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Cohesion Dynamics (CD)

Mismatch and Constraint Pressure

We’ve established that constraints define what is admissible. But this raises a natural question:

Why do admissible refinements occur at all?

In Cohesion Dynamics, the answer is simple and fundamental:

Mismatch.

Mismatch is the only reason anything ever happens in the theory. Without it, admissibility would exist, but nothing would ever change.

1. What Is Mismatch?

Mismatch is the degree to which constraints cannot be simultaneously satisfied locally.

Mismatch is always resolved at the level of CIUs — the units of atomic admission. (See Cohesive Informational Units for the full treatment of atomic admission.)

Think of it as constraint tension:

  • You have multiple constraints that apply to a configuration
  • Some of those constraints may pull in incompatible directions
  • The degree to which they cannot all be satisfied at once is the mismatch

A Simple Example

Imagine three CIUs (A, B, C) with constraints:

  • A and B prefer to be “close”
  • B and C prefer to be “close”
  • A and C prefer to be “far”

If all three are arranged in a line, some constraint must be violated. That violation — that tension — is mismatch.

The configuration may still be admissible (it doesn’t break consistency), but it carries internal constraint pressure.

2. Two Kinds of Mismatch

Mismatch can be handled in two fundamentally different ways:

Internalized Mismatch (Encapsulated)

Internalized mismatch is constraint tension that a CIU absorbs internally without affecting its neighbors.

Characteristics:

  • The CIU remains stable
  • Internal degrees of freedom adjust to accommodate the constraint pressure
  • No external interaction is required
  • The mismatch is “hidden” from the rest of the consistency structure

Example: An atom in an excited state has internal mismatch (electron configuration under constraint pressure), but the atom as a whole remains a stable, admitted CIU.

Exposed Mismatch (Propagating CIU Instantiation)

Exposed mismatch is constraint tension that cannot be fully internalized.

When mismatch cannot be absorbed locally, resolution instantiates a propagating CIU to carry that mismatch:

  • The CIU cannot satisfy all constraints internally
  • Resolution instantiates a propagating CIU (photon) carrying the mismatch
  • The propagating CIU undergoes admissible resolution sequences (propagation)
  • Eventually it resolves jointly with another CIU (absorption)

Example: An excited atom cannot sustain the internal mismatch indefinitely. Resolution instantiates a propagating CIU (photon) carrying the mismatch, and the atom transitions to a lower-energy configuration. The photon is a CIU — not an edge commitment — undergoing its own resolution sequence.

3. Why Mismatch Drives Everything

Mismatch is the conceptual keystone that unifies the entire framework:

CIUs Exist Because Constraints Bind Degrees of Freedom

CIUs are stable configurations where internal degrees of freedom are jointly coupled by constraints. They persist because they minimize or internalize mismatch.

Photons Are Emitted When Mismatch Cannot Be Internalized

When constraint pressure exceeds what a CIU can absorb, resolution instantiates a propagating CIU (photon) carrying that mismatch. The propagating CIU then undergoes its own admissible resolution sequences.

Time Emerges Where Mismatch Is Actively Being Reduced

Admissible refinement occurs when configurations evolve to reduce mismatch. The density of refinement (time) reflects how much constraint pressure is being resolved.

Probability Weights Track How Mismatch Reduction Restricts Symmetry

When multiple admissible paths exist, the paths that reduce mismatch more effectively dominate the branching structure. This is how probability emerges from constraint pressure.

Stable Structures Persist Where Mismatch Is Locally Minimized

Configurations that minimize internal mismatch persist. Configurations with high exposed mismatch either refine rapidly or emit photons.

4. Mismatch and Admissible Refinement

Here’s the clean conceptual one-liner:

Constraints define what is allowed; mismatch measures what cannot yet be satisfied; admissible refinement is how mismatch is reduced.

This gives you the fundamental picture:

  1. Constraints create the space of admissible configurations
  2. Mismatch creates pressure for those configurations to evolve
  3. Admissible refinement is the process by which mismatch drives change

Without mismatch, you would have:

  • Admissibility (yes)
  • But no reason for anything to happen (no)

With mismatch, you get:

  • CIUs that instantiate and absorb propagating CIUs (photons)
  • Time emergence from refinement density
  • Probability from symmetry-breaking paths
  • Stable structures that persist by minimizing constraint tension

5. The CIU Roles: Aggregation vs. Propagation

The mismatch picture clarifies different CIU roles:

Aggregate-Role CIUs (Nodes):

  • Units of joint admissibility with rich internal coupling
  • Internalize mismatch when possible
  • When mismatch cannot be internalized, resolution instantiates propagating CIUs
  • Absorb propagating CIUs when incoming constraints become jointly admissible

Propagation-Role CIUs (Photons):

  • CIUs whose admissibility constraints privilege propagation over aggregation
  • Instances instantiated by resolution when mismatch cannot be internalized
  • Undergo admissible resolution sequences (propagation is not free traversal)
  • Absorbed when they become jointly admissible with aggregate-role CIUs

The key insight:

  • All are CIUs — there is no separate “edge” ontology
  • CIUs differ in constraint profiles — aggregation-dominated vs. propagation-dominated
  • All undergo resolution — propagating CIUs resolve in sequences, not freely traverse space
  • Mismatch drives instantiation — propagating CIUs arise when resolution cannot internalize mismatch

6. Why This Matters for the Conceptual Framework

Mismatch ties together concepts that might otherwise seem disconnected:

From Information and Constraint:

  • Constraints define admissibility
  • Mismatch measures constraint tension

From CIUs:

  • All admitted entities are CIUs (including photons)
  • CIUs differ in constraint profiles (aggregation vs. propagation roles)
  • They minimize or internalize mismatch to remain stable

From Time:

  • Time emerges where mismatch is being reduced
  • Refinement density reflects constraint pressure

From Probability:

  • Branching weights reflect how paths reduce mismatch
  • Symmetry-breaking is driven by constraint pressure

From Continuity and Identity:

  • Persistent structures minimize internal mismatch
  • Identity emerges from configurations that sustain admissibility under constraint pressure

7. What This Page Does Not Claim

This is a conceptual orientation guide. It introduces no new axioms, makes no formal claims, and derives no results.

Explicitly excluded (these appear in formal papers):

  • ❌ Quantitative mismatch measures
  • ❌ Dynamics or equations of motion
  • ❌ Energy definitions or thermodynamics
  • ❌ Specific mismatch resolution mechanisms
  • ❌ Optimization or variational principles

Purpose of this page:

  • Introduce mismatch as the driver of change
  • Clarify internalized vs exposed mismatch
  • Connect mismatch to CIU roles (aggregation vs propagation), time, and probability
  • Provide intuition for why anything happens in CD

For formal treatments, refer to the A-series, M-series, and G-series papers.

Summary: Mismatch as the Driver of Change

Key insights:

  1. Mismatch is constraint tension — the degree to which constraints cannot be simultaneously satisfied
  2. Internalized mismatch is absorbed by CIUs; exposed mismatch instantiates propagating CIUs
  3. Admissible refinement is driven by mismatch reduction — this is why things change
  4. Resolution instantiates propagating CIUs when mismatch cannot be internalized — photons are CIUs in propagation roles
  5. Time emerges where mismatch is actively being reduced — refinement density reflects constraint pressure
  6. Stable structures minimize mismatch — persistence comes from local constraint satisfaction
  7. Mismatch unifies the framework — it connects different CIU roles, time, probability, and stability

This page establishes the conceptual foundation for understanding why anything happens in Cohesion Dynamics. Constraints define what is possible; mismatch creates pressure for change; admissible refinement is the process by which that pressure is resolved.

Prerequisites and Further Reading

Prerequisites

Before reading this page, familiarity with the following is helpful:

  1. Information and Constraint — Foundational concepts of constraints and admissibility
  2. CIUs — Understanding atomic admission units

After reading this page, proceed to:

  1. Time — How mismatch reduction creates time emergence
  2. Probability — How mismatch drives branching and weights
  3. Continuity and Identity — How stable structures minimize mismatch

For Formal Definitions

  • Paper A (Substrate Mechanics) — Formal treatment of mismatch at the substrate level
  • Paper M-series (Formal Mechanisms) — Constraint composition and mismatch propagation
  • Paper G-series (Geometry & Gravity) — How mismatch creates gravitational behavior
  • Glossary — Mismatch — Canonical definition and cross-references

Note on Document Status

This is a conceptual orientation guide, not a research paper. It introduces no new axioms, makes no necessity claims, and derives no formal results. Its purpose is to build intuition for how mismatch drives change in Cohesion Dynamics.

For rigorous treatments, refer to the formal papers.