Contextual Compute: The General Theory of Computation

K-Machine and Participant-Indexed Computational Model

Value is categorically distinct from information — a non-separable joint state 
of Participant, Context, and Content that cannot be embedded in any 
information-theoretic structure without destruction. This categorical fact 
demands a computational response: any machine that correctly computes value 
must have a participant dimension that the Turing Machine does not have.

This paper introduces that machine — the K-Machine. The K-Machine extends 
the Turing Machine by one primitive dimension — WHO — alongside the three 
classical dimensions of WHAT, WHERE, and HOW. The Recovery Theorem establishes 
that anonymous global computation is recovered exactly when the participant 
dimension is set to the trivial unit object. Every Turing-computable function 
is K-Machine computable. The inclusion is strict: participant-indexed 
computation subsumes classical computation, not the reverse.

The geometric content is formalised through differential geometry: participants 
as points on a smooth manifold, context as tangent space, interactions as 
geodesics. The Krama Context Clock provides the local temporal structure. 
Four structural consequences follow: structural parallelism, local finality, 
Emergent Participant Intelligence, and security from the holonomy of the 
participant manifold.

Companion paper to: Value, Information, and the Cartesian Degeneracy 
(CC2, Zenodo, https://doi.org/10.5281/zenodo.19148908) and PIC: Operational 
Semantics of Participant-Indexed Computation (CC4, Sarva Labs, March 2026).