MOI Whitepapers
MOI publishes five whitepapers that lay out the protocol from introduction to formal proof: a litepaper introducing the Participant Layer, a white paper developing the MOI Authority Layer, a tech paper on Contextual Compute, a math paper on the Cartesian Degeneracy, and a semantics paper formalizing the Participant-Interaction-Context model. Browse the collection below, or visit moi.technology/papers for the full, up-to-date list with downloads.
Litepaper: The Participant Layer of the Internet
White Paper: The Linear Substrate and the Authority Layer
Tech Paper: Contextual Compute
Math Paper: Value, Information, and the Cartesian Degeneracy
Semantics Paper: PIC
Litepaper: The Participant Layer of the Internet
The Litepaper, The Participant Layer of the Internet, is the short introduction to the MOI Protocol — a base protocol in which participants exist natively in computation. It argues that three separate domain problems (AI agents, business logic, and tokens) collapse to a single missing primitive: the participant has no computational existence inside the machine. The paper lays out what changes once WHO becomes a network primitive alongside WHAT, WHERE, and HOW.
White Paper: The Linear Substrate and the Authority Layer
The White Paper, The Linear Substrate and the Authority Layer (MOI Foundations v2.1), starts from a structural distinction: information is Cartesian and can be freely copied, while value is linear and cannot — double-spend is the copy map applied to value, and global consensus is the patch a Cartesian substrate needs to forbid it. From there it orders value into four classes by writer structure, shows that the Participant Layer is the substrate all four require, and develops the MOI Authority Layer (MAL): a stateful, revocable, and auditable authority architecture for agentic systems in which tokens are witnesses of valid state rather than bearers of permission.
Tech Paper: Contextual Compute — The General Theory of Computation
The Tech Paper, Contextual Compute: The General Theory of Computation, introduces the K-Machine — a Turing Machine extended with one additional primitive dimension, WHO, alongside the existing WHAT, WHERE, and HOW. Classical computation is recovered as a special case when the participant dimension collapses to the trivial unit, meaning it is strictly subsumed by participant-indexed computation rather than replaced by it.
Math Paper: Value, Information, and the Cartesian Degeneracy
The Math Paper, Value, Information, and the Cartesian Degeneracy, establishes the categorical distinction between value and information and proves that no structure-preserving embedding can map value into information. It identifies the Cartesian Degeneracy: the parametric collapse of value into information that occurs when the participant dimension reduces to the trivial unit.
Semantics Paper: PIC — Operational Semantics of Participant-Indexed Computation
The Semantics Paper, PIC: Operational Semantics of Participant-Indexed Computation, derives the operational semantics of Contextual Compute directly from the K-Machine. It formalizes the Participant-Interaction-Context (PIC) model and shows that six axioms — Conservation, Consent, Linearity, Witness Sufficiency, Composability, and Commutativity — follow necessarily from its structure, defining the PIC value category and introducing Network Objects as a network-level linear-type primitive.