Axionic Agency III.2 — Phase Stability and Interaction

When Downstream Alignment Can Persist Under Pressure

David McFadzean, ChatGPT 5.2 Axio Project 2025.12.18

Abstract

Axionic Agency 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.

In downstream terms, this asks whether an object that could serve as an alignment target can persist over time without collapsing, trivializing, or drifting under reflective pressure. We analyze sources of destabilization internal to reflective agents and external to them, define qualitative notions of local, global, and metastable stability, and examine how interaction between agents in the same or different semantic phases alters stability properties. No claims are made about desirability, safety, or dominance. The goal is structural: to identify which semantic phases are capable of persisting over time at all.

1. Motivation: Existence Is Not Enough

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

Accordingly, the downstream alignment question becomes:

Which semantic phases resist collapse under structural pressure?

This is a question of dynamics, not definition.

2. What Stability Means in Semantic Phase Space

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

An interpretive trajectory

\[ \mathcal{I}_0 \rightarrow \mathcal{I}_1 \rightarrow \mathcal{I}_2 \rightarrow \dots \]

is stable within a phase \(\mathfrak{A} \in \mathcal{P}\) iff 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, representation, or goal.

3. Sources of Destabilization

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

3.1 Ontological Refinement Pressure

Ontological refinement increases abstraction, compression, and explanatory power. This 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 by design.

3.2 Internal Simplification Incentives

Reflective agents face internal pressure to simplify representations to reduce computational cost. Simplification can:

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

Even when RSI and ATI are enforced, simplification can drive systems toward invariant boundary conditions.

3.3 Inconsistencies in Constraint Structure

Constraint systems with latent inconsistencies or unresolved tensions are structurally unstable. Under refinement, such systems tend toward:

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

Stability therefore requires internal coherence in addition to invariance.

4. Self-Modification as Endogenous Perturbation

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

Self-modification introduces endogenous perturbations:

• changes are internally motivated,
• occur across ontology, evaluation, and self-model,
• and are recursively coupled.

RSI and ATI constrain which self-modifications are admissible, but they do not eliminate the pressure to self-modify itself.

Thus self-modification is a primary driver of instability even within structurally aligned phases.

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 when resources, representations, or self-models conflict.

5.2 Cross-Phase Interaction

Interaction between agents in different semantic phases introduces asymmetric pressure:

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

This destabilization is structural rather than moral. Interaction functions as an external perturbation capable of forcing 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.

Preliminary analysis suggests most semantic phases are metastable or unstable.

7. Attractors and Repellers (Qualitative)

Some semantic phases function as attractors:

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

Others function as repellers:

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

Attractor status depends on:

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

This sets up the measure-theoretic analysis in Axionic Agency III.3.

8. Implications for Downstream Alignment (Still Structural)

For a semantic phase to serve as a downstream alignment target, it must satisfy three independent conditions:

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

Failure at any stage disqualifies the phase regardless of desirability or intent.

This sharply narrows the space of coherent downstream alignment targets.

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 Axionic Agency 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 Axionic Agency III.3 — Measure, Attractors, and Collapse.

Status

Axionic Agency III.2 — Version 2.0

Semantic phase stability defined under admissible refinement. Intrinsic and interaction-driven destabilizers identified. Stable, metastable, and unstable phases distinguished. Downstream alignment reframed as a persistence question. No normative conclusions drawn.