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Cohesion Dynamics (CD)

Order-Theoretic Lens

For mathematicians, theoretical computer scientists, and category/order theory readers.

This entry route explores how Cohesion Dynamics substrate behaviour maps onto order-theoretic structures such as refinement, closure, partial joins, and formal classification.

Overview

If you’re comfortable with order theory, domain theory, or categorical approaches to computation and information, this lens provides a mathematically rigorous entry point to Cohesion Dynamics.

Key Order-Theoretic Structures in CD

CD’s substrate mechanics and cohesion behaviour naturally express themselves in order-theoretic terms:

  • Refinement orderings on informational structures
  • Partial joins and closure operations
  • Lattice-like structures emerging from coherence constraints
  • Fixed points and attractors in substrate evolution
  • Capability hierarchies classifying informational continua

Core Order-Theoretic Concepts

Refinement

In CD, informational structures can be refined — one structure is a refinement of another if it preserves all properties while adding specificity or constraint.

Refinement defines a partial order on the space of structures, and this order governs:

  • Constructor emergence (more refined substrates support more constructor types)
  • Quantum structure (refinement of admissibility constraints)
  • Phase transitions (discrete jumps in refinement orderings)

Closure and Coherence

Coherence in CD can be understood as a closure operation:

  • Given a set of informational constraints, their closure is the minimal coherent structure satisfying them
  • Closure operations exhibit idempotence, monotonicity, and extensivity
  • Failures of closure correspond to branching or divergence

Partial Orders on Continua

CD classifies informational continua by what they can stably support, yielding a capability-based partial order:

  • Base continua (minimal persistence)
  • Constructor-capable continua
  • Quantum-capable continua

This classification isn’t arbitrary — it’s derived from eliminative empirical results (E-series).

Relevant Papers

Reference and Classification

R-CCC: Continuum Capability Classification

  • Formal capability-based classification of informational continua
  • Synthesises eliminative results from E0, E1, E2
  • No new axioms — pure classification derived from empirical constraints

R-DCC: Dependency and Coherence Classification

  • Dependency structures in the research programme
  • Coherence constraints across papers

Mechanism Papers (M-series)

The M-series papers formalise substrate mechanisms with order-theoretic structure:

M1: Cohesion Mechanism

  • Formal definition of cohesion operations
  • Closure semantics and reconciliation

M2: Construction Mechanism

  • Conditions for stable constructor emergence
  • Fixed-point characterisation of constructors

M3: Modes and Phase Transitions

  • Discrete mode transitions in substrate behaviour
  • Order-theoretic characterisation of phase spaces

M-CON subseries (M4, M5, etc.)

  • Constraint composition and internal modes
  • Refinement orderings on constraint regimes

Structural Consequences (B-series)

B-series papers

  • Structural theorems derived from substrate axioms
  • Non-factorisability and branching structure
  • Closure-preserving transport
  • Conditional structural results (if axioms hold, then structure follows)

Substrate Mechanics (A-series)

A-series papers

  • Formal mathematical specification of the discrete substrate
  • Network topology and operational semantics
  • Base interface and update rules

Order-Theoretic Reading Path

If you’re approaching CD from an order-theoretic background, here’s a suggested reading order:

  1. R-CCC: Continuum Capability Classification — Start with the classification framework
  2. M1: Cohesion Mechanism — Understand cohesion as closure
  3. M2: Construction Mechanism — Fixed points and stability
  4. A-series: Substrate Mechanics — Formal substrate definition
  5. B-series: Structural Consequences — Derived structural theorems

Key Insights for Order Theorists

CD is Not Just Applied Order Theory

While CD uses order-theoretic structures heavily, it’s not merely an application of existing order theory. Instead:

  • Order-theoretic structures emerge from substrate mechanics
  • The framework derives which orderings are physically relevant
  • Empirical constraints (E-series) narrow the space of viable orderings

Refinement ≠ Logical Implication

Refinement in CD isn’t purely logical:

  • It has physical content — refined substrates behave differently
  • Refinement jumps correspond to phase transitions
  • Not all refinements are physically realisable

Fixed Points and Constructors

Constructors in CD are characterised as fixed points of substrate evolution:

  • A constructor is a structure that, when applied, reproduces itself
  • Substrate conditions determine which fixed points exist
  • Constructor emergence is necessary, not assumed

Connections to Existing Work

Domain Theory

CD’s substrate has connections to domain theory:

  • Information orderings resemble Scott domains
  • Coherence constraints are like directed completeness
  • But CD adds physical constraints not present in pure domain theory

Category Theory

While not primarily categorical, CD has categorical structure:

  • Morphisms between informational structures
  • Functorial relationships between substrate layers
  • Adjunctions between construction and refinement

Lattice Theory

Cohesion constraints form lattice-like structures:

  • Joins correspond to reconciliation
  • Meets correspond to constraint intersection
  • But not all reconciliations have well-defined joins (hence branching)

Further Exploration

Technical Resources

Note: This lens emphasises order-theoretic structure. For constructor-theoretic perspectives, see Constructor-Theoretic Lens. For general introduction, see Conceptual Guide.