Paper F1 — Constraints

Cohesion Dynamics (CD)
Metaphysical Foundations of Constraint, Error Correction, and Continuum Formation

Abstract

This paper establishes the metaphysical foundations of Cohesion Dynamics by formalising the role of constraints, tolerance, and error correction in an informational ontology. Information is taken as ontologically primitive and necessarily existent. Meaning, structure, continuity, and physical law arise not from information alone, but from systems of constraints that act upon it. Crucially, constraint satisfaction is binary and exact: information either satisfies a constraint or it does not. Apparent tolerance, robustness, or error margins arise from additional admission constraints that define which informational states may co-evolve within a given continuum. This paper positions error correction not as a relaxation of law, but as a necessary condition for scalable, persistent structure, and prepares the conceptual ground for later formalisation and physical instantiation.

1. Ontological Premise: Information and Existence

Cohesion Dynamics begins from a single ontological commitment:

Information necessarily exists and cannot be destroyed.

This is not an axiom in the conventional sense, but a description of ontological status. “Non-existence” is not a state information can enter. As such, information forms an embedding space: all that exists is informational, and all informational configurations are subject to constraint.

This ontological constraint is global and inescapable. Even when informational structures diverge, partition, or lose mutual coherence, they do not escape this constraint. Existence is therefore the most fundamental and universal constraint under which all further structure arises.

2. Constraints as the Source of Meaning

Unconstrained information is maximally permissive and therefore semantically empty. Meaning arises only when information is constrained.

A constraint is a rule that admits or excludes informational states. Constraint satisfaction is binary: a state either satisfies a constraint or it does not. There is no notion of partial, approximate, or fuzzy constraint satisfaction at the substrate level. Determinism depends on this exactness.

Different systems of constraints give rise to different domains of meaning. Physics, mathematics, computation, and cognition can all be understood as informational systems operating under different constraint regimes.

3. Exact Constraint Satisfaction and Determinism

All constraints in Cohesion Dynamics are satisfied exactly. If a state does not satisfy a constraint, it is not a valid state under that constraint system.

This exactness is essential:

It preserves determinism.
It prevents ambiguity in state evolution.
It avoids teleology or substrate “choice”.

The substrate does not select between imperfect solutions. All valid solutions that satisfy constraints exist. What differs is which solutions may co-evolve together, a distinction introduced by additional constraints.

4. Informational Domains, Subdomains, and Tolerance

At the ontological level, information exists necessarily. Its only global constraint is existence itself. This defines a maximally permissive informational domain: information may take any form, configuration, or relational structure, provided it exists.

All further structure arises through the introduction of additional constraints, which define informational subdomains.

An informational domain is defined by a set of constraints. A state is valid within a domain if and only if it satisfies all constraints that define that domain. Subdomains arise when further constraints are added. Crucially:

Constraints are additive, never subtractive
A subdomain inherits all constraints of its parent domain
A state admissible in a subdomain must satisfy both parent and subdomain constraints

This induces a nested, hierarchical structure of domains, where each level is defined by increased constraint specificity.

What appears in physical systems as tolerance, robustness, or error margin does not arise from approximate or partial constraint satisfaction. Constraint satisfaction is always binary. Instead, tolerance is itself an additional constraint that governs domain admission.

A tolerance constraint specifies a bounded region of state-space within which states are admissible to a given domain. Either a state lies within this bound, or it does not. There is no ambiguity.

When a state exceeds tolerance:

It does not violate ontology
It is not destroyed
It simply ceases to be admissible within that domain

The state continues to exist and remains subject to all higher-level (parent) constraints, but it no longer participates in the constrained dynamics of that domain.

Tolerance therefore functions as:

A domain boundary, not a relaxation of law
A protective admission constraint that preserves coherence
A mechanism that prevents unbounded mismatch from destabilising a domain

Error correction, convergence, and robustness arise entirely within the space of admissible states. They do not rely on violating constraints, only on selecting among admissible alternatives.

This framing naturally explains divergence: when co-evolving states can no longer satisfy a shared tolerance constraint, they do not “fail”. They separate into distinct domains, each continuing under the same inherited constraints but no longer bound to the same subdomain constraints and dynamics.

In this sense, tolerance does not soften determinism; it creates domains in which determinism remains viable. By excluding states beyond tolerance, domain admission boundaries prevent error propagation and preserve the domain’s semantic integrity.

5. Mismatch and Error Correction

Mismatch is a comparative measure between admissible states. It quantifies relational tension under a given constraint system but does not represent constraint violation.

Mismatch plays a critical role:

It enables ranking of admissible transitions.
It supports local error correction.
It allows systems to converge toward stable configurations.

Mismatch is therefore not permissiveness, but guidance within legality.

Error correction arises when local update rules preferentially reduce mismatch while remaining within all constraints. This is the foundation of stability, persistence, and later, construction.

6. Why Error Correction Is Necessary

A system with no tolerance constraint is brittle. A single deviation immediately excludes a state, preventing scalable structure. This is analogous to systems with no noise margin: a single error causes total failure.

Digital computation works not because it tolerates incorrect states, but because it constrains information within admissible bounds and actively corrects deviations. The same principle applies universally.

Error correction is therefore not optional. It is a necessary condition for:

Persistence across time
Scalability of structure
Construction and replication
Any non-trivial continuum

7. Continuums as Constrained Co-Evolution

A continuum is not the totality of information. It is a cohesive subdomain in which informational states co-evolve under shared constraints and admission rules.

When states can no longer co-evolve within tolerance, divergence occurs. Divergence does not destroy information or laws. It partitions informational evolution into distinct domains that no longer share a common continuum.

Importantly:

Global constraints remain invariant across divergence.
Diverged systems are still subject to the same laws.
What changes is mutual admissibility, not ontology.

This framing accommodates phenomena such as horizons, black holes, and cosmological partitioning without invoking new laws.

8. Divergence and Constraint Inheritance

During divergence, informational systems do not shed constraints. They lose compatibility with a particular continuum’s admission rules.

Thus, constraints “travel” with diverged systems because they were never local to the continuum in the first place. They are global properties of informational existence.

This explains why extreme systems (e.g. black holes) continue to obey universal constraints while no longer participating in the parent continuum’s causal structure.

9. Constructivity and Further Constraints

Because information is ontologically constrainable, additional layers of constraint may be imposed without contradiction. This is what makes construction possible.

Later papers will show how specific classes of constraints enable:

Persistent composites
Replication
Hierarchical construction
Mode formation
Physical law in our universe

Paper F1 provides the metaphysical groundwork for these developments without presupposing any particular physical instantiation.

10. Summary

Information necessarily exists and cannot be destroyed.
Constraints give information meaning.
Constraint satisfaction is exact and binary.
Tolerance is an admission constraint, not approximation.
Mismatch enables error correction within legality.
Continuums are constrained co-evolutionary domains.
Divergence partitions evolution without changing laws.
Error correction is essential for scalable structure.

This framework establishes the metaphysical conditions under which physics, computation, and constructors can emerge, preparing the ground for formalisation (M-papers) and physical instantiation (A/B papers).