were attempted and failed — as a first-class object within Verified Causal Structures. We prove that negative knowledge carries information strictly additional to positive knowledge: even with complete records of all successful trajectories, the marginal information from a single verified failure can be non-zero. We define a tripartite ontology — matter (verified successes), antimatter (verified failures), dark matter (unattested space) — and propose a trajectory marketplace that prices and settles negative knowledge alongside positive knowledge.

1. The Information of Failure

Theorem (Strictly Additional Information). The mutual information between a future query and a failure attestation is, in general, non-zero conditional on the full set of success attestations. Failure is not redundant.

2. Tripartite Ontology

We partition claim-space into matter (positive verified), antimatter (negative verified), and dark matter (unattested). Each is a measurable set with distinct economic and epistemic properties.

3. Trajectory Events

A trajectory event is the canonical attested record of an attempt: its preconditions, intervention, and outcome — including failure outcomes. Trajectory events are the substrate of both positive and negative knowledge.

4. Trajectory Marketplace

We propose a marketplace where agents pay to query the trajectory record before attempting work. Failure attestations carry positive market value, reversing the standard incentive to suppress negative results.

5. Conclusion

Treating negative knowledge as a first-class object closes a major efficiency gap in agent economies and produces previously impossible epistemic services.

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