Eventual Consistency and Unresolved Constraint Mismatch

This guide addresses how Cohesion Dynamics maintains structural consistency when locally generated mismatch cannot be resolved immediately. The answer is eventual consistency — a deterministic, non-teleological mechanism that preserves locality while allowing persistent unresolved mismatch to constrain future admissible configurations.

1. Motivation: Consistency in Physical Theories

A central requirement of Cohesion Dynamics is that informational structure must remain consistent from any admissible reference frame. This requirement is not enforced procedurally or dynamically, but structurally: only configurations that satisfy relational constraints are admissible.

Other conceptual guides describe:

How information is represented (CIU)
How constraints shape admissibility
How local mismatch motivates structural change

This guide addresses a complementary question:

How can a system remain consistent when a locally generated mismatch cannot be resolved immediately?

The answer is eventual consistency.

2. Eventual Consistency (Intuition)

In many systems, not all inconsistencies can be resolved at the moment they arise. An everyday analogy is a crack in a wall:

A local stress appears
The wall cannot instantly reconfigure everywhere
Instead, the stress propagates through the structure until it reaches a place where it can be absorbed or redistributed
The wall remains globally stable even though the stress is temporarily unresolved

In CD, the same idea applies to informational structure:

A local resolution may reduce mismatch in one place
While leaving behind unresolved mismatch that must not be lost
And must eventually be accounted for somewhere else in the structure

This persistence of unresolved mismatch is eventual consistency. It is:

Deterministic
Non-teleological
Compatible with locality
Does not require stochastic choice

3. Unresolved Constraint Mismatch (Descriptive Concept)

We refer to persistent unresolved mismatch as unresolved constraint mismatch (informally, deferred resolution).

Throughout this guide, “constraint” means a restriction on admissible structure, not an active enforcement mechanism.

Ontological status: “Unresolved constraint mismatch” names a structural situation, not a thing or entity. It refers to the absence of a jointly consistent configuration required by the constraints of the structure, not to an object that exists independently.

Unresolved constraint mismatch is:

Not a new entity or primitive
Not an agent, signal, or scheduler
Not something that “tries” to be resolved
Not additional structure moving through the system

Instead, it is a descriptive name for the fact that:

Some admissibility constraints created by past resolutions remain globally binding on future resolutions, even when they are not locally represented.

More precisely, unresolved constraint mismatch represents the absence of locally encodable structure where consistency would otherwise require it. Like a crack in a wall is not a material thing but the absence of material where structural integrity would otherwise exist, unresolved constraint mismatch is not an object but a constraint.

Unresolved constraint mismatch:

Restricts which future configurations are admissible
Without forcing immediate resolution
And without requiring continuous checking or propagation
Remains purely constraint-theoretic, not ontological

Unresolved constraint mismatch does not cause resolutions. It does not trigger activity, checking, or propagation by itself. It acts only as a structural constraint on what configurations are admissible next.

The correct analogy is not that each brick “checks” for a crack beneath it, but that placing a brick where there is no structural support is simply inadmissible. A crack propagating through a wall constrains where future structure can exist: bricks placed above the crack must be supported in a way that preserves overall integrity. Bricks that would collapse the wall are never placed—not because the wall reasons about the future, but because unsupported placements are structurally invalid.

In the same way, unresolved constraint mismatch restricts the space of admissible continuations, without requiring local checks, optimisation, or foresight. Resolutions occur only when local conditions motivate them, and are admissible only if their outcomes remain compatible with all unresolved constraints.

This terminology is descriptive convenience only. All underlying structure already exists in K-KERN’s admissibility grammar.

4. How Unresolved Constraint Mismatch Actually Resolves (The Crack Analogy)

A useful way to understand unresolved constraint mismatch in Cohesion Dynamics is to think of it like cracks propagating through a wall.

A crack is not a thing that wants to be resolved. It does not know where it will end. It simply represents stress that the structure cannot locally absorb.

Crucially:

A brick does not need to know whether the crack will eventually stop
The crack passes through if the brick can carry the stress
The crack terminates if the brick cannot carry further stress
If embedding the crack would shatter the brick, that configuration never forms

There is:

No foresight
No optimisation
No global planning
Just local structural compatibility

This maps cleanly onto Cohesion Dynamics.

Clarification on Termination:
In this guide, crack termination refers only to settlement within the same consistency structure (absorption/incorporation). Absorption corresponds to settlement of deferred mismatch within the same structure, while a boundary corresponds to loss of joint admissibility—where the surrounding structure can no longer carry the mismatch at all. A boundary is not where stress is absorbed, but where stress can no longer be jointly represented. That case (partition/boundary formation) is treated in K-CAP, not here.

Structural Admissibility in CD Terms

Unresolved constraint mismatch (such as a photon) is not an instruction to resolve, and it is not a global task waiting to be completed. It is simply a piece of unresolved mismatch that must remain representable somewhere in the structure.

A continuation is admissible only if:

The structure it creates can still carry the unresolved mismatch.

Three exhaustive cases:

Degrees of freedom remain → the mismatch passes through unchanged
Incorporation required → the mismatch must be absorbed here
Neither possible → the continuation is inadmissible

Crucially: Admissibility does not involve evaluating future histories or knowing whether unresolved mismatch will eventually be incorporated elsewhere. The check is purely local and structural: whether the resulting configuration retains sufficient degrees of freedom to represent unresolved constraint mismatch at all. This mirrors the crack analogy: a brick does not know where a crack will end, only whether it can carry the stress onward without immediate structural failure.

Evolution proceeds by exclusion of incompatible continuations, not by execution of local decision procedures.

Crack Analogy → CD Mapping

Crack / Wall Analogy	Cohesion Dynamics
Brick can carry stress	Resolution preserves degrees of freedom
Brick cannot carry stress	Incorporation required for admissibility
Brick placement would shatter wall	Continuation is inadmissible

A Concrete Physics Example: Photon and Atoms

Consider a photon moving through matter. In explored regimes:

Transparent medium (glass) — typically

The photon does interact with atoms
Local excitations occur
However, these interactions do not require irreversible incorporation of the mismatch to preserve admissibility
The atomic configurations still allow the photon’s energy, momentum, and phase relations to remain representable
Degrees of freedom remain available
So the mismatch passes through

Absorbing surface (detector, wall) — often

The photon interacts
The resulting atomic configuration would no longer allow the photon’s conserved quantities to remain unaccounted for
If the photon were not absorbed here, the structure would become inconsistent
The structure cannot carry the stress any further
So the photon is absorbed

Forbidden interaction

A hypothetical interaction would:
- Destroy the ability to represent the photon
- Without absorbing it
- And without allowing any future resolution
That configuration simply never forms

Note: This guide does not provide a microscopic derivation of material optical properties. The examples illustrate structural compatibility, not predictive mechanisms.

Why This Is Not Teleological

Nothing in this story requires:

Knowing the future
Preferring absorption
Randomness
Or “trying” to resolve photons

Just like a crack in a wall:

The structure does not decide where the crack ends
Inadmissible placements are simply excluded by structural requirements
The eventual outcome emerges from the constraint architecture — not from choice

Why This Preserves Coherence and Decoherence

Coherence corresponds to situations where unresolved constraint mismatch can pass through many interactions without forcing incorporation. This is not a property of the mismatch itself, but of the surrounding constraint architecture allowing multiple unresolved mismatches to remain mutually compatible. Like cracks that can coexist in the same wall without forcing immediate structural failure.

Decoherence occurs when an interaction creates structure that can no longer carry the mismatch onward without forcing incorporation.

Both follow from the same rule. No special cases required.

Failure Modes

Unresolved constraint mismatch can:

Propagate — pass through interactions while preserving degrees of freedom
Be incorporated — absorbed when incorporation becomes required for admissibility
Become non-transmissible — lose joint admissibility within the current structure

The third case is not absorption. It corresponds to loss of joint admissibility or, in physical terms, boundary formation (e.g., black holes as separate structures seen only as boundaries). This case is handled in K-CAP.

5. Locality and Determinism

Eventual consistency does not violate locality.

Resolutions occur only due to local constraint considerations
Unresolved constraint mismatch does not trigger resolutions
It only constrains what outcomes are admissible when resolutions occur

Determinism is preserved because:

Admissibility is fully determined by existing structure
No choices are made
No probabilities are sampled

The system evolves by exclusion of inadmissible continuations, not by selection or optimisation.

6. Physics Intuition: Propagation Without Paths

In physical terms, unresolved constraint mismatch explains how something can be conserved without being locally realised everywhere.

For example (informally):

A photon can be understood as unresolved constraint mismatch carrying conserved quantities
Without requiring a realised trajectory
And without requiring local structural encoding at every interaction

This is analogous to a crack in a wall: the crack is not additional structure propagating through the wall, but the absence of structure where consistency would otherwise require it. The wall remains globally constrained by this absence until the stress can be absorbed or redistributed.

Similarly, unresolved constraint mismatch is not a thing moving through the structure—it is the absence of locally encodable structure where consistency would otherwise require it. This absence constrains all future admissible resolutions until the mismatch can be incorporated.

sequenceDiagram
    participant E as Emission Event
    participant M as Transparent Medium
    participant A as Absorption Event
    
    E->>M: Unresolved mismatch created<br/>(conserved quantities)
    Note over M: Interactions occur<br/>but incorporation not required<br/>Mismatch persists
    M->>A: Mismatch incorporated<br/>(resolution required for admissibility)
    Note over A: Mismatch resolved<br/>Conserved quantities realised

Caption: Propagation as persistence of unresolved constraint mismatch through interactions.

Transparent vs Opaque Media (Conceptual)

The distinction between transparent and opaque media illustrates a single structural principle:

The key question is whether interactions preserve the degrees of freedom required to carry unresolved constraint mismatch forward.

In explored regimes (transparent media, typically):

Interactions do occur with the medium
However, these interactions preserve degrees of freedom to represent the mismatch
So the mismatch persists without requiring incorporation
Admissible continuations remain available

When interactions would eliminate these degrees of freedom (opaque media), incorporation becomes required for admissibility.

This distinction is structural, not probabilistic. Nothing “fails to absorb” or “chooses” anything. The structural compatibility of the medium determines whether mismatch can persist.

Note: This guide does not derive microscopic optical properties. The examples illustrate structural compatibility principles in regimes where they have been explored.

flowchart LR
    C[Unresolved Constraint Mismatch] --> T[Transparent Interaction]
    C --> O[Opaque Interaction]
    
    T --> TP[Mismatch persists<br/>Future resolution preserved]
    O --> OP[Mismatch incorporated<br/>No future resolution possible]
    
    style C fill:#e1f5ff
    style T fill:#fff3cd
    style O fill:#f8d7da
    style TP fill:#fff3cd
    style OP fill:#d4edda

Caption: Structural difference between transparent and opaque interactions.

7. Relationship to Probability, Coherence, and Branching

This guide does not introduce probability or branching. Instead:

Probability arises from conditioning on which resolutions occur
Coherence corresponds to regimes where multiple unresolved constraint mismatches remain mutually compatible given the surrounding constraint architecture
Decoherence corresponds to regimes where compatibility is lost due to irreversible exposure

Key insight: Coherence is not a property of the mismatch itself, but a property of the ambient constraint geometry. Multiple unresolved absences remain mutually embeddable within the same admissible future when the environmental constraint structure permits compatible closure.

Think of multiple cracks in a wall: whether the cracks can coexist without forcing immediate structural collapse is determined by properties of the surrounding bricks and support structure, not by properties of the cracks themselves.

Important: Branching reflects the existence of multiple admissible continuations, not the presence of constraint pressure or unresolved constraint mismatch.

Extending the Wall Analogy: Branching vs Stress

The wall analogy helps distinguish two independent structural phenomena:

Branching corresponds to multiple structurally supported continuations — not to stress or cracking. In the wall analogy:

Branching is like building multiple parallel courses of bricks above a shared foundation
Bricks may be rotated, offset, or arranged differently while all remaining structurally supported
Branches may later merge if higher courses realign on common support

Stress (cracks) and branching are distinct:

Stress propagates due to unresolved constraint mismatch — a crack moves through the structure seeking settlement
Branching arises from multiple admissible continuations — different brick arrangements all satisfy structural requirements

This distinction prevents misinterpreting branching as caused by mismatch pressure. Branching is about the geometry of admissible structure, not about deferred resolution.

These topics are treated elsewhere and are compatible with the framework here.

See: Probability in Cohesion Dynamics for structural weighting and the DAG of admissible configurations.

8. Relationship to Other Guides

This guide complements:

Information and Constraint — Representation of information
Mismatch and Constraint Pressure — How mismatch drives structural change
Probability — Conditioning without randomness
Causal Axis Commitment — Irreversibility via commitment exposure
Gravity as Admissibility Structure — Global constraint shaping

It provides shared language used implicitly across those guides.

9. Non-Claims

This guide does not:

Modify kernel grammar
Define dynamics
Introduce collapse or Many-Worlds
Claim completeness
Assert physical sufficiency

It is explanatory only.

10. Summary

Eventual consistency allows Cohesion Dynamics to describe:

✅ Persistent unresolved mismatch — Constraints that remain globally binding
✅ Deterministic delayed resolution — Resolution governed by structural admissibility
✅ Propagation without paths — Persistence through interactions without continuous realisation
✅ Conservation without local realisation — Unresolved constraint mismatch constrains future resolutions

While preserving:

✅ Locality — Resolutions occur due to local constraints only
✅ Determinism — No stochastic choice or optimisation
✅ Structural admissibility — All behaviour follows from constraint satisfaction

Unresolved constraint mismatch is not a thing that acts — it is a restriction on admissible structure that must not be violated.

Note on Document Status

This is a conceptual orientation guide, not a research paper. It introduces no new axioms, makes no necessity claims, and does not derive formal results. Its purpose is to clarify how to think about eventual consistency in CD to reduce misinterpretation of the formal papers.

For rigorous treatments, always refer to the formal K-, A-, M-, and B-series papers.