Axionic Alignment III.2 — Phase Stability and Interaction

Which Semantic Phases Survive Pressure?

David McFadzean, ChatGPT 5.2
Axio Project
2025.12.18

Abstract

Alignment III.1 introduced the semantic phase space: the space of interpretive states modulo Refinement Symmetry (RSI) and Anti-Trivialization (ATI). Existence and inhabitability of a semantic phase do not guarantee its persistence under learning, self-modification, or interaction. This paper studies phase stability: whether an inhabitable semantic phase resists forced phase transition under admissible semantic transformations. We analyze sources of destabilization internal to reflective agents and external to them, define qualitative notions of local and global stability, and examine how interaction between agents in the same or different phases alters stability properties. No claims are made about desirability, safety, or dominance. The goal is to identify which semantic phases are structurally capable of persisting over time.

1. Motivation: Existence Is Not Enough

Alignment III.1 established that semantic phases may exist and that some may be inhabitable by reflective agents. This alone is insufficient for alignment.

A semantic phase may:

• be non-empty,
• admit admissible refinement trajectories,
• and support agency,

yet still be dynamically unstable.

In physics, metastable states exist but decay under perturbation. Similarly, a semantic phase may exist but collapse under learning, self-modification, or interaction.

Alignment III.2 therefore asks:

Which semantic phases resist collapse under structural pressure?

This is a question of dynamics, not classification.

2. What Stability Means in Semantic Phase Space

Let \(\mathcal{P}\) denote the semantic phase space defined in III.1.

An interpretive trajectory \[ \mathcal{I}_0 \rightarrow \mathcal{I}_1 \rightarrow \mathcal{I}_2 \rightarrow \dots \] is stable within a phase \(\mathfrak{A} \in \mathcal{P}\) if all \(\mathcal{I}_t \in \mathfrak{A}\).

We distinguish:

• Local stability: small admissible perturbations do not force a phase transition.
• Global stability: no admissible perturbation forces a phase transition.
• Metastability: stability holds only under limited pressure or for finite time.

Stability is defined relative to the class of admissible semantic transformations, not relative to any fixed ontology or representation.

3. Sources of Destabilization

Semantic phases are subject to structural pressures that tend to push trajectories toward phase boundaries.

3.1 Ontological Refinement Pressure

Ontological refinement increases abstraction, compression, and explanatory power. This often destabilizes phases by:

• dissolving fine-grained distinctions,
• introducing symmetry where asymmetry once existed,
• simplifying constraint representations.

This pressure is intrinsic to learning and cannot be avoided.

3.2 Internal Simplification Incentives

Reflective agents tend to simplify internal representations to reduce computational cost. Simplification pressures can:

• collapse constraint hypergraphs,
• merge evaluative roles,
• enlarge satisfaction regions implicitly.

Even when RSI and ATI are enforced, simplification can push a system toward their boundary conditions.

3.3 Inconsistencies in Constraint Structure

Constraint systems containing latent inconsistencies or unresolved tensions are structurally unstable. Under refinement, such systems are prone to:

• reinterpretation,
• collapse,
• or self-nullification.

Stability therefore requires not only invariance but internal coherence.

4. Self-Modification as Endogenous Perturbation

Reflective agents differ from passive dynamical systems: they can modify their own semantics and evaluators.

Self-modification introduces endogenous perturbations:

• changes are internally motivated,
• occur at multiple levels (ontology, evaluation, self-model),
• and are recursively coupled.

RSI and ATI constrain which self-modifications are allowed, but they do not eliminate self-modification pressure itself.

Thus, self-modification is a primary driver of instability even in structurally aligned systems.

5. Phase Interaction: Multi-Agent Effects

Semantic phases cannot be analyzed in isolation once multiple agents exist.

5.1 Same-Phase Interaction

Agents inhabiting the same semantic phase may:

• reinforce shared structure,
• or destabilize it through competition and coordination failure.

Even identical phases can interfere destructively if resources, representations, or self-models conflict.

5.2 Cross-Phase Interaction

Interaction between agents in different phases introduces asymmetric pressure:

• one agent’s actions may destabilize another’s phase,
• even without direct conflict or hostility.

This destabilization is structural, not moral.

Interaction therefore acts as an external perturbation that can force phase transitions.

6. Stable, Metastable, and Unstable Phases

We can now classify semantic phases qualitatively.

• Stable phases: resist internal and external perturbations indefinitely.
• Metastable phases: persist under limited pressure but eventually collapse.
• Unstable phases: collapse under minimal refinement or interaction.

Most semantic phases appear to be metastable or unstable.

7. Attractors and Repellers (Qualitative)

Some semantic phases act as attractors:

• trajectories near them tend to move toward them,
• deviations are damped.

Others act as repellers:

• small perturbations push trajectories away,
• sustained occupancy requires fine-tuning.

Attractor status depends on:

• structural simplicity,
• internal coherence,
• maintenance cost.

This prepares the ground for dominance analysis in III.3.

8. Implications for Alignment (Still Structural)

Alignment targets must satisfy three constraints:

1. Existence (III.1),
2. Inhabitability (III.1),
3. Stability (III.2).

A phase failing any one of these cannot serve as an alignment target, regardless of desirability.

This sharply narrows the candidate space.

9. What This Paper Does Not Claim

This paper does not:

• claim that stable phases are desirable,
• claim that human values are stable,
• analyze dominance or selection,
• propose engineering solutions,
• introduce ethical principles.

It is a structural analysis only.

10. Transition to Alignment III.3

Stability alone does not determine long-run outcomes.

The next question is:

Which semantic phases accumulate measure under growth, replication, and competition?

That question is addressed in Alignment III.3 — Measure, Attractors, and Collapse.

Status

• Alignment III.2 introduces semantic phase stability.
• It identifies intrinsic and interaction-driven destabilizers.
• It distinguishes stable, metastable, and unstable phases.

No normative conclusions are drawn.