Realm

Principles

Formal and modeling disciplines that keep distinctions precise across the graph.

Entries

Adjunctions

Adjunctions describe paired constructions that translate between domains in the best available way, even when the translations are not inverses.

Algebras and Coalgebras

Algebras and coalgebras provide complementary ways to model construction and behavior.

Asynchronous Computability Theorem

The asynchronous computability theorem characterizes which distributed tasks can be solved wait-free in an asynchronous read/write system.

CALM Theorem

The CALM theorem, "Consistency as Logical Monotonicity", states that a program has a consistent, coordination-free distributed implementation if and only if it can be expressed in monotonic logic.

Categorical principles provide modeling discipline for the Cohesive System Model. They are not the entry point for ordinary readers, but they help keep distinctions precise when relating domain semantics, system graph, operational concerns, and realization substrate.

Compositionality

Compositionality is the principle that complex systems should be understood from parts and the rules by which those parts compose.

Database Sheaf Semantics

Database Sheaf Semantics views a database schema as a category, a database instance as a structure-preserving functor into sets, and local database views as sections that can be restricted, compared on overlaps, and sometimes glued into a coherent larger instance.

Duality and Symmetry

Duality and symmetry are principles for recognizing paired concepts that explain one another through reversal, complementarity, or mirrored structure.

Enrichment and Order

Enrichment adds structure to relationships. Instead of merely asking whether a relationship exists, an enriched view asks what kind of value the relationship has: order, distance, cost, probability, time, authority, confidence, or information.

Equivalence vs Equality

Equivalence and equality should not be confused.

Event-State Duality

Event-state duality is a modeling principle and an instance of duality and symmetry: the relationship between two views of behavior:

Fibrations and Indexed Structure

Fibrations and indexed structure describe situations where each object in a base domain has a category of things lying over it.

Fixed Points

A fixed point is a value, structure, or behavior that a specified transformation leaves unchanged:

Functional Programming

Functional programming describes computation primarily through values, functions, composition, and evaluation rather than through a distinguished sequence of commands that mutate shared state.

Functoriality

Functoriality is the principle that a mapping between domains should preserve the structure that matters: identities, relationships, composition, and change.

Glitch Principle

The glitch principle states that a non-trivial device making a discrete decision among finitely many outcomes from a continuous range of possible inputs cannot guarantee a uniform finite decision time for every input.

Glossary

This glossary collects compact vocabulary used across the Cohesive system model. Terms that acquire their own distinctions, relations, and realization obligations are promoted into graph nodes rather than remaining glossary-only definitions.

Happened-Before

Happened-before is a strict partial order over occurrences that preserves potential causal influence without requiring one global clock or one total execution order.

Monads Monoids and Duals

Monads, monoids, and their duals provide recurring patterns for sequencing, accumulation, context, observation, and composition.

Naturality

Naturality is the principle that a transformation should be independent of arbitrary representation choices. It should commute with the structure-preserving maps between representations.

Nondeterminism and Choice

Nondeterminism describes a model in which one context admits more than one possible continuation. Choice describes how, where, or by whom that multiplicity is resolved.

Optics and Lenses

Optics are structured ways to focus on, observe, transform, or update part of a larger structure.

Process Theories

Process theories are modeling disciplines for work, interaction, change, and behavior that unfold over time.

Programming Paradigms

Programming paradigms are recurring ways of interpreting and organizing computation. They select which structures are primary, which composition laws matter, and which operational details are left to a language, compiler, runtime, or other realization.

Queueing Theory

Queueing theory is the mathematical and operational discipline for reasoning about work that arrives, waits, receives finite-capacity service, moves among resources, and completes.

Recursion

Recursion defines a value, structure, or behavior in terms of other instances of the same form. The recursive reference may point to a smaller component, a prior step, a nested process, or another derivation of the same relation.

Reduction, Evaluation, and Confluence

Reduction, evaluation, and confluence describe how a computation advances through possible intermediate expressions or states, how an execution strategy selects a path, and when divergent paths remain semantically coherent.

Relational and Logic Programming

Relational and logic programming are approaches in which programs state which combinations of values, facts, or terms hold or are admissible, rather than prescribing only a function from distinguished inputs to distinguished outputs.

Sheaves and Gluing

Sheaves and gluing provide a local-to-global principle for systems of observations: many observers, contexts, processors, time intervals, schemas, views, or execution cuts may each see part of a system, and the model needs to say when those partial views agree enough to form a coherent larger view.