Paper M5 — Constructor Emergence in Cohesive Continua

Version: v0.4 (Revised)
Programme: Cohesion Dynamics / Stable Constructors
Status: Draft for internal circulation

Abstract

We investigate how constructors—entities that preserve and reproduce specific patterns through interaction—can emerge within a cohesive informational continuum. While the substrate must be intrinsically constructive in an ontological sense (preserving information and repairing inconsistency), we show that pattern-specific constructors are not fundamental. Instead, they emerge only when additional structural conditions are satisfied.

Using a sequence of toy models and empirical simulation phases, we identify three necessary precursor properties—selectivity, persistence, and reusability—and demonstrate that these arise from a minimal additional mechanism: admissible move precedence, a local rule that deterministically selects among allowed updates to minimise mismatch.

We report the first observation, within this framework, of entities exhibiting self-repair, replication, and functional preservation—meeting a practical definition of emergent constructors—while also identifying the missing ingredients required for hierarchical construction.

1. Introduction

Modern physics successfully describes the behaviour of a continuum, yet the emergence of persistent, function-preserving structures—atoms, molecules, cells, machines—remains conceptually opaque. Constructor Theory proposes that such entities are central, but does not explain how they arise from underlying dynamics.

Cohesion Dynamics (CD) approaches this problem from a different angle:
starting with information as ontological, and studying how cohesion, admissibility, and mismatch reduction give rise to a continuum, and subsequently to higher-order structure.

This paper addresses a precise question:

Given a cohesive continuum, what additional mechanisms are required for constructors to emerge?

2. Ontological Construction vs Emergent Constructors

A crucial distinction underpins this work.

2.1 Ontological construction (fundamental)

Because information is ontological and cannot be destroyed, any viable substrate must be intrinsically constructive. This means it must support:

error detection
error correction
admissibility constraints
recovery from local inconsistency

These properties are not emergent; they are required for any continuum to exist.
They correspond to ontological (O) and reality-level (R) axioms.

Examples include:

conservation laws
reversibility constraints
consistency checks
divergence leading to partition, not failure

Without this intrinsic construction, no time, causality, or physics is possible.

2.2 Emergent constructors (non-fundamental)

By contrast, the subject of this paper is pattern-specific constructors:

Entities that preserve particular internal organisations through interaction, and can induce the same organisation in other systems.

These are:

selective (not everything binds)
local (operate through interaction)
contingent (do not appear in all continua)
historically stable (persist through perturbation)

Atoms and living cells are examples of this second sense of constructor.

This paper concerns how this second sense emerges from the first.

3. Continuum Preconditions (Summary)

Previous papers establish the background conditions:

Paper F: Information substrate and cohesion primitives
Paper A: Height, mismatch, and admissibility
Paper B: Emergent continuum physics and divergence

From this, we assume a C-class substrate:

local updates
global consistency
divergence resolved via partition
time as an emergent coordination field

Such a continuum is necessary but not sufficient for constructors.

4. Empirical Programme Overview

We conducted a staged empirical programme using progressively enriched toy models and simulators.

Identified precursor properties

Reusability (P2) — patterns can be re-engaged after interaction
Selectivity (P3) — only compatible entities interact coherently
Persistence (P1) — composites remain stable over long durations

Each was tested and isolated across Phases 9–11.

5. Why Simple Mechanisms Fail

Several plausible mechanisms were tested and found insufficient on their own:

Inertia / memory: slows change but does not create attractors
Energy accumulation: bookkeeping without behavioural consequence
Continuous coupling: allows interaction but not durable structure

These mechanisms preserve motion, not organisation.

6. Admissible Move Precedence (Key Mechanism)

6.1 Definition

Let $\mathcal{A}$ be the set of admissible updates (those respecting W-tolerance).
Precedence selects:

\Delta^* = \arg\min_{\Delta \in \mathcal{A}} M(s + \Delta)

That is, among allowed moves, choose the one that most reduces mismatch.

6.2 Why precedence matters

This introduces:

local determinism without global planning
convergence toward stable configurations
continuous error correction at the level of pattern

Importantly, precedence does not override admissibility—it operates within it.

7. Phase 11 Results: Persistence

With precedence enabled:

Mean composite lifetime increased 31× over baseline
Phase-locked configurations became stable attractors
Composites survived repeated perturbations

This establishes persistence as an emergent property.

8. Phase 12 Results: Constructor Properties

Using precedence-stabilised composites, we tested four constructor criteria.

8.1 Maintenance (Self-Repair)

100% recovery from phase, timing, and W perturbations
Recovery time $\sim 400\times$ faster than formation

8.2 Reproduction (Template Replication)

Stable composites induced identical structures in nearby compatible regions
Parent composite remained intact
Structural similarity = 1.0

8.3 Functional Preservation

Internal phase relationships preserved under systematic change
Robust under noise up to finite tolerance

8.4 Hierarchy (Failed)

No composite-of-composites formed
Indicates missing higher-level coupling mechanisms

9. Interpretation: What a Constructor Is

From these results, a constructor is characterised by:

Selective interaction (via W-gating)
Persistent internal organisation (via precedence)
Error-corrective dynamics (local mismatch minimisation)
Template capacity (structure induces structure)

No explicit “constructor primitive” is required.

10. Relation to Existing Theories

Constructor Theory (Deutsch): Identifies the concept but not the mechanism
Autocatalytic sets: Lack explicit error correction
CA-based life models: Often rely on fine-tuned rules

Cohesion Dynamics differs by grounding construction in admissibility + precedence, not special update laws.

11. Limitations and Open Problems

No hierarchy without explicit composite-level coupling
No resource competition or evolutionary dynamics yet
No universality demonstrated

These motivate Phase 13.

12. Conclusion

We have shown that:

A cohesive continuum alone does not yield constructors
Ontological error correction is necessary but insufficient
Admissible move precedence is the minimal additional ingredient enabling:
- persistence
- self-repair
- reproduction
- functional preservation

Constructors emerge not by adding force or memory, but by local deterministic selection within constraints.

This establishes a concrete, testable pathway from continuum physics to organised complexity.

The broader classification of continuum capability levels is presented in R-CCC (Continuum Capability Classification).

Acknowledgements

This work is part of the Stable Constructors Programme within Cohesion Dynamics.

One-line Summary

Constructors emerge when intrinsically error-corrective continua are augmented with deterministic precedence among admissible updates, enabling persistent, self-repairing, and replicating patterns without global control.