Paper M1 — Constructive Viability in Constrained Informational Domains

Cohesion Dynamics (CD)
Necessary Conditions for Construction Prior to Physical Law

Abstract

This paper investigates the conditions under which construction is possible within constrained informational domains. Building on the metaphysical framework established in Paper F1, which formalises information, constraints, domains, tolerance, and divergence, we do not re-derive ontology. Instead, we ask a narrower and more technical question: why do some constrained domains permit construction while others remain sterile?

We show that construction is impossible in domains that enforce perfect rigidity or zero mismatch. Instead, construction requires bounded mismatch, enforced through tolerance-based domain admission, coupled with deterministic constraint satisfaction. Mismatch is not a flaw or approximation; it is a necessary structural degree of freedom that enables reuse, repair, convergence, and composition. This paper establishes mismatch and tolerance as pre-constructive conditions, without yet invoking specific coupling mechanisms, constructors, or physical instantiations.

1. Scope and Relation to F1

This paper assumes the ontological and metaphysical foundations established in Paper F1:

Information necessarily exists and cannot be destroyed
Constraints are exact and binary
Domains are defined by additive sets of constraints
Tolerance is a domain-admission constraint, not approximate law
Divergence produces partitions, not failure

We do not repeat these arguments here. Instead, we take them as given and examine their consequences for constructive viability.

The central question of this paper is:

Given an informational domain defined by exact constraints, what additional structural properties are required for construction to be possible at all?

2. What Is Meant by “Construction”

In Cohesion Dynamics, construction refers to the ability of informational structures to:

Persist through interaction
Recover from perturbation
Reuse internal structure
Compose into larger structures
Maintain identity across time

This definition is deliberately weaker than “constructor” in the full sense. At this stage, we are not concerned with reproduction, universality, or task performance. We are concerned only with whether any constructive behaviour is possible.

A domain that cannot support these properties is constructively sterile, even if it is internally consistent and deterministic.

3. The Failure of Perfect Constraint Domains

Consider a domain defined by a set of exact constraints with no tolerance.

In such a domain:

Every valid state must satisfy all constraints exactly
Any deviation immediately violates domain admission
No alternative admissible states exist once a perturbation occurs

This leads to two pathological outcomes:

Fragility
A single perturbation removes the state from the domain entirely. No recovery is possible.
Stasis
If perturbations are disallowed entirely, the system must freeze into a fixed point or cycle.

In both cases, construction is impossible. There is no room for adaptation, repair, or reuse.

This mirrors the failure of systems with zero noise margin: determinism is preserved, but scalability is lost.

4. Mismatch as a Structural Degree of Freedom

The key insight is that mismatch is not a violation of constraints.

Mismatch refers to differences between co-evolving states within the set of admissible states of a domain. It exists only because:

The domain admits a set of valid states, not a single state
Tolerance constraints define a bounded region of admissible variation

Mismatch therefore arises inside the domain, not outside it.

Formally, mismatch is:

Bounded
Structured
Subject to correction
Never unconstrained

Without mismatch:

There are no alternative admissible states
There is no gradient toward recovery
There is no capacity for convergence

Mismatch is thus a necessary degree of freedom for construction.

5. Tolerance as a Constructive Enabler

Tolerance is often misunderstood as “approximate constraint satisfaction.” This is incorrect.

In Cohesion Dynamics:

Constraint satisfaction is always exact
Tolerance is an additional binary constraint that defines domain admission

A tolerance constraint specifies a bounded region of state space within which states are admissible to a domain. Either a state lies within this region, or it does not.

From a constructive perspective, tolerance enables:

Multiple admissible states
Recovery pathways after perturbation
Reuse of structure across interactions
Gradual convergence without violating determinism

Crucially, tolerance does not weaken law. It protects the domain by excluding states that would destabilise it.

6. Why Error Correction Is Inevitable

Once a domain admits multiple states, interactions will generally move states within the admissible region.

If the domain is to persist, it must exhibit error-corrective behaviour, meaning:

Perturbations are mapped to other admissible states
Dynamics tend to remain within the tolerance boundary
No single perturbation forces domain exit

Error correction is therefore not an added mechanism. It is an unavoidable consequence of:

Exact constraints
Tolerance-based admission
Deterministic evolution

Any domain that persists over time must implicitly correct errors, or it will fragment immediately.

7. Divergence and Constructive Limits

When mismatch exceeds tolerance, a state is no longer admissible to the domain.

Importantly:

The state is not destroyed
Ontological constraints still apply
Parent-domain constraints are still satisfied

What occurs is domain divergence: the state ceases to participate in the constructive dynamics of that domain.

From a constructive standpoint, this sets a hard limit:

Construction is possible only within tolerance
Beyond tolerance, continuity of construction ends

This explains why constructive domains are necessarily bounded, finite, and local.

8. Necessary Conditions for Construction (Summary)

We can now state the minimal conditions required for construction:

Exact, deterministic constraints
Additive domain structure
Tolerance-based domain admission
Bounded mismatch within admissible states
Implicit error correction through admissible dynamics

None of these conditions guarantee construction. But without all of them, construction is impossible.

9. What M1 Does Not Claim

This paper does not claim:

That constructors already exist
That specific coupling mechanisms are sufficient
That physical law has been derived

Those questions are addressed in later M-papers and empirical phases.

M1 establishes only this:

Construction is impossible without bounded mismatch and tolerance-based domain admission, even in a perfectly deterministic informational ontology.

10. Transition to M2

Having established the necessity of mismatch and tolerance for construction, the next question is:

How must admissible dynamics be structured so that constructive behaviour actually emerges?

This is the subject of Paper M2, which introduces admissible moves, precedence, and the formal structure of constructive dynamics.