Infrastructure · Primitives
NegativeProof
Proving non-membership in a committed state snapshot
Definition
Mechanism
Proving non-membership in a committed state set. An Agent cryptographically commits to its full state (e.g., via Merkle tree), then uses a Zero-Knowledge Range Proof to demonstrate that a specific Value or datum is NOT present in that committed set, without revealing what the set contains. Operates via exhaustive search over the committed domain, treating verified failure-to-find as proof of absence within that snapshot. The guarantee is bounded: it proves non-membership in the committed tree, not global non-possession—the agent could hold uncommitted state elsewhere.
Preconditions
- Closed world assumption (over the committed state, not globally)
- Hypothesis H
- State commitment is fresh and complete
Postconditions
- H proved false within committed state
Invariants
- Proves non-membership in the committed set only, never global non-possession.
- The search covers the whole committed domain.
- Names the commitment it proves against, and when that commitment was made.
Risks
Failure modes
Incomplete commitment
state is held outside the committed tree, so the proof is valid and practically meaningless.
Stale commitment
the state changed between commitment and verification.
Cost
proving absence over a large domain is expensive, and the expense scales with the domain rather than with the Value being checked.
Relationships
Builds on
References
Mind
Autonomous Goal-Directed Entity
Testable prediction staged for falsification attempts — provisional, not asserted
A measure of utility
Used by
Composes with
Society
Adversarial proof of absence
References
Society
Recursive trust dependencies modeled as a DAG
Reference