Entanglement is a relation that maps a pair of identities to a scalar. Different kinds of entanglement may have different codomains, but usually entanglement is normalised to a unitless real number between 0 and 1, which may be rounded to a fixed precision (up to and including the 1-bit entanglement of 0 or 1). There are many different measures, or dimensions, of entanglement, which can themselves be composed in different ways. Entanglement can be asymmetric, if the order of identities matters, or symmetric, if it doesn't (entanglement a b = entanglement b a). Entanglement is generally defined recursively over the network of identity relations, such that the system can build up a unified model from purely local agent user inputs. Such a measure is useful primarily because it allwos comparison, which in turn can be used for ordering and choice. To prime intuition, let's go through a few examples:

  • Directed follower entanglement, which can be measured from the directed relationship DAG, is a measure of directed flow in following relationships.
  • Friendship entanglement, which can be measured from the bilateral relationship DAG, is a measure of mutual friendship.
  • Many kinds of entanglement can be measured from the cryptographic kudos system, including:
    • Mutual liquidity is a measure of degree of interconvertability of two cryptographic kudo denominations.
    • Mutual volume is a measure of degree of exchange of two cryptographic kudo denominations.
    • Mutual price is a measure of degree of asymmetry of two cryptographic kudo denominsations.
  • Physical latency entanglement, which can be sampled (purely locally) from the physical network abstraction layer, is a measure of physical distance (latency).

As an external output of the system, entanglement measures can be used to inform ranking and choice in the external world. For example, directed follower entanglement or friendship entanglement might be used to select and order information displayed on a user interface, while mutual liquidity might be used to make a decision about trustworthiness or resource access control. Different measures of entanglement are suited for different purposes, and non-fungibility of entanglement measures is essential, as this allows the system to model a higher-dimensionality identity relationship space. Entanglement can usually be proved from the logical DAG (local physical latency is an exception here) to a third party without revealing any other information (possibly with a ZKP).

As data available to agents, entanglement measures can also be used to automate certain decisions about which identities to rely on for parts of system operation, including data storage, consensus provisioning, compute delegation, and gossip paths (especially those which might leak some information). In this sense, the gestalt forms a feedback system, for entanglement, which is an output of the system, is fed-back into decisions which change the system's future state. Entanglement measures such as physical latency and mutual kudo liquidity may be combined with self-reported storage and compute availability of other agents, for example, in order to automatically select agents with whom to store data and exchange compute (subject also to redundancy requirements).

Entanglement measures can be composed, generally either multiplicatively or additively (though other compositions are possible), or even inverted - which may be helpful where resilience is desired, e.g. one may want to hold a certain amount of uncorrelated cryptographic kudo denominations. Entanglement may also be rounded to fixed-precision, which may be prudent to avoid giving a false impression of accuracy where the system is merely precise, but also helpful in order to limit computational expenditure required to compute it (relations are often definited recursively).