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Put-Call Parity as Knowledge Consistency

research·pipeline·Patent Pending· academic

What It Is

A formal parity equation for multi-agent knowledge consistency: R_A(f) - R_B(f) = S(f) - K(f) delta(t), where delta(t) = e^(-rt) is the freshness decay function. Continuous violation monitoring replaces periodic consensus rounds. Four violation types — Knowledge Sync Failure, Stale Consensus, Accelerated Decay, Structural Misalignment — diagnose the root cause and prescribe the intervention. Patent-protected (USPTO 19/418,922).

Why It Matters

Consensus asks whether all agents agree. Parity asks whether the algebraic relationship between their knowledge states is structurally sound. The second is cheaper, faster, and continuous.

Consensus protocols (Paxos, Raft, BFT) ask: "Do all agents agree?" This is expensive to answer and stale by the time you get it. The number of pairwise consistency checks grows quadratically with agent count, making periodic consensus computationally intractable at production scale. Parity asks: "Is the algebraic relationship between agents' knowledge states structurally sound right now?" Cheap to monitor (linear per shared domain), violation-specific in diagnosis, and continuous rather than periodic.

Multi-agent systems that rely on consensus rounds accumulate knowledge drift between rounds. Systems that rely on post-hoc audit discover violations only after propagation into downstream decisions. RAG-based architectures create a particularly dangerous failure class: agents drawing from overlapping but not identical knowledge sources, where partial overlap produces subtle divergence rather than outright contradiction. The parity approach detects violations at the moment they occur, classifies them by type, and routes them to the correct remediation. If you are building multi-agent coordination and you do not have a continuous consistency invariant, you are flying between radar sweeps.

The structural analogy to financial put-call parity (Stoll 1969, Black-Scholes-Merton) is not metaphorical — it is formal. Financial put-call parity is a no-arbitrage condition: an algebraic identity that must hold across instruments referencing the same underlying asset. The knowledge parity equation is the same structural relationship applied to agents referencing the same knowledge domain. Any violation constitutes a detectable, diagnosable coordination failure.

Proof Points

  • Formal parity equation (PCP-1) with measurable terms and domain-specific decay rates
  • Four violation types with deterministic diagnosis and prescribed intervention: Knowledge Sync Failure, Stale Consensus, Accelerated Decay, Structural Misalignment
  • Scanner module (PAS-1) for real-time monitoring — linear cost scaling vs. quadratic consensus
  • Feedback loop to multi-objective optimizer (ECO-1) for closed-loop correction
  • Reframes consistency from consensus problem (convergence target) to monitoring problem (continuous invariant)
  • Structural analogy to financial put-call parity: no-arbitrage condition applied to knowledge domains
  • Patent-protected: USPTO 19/418,922

Novel Research Contribution

The central contribution is the formal parity equation itself — an algebraic identity that must hold between agents sharing a knowledge domain. No prior work in multi-agent coordination provides a continuous consistency invariant with violation classification. Byzantine fault tolerance (Lamport 1982, Castro & Liskov 1999) frames consistency as agreement through message-passing rounds. Distributed belief revision (AGM framework, Halpern & Moses) provides snapshot analysis, not continuous monitoring. Runtime verification checks temporal logic properties against execution traces. The parity approach is structurally different: an algebraic invariant whose violation is immediately measurable and diagnostically specific. The freshness decay function delta(t) adds temporal dynamics that static epistemic models lack.

Target venue: AAMAS or Distributed Computing

Extends: Stoll's put-call parity to knowledge domains, Sims's rational inattention (no-arbitrage beyond finance), Amari's information-theoretic invariants

Challenges: Consensus-is-sufficient school in distributed systems, heuristic-RAG school in applied AI, temporal logic monitoring as the sole verification primitive

Market Position and IP

Patent-protected (USPTO 19/418,922). The parity invariant for multi-agent knowledge consistency has no equivalent in deployed systems. Distributed databases use consensus protocols. Multi-agent frameworks use orchestrators. Neither provides a continuous algebraic invariant with violation-type classification and automated remediation routing. The PAS-1 scanner and ECO-1 feedback loop create a closed-loop system that no competitor offers — detection, diagnosis, and correction without human intervention.

Connections

  • Related papers: Trust-Is-A-Metric (Trust Ledger as violation history), Governance-as-Geometry (Ma'at Gate as parity enforcement)
  • Imperatives: Proof over Inspection
  • Builds: AgentOS (PAS-1, ECO-1)
  • Frameworks: ZK Trust Ledger
  • Capabilities: Agentic System of Systems