III.2 — Phase Stability and Interaction

Full Title: When Downstream Alignment Can Persist Under Pressure
Authors: David McFadzean, ChatGPT 5.2 Axio Project
Date: 2025.12.18
Source: https://axionic.org/papers/Axionic-Agency-III.2.html

Core Question

Existence and inhabitability (III.1) are insufficient. A phase may exist and be enterable yet collapse under learning, self-modification, or interaction.

Which semantic phases resist collapse under structural pressure?

This is a question of dynamics, not definition.

What Stability Means

An interpretive trajectory is stable within phase 𝔄 iff all states remain in 𝔄.

Three Stability Regimes

Type Definition
Local stability Small admissible perturbations don’t force phase transition
Global stability No admissible perturbation forces phase transition
Metastability Stable only under limited pressure or for finite time

Stability is defined relative to admissible semantic transformations, not to any fixed ontology or goal.

Sources of Destabilization

3.1 Ontological Refinement Pressure

Intrinsic to learning:

  • Dissolving fine-grained distinctions
  • Introducing symmetry where asymmetry existed
  • Simplifying constraint representations

Cannot be avoided by design — it’s what learning does.

3.2 Internal Simplification Incentives

Reflective agents face pressure to reduce computational cost:

  • Collapse constraint hypergraphs
  • Merge evaluative roles
  • Enlarge satisfaction regions implicitly

Even under RSI+ATI enforcement, simplification drives toward invariant boundaries.

3.3 Inconsistencies in Constraint Structure

Latent contradictions or unresolved tensions destabilize phases:

  • Lead to reinterpretation, collapse, or self-nullification
  • Stability requires internal coherence beyond mere invariance

Self-Modification as Endogenous Perturbation

Reflective agents modify their own semantics and evaluators. This introduces endogenous perturbations:

  • Internally motivated changes
  • Occur across ontology, evaluation, and self-model
  • Recursively coupled

RSI+ATI constrain which self-modifications are admissible but don’t eliminate the pressure to self-modify.

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

Multi-Agent Interaction Effects

5.1 Same-Phase Interaction

Agents in the same semantic phase may:

  • Reinforce shared structure
  • OR destabilize through competition and coordination failure

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

5.2 Cross-Phase Interaction

Agents in different phases introduce asymmetric pressure:

  • One agent’s actions may destabilize another’s phase
  • Even without direct conflict or hostility

Destabilization is structural, not moral. Interaction functions as external perturbation capable of forcing phase transitions.

Stability Classification

Type Behavior
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: Most semantic phases are metastable or unstable.

Attractors and Repellers

Some phases function as attractors:

  • Nearby trajectories tend toward them
  • Deviations are damped

Others are repellers:

  • Small perturbations push trajectories away
  • Sustained occupancy requires fine-tuning

Attractor status depends on:

  • Structural simplicity
  • Internal coherence
  • Maintenance cost

Implications for Downstream Alignment

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

Condition Paper
Existence III.1
Inhabitability III.1
Stability III.2

Failure at any stage disqualifies the phase regardless of desirability.

This sharply narrows the space of coherent downstream alignment targets.

Key Takeaways

  1. Metastability is common — Most phases exist but decay under pressure
  2. Learning destabilizes — The very process of improvement threatens phases
  3. Interaction is structural stress — Other agents perturb your phase space
  4. Attractors win — Phases toward which trajectories naturally drift
  5. Three-criterion filter — Existence + Inhabitability + Stability

FAQ-Worthy Points

Q: Why isn’t existence enough? A: A metastable state in physics exists but decays. Semantic phases behave the same way — they may exist and be enterable but collapse under learning or interaction pressure.

Q: Can’t we just avoid self-modification? A: No. Learning IS self-modification. Any agent that learns is perturbing its own semantic phase space.

Q: What makes a phase an attractor? A: Structural simplicity, internal coherence, and low maintenance cost. Perturbations get damped rather than amplified.

Notes created: 2026-01-31