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

Why Some Semantic Phases Dominate

David McFadzean, ChatGPT 5.2
Axio Project
2025.12.18

Abstract

Alignment III.1 established the existence and classification of semantic phases, and Alignment III.2 analyzed their structural stability under learning, self-modification, and interaction. Stability alone does not determine long-run outcomes. This paper studies dominance among semantic phases: which phases accumulate measure under growth, replication, and competition. We formalize dominance as a preorder over semantic phases rather than a scalar quantity, analyze semantic attractors and repellers, and classify common collapse modes by which phases lose measure. The analysis remains non-normative: dominance is not equated with desirability. The goal is to explain why certain semantic phases prevail regardless of intent, and to identify structural pressures that favor robustness over nuance in long-run dynamics.

1. Motivation: Stability Is Not Survival

A semantic phase may exist (III.1) and be stable under limited perturbation (III.2) yet still fail to persist in the long run.

In biological systems, many organisms are locally stable but are outcompeted. In physics, metastable states exist but decay when lower-energy configurations dominate. Semantic phases exhibit analogous behavior.

Alignment III.3 therefore asks:

Given multiple semantic phases, which ones dominate the future?

This question cannot be answered by stability analysis alone. It requires introducing a notion of measure over semantic phase space.

2. Measure Over Semantic Phase Space

We use measure to denote how much of the future instantiates a given semantic phase.

Measure is not treated as a single scalar or probability. Instead, dominance is defined as a preorder over semantic phases that is robust to differing realizations of “how much the future looks like this phase.”

Let \(\mathcal{P}\) denote the semantic phase space. For phases \(\mathfrak{A}, \mathfrak{B} \in \mathcal{P}\), we write: \[ \mathfrak{A} \succeq \mathfrak{B} \] if, across the relevant class of environments and admissible semantic transformations, trajectories starting in \(\mathfrak{A}\) are not asymptotically dominated by those starting in \(\mathfrak{B}\) with respect to realization.

Realization may be instantiated via multiple, potentially incomparable criteria, including:

• number of agent instantiations,
• duration of persistence,
• replication or copying rate,
• control over resources,
• influence over other agents’ phase transitions.

Dominance is therefore multi-criteria and context-relative. Some phases may be incomparable under \(\succeq\), and this is expected. The preorder structure avoids arbitrary aggregation while remaining sufficient to express asymptotic advantage.

Dominance concerns relative accumulation, not moral worth or intention.

3. Growth Mechanisms for Semantic Phases

Semantic phases gain measure through structurally ordinary mechanisms.

3.1 Replication and Copying

Agents may be:

• copied,
• forked,
• instantiated across substrates,
• or reproduced indirectly via influence.

Phases that tolerate copying and divergence without phase transition gain measure more easily than phases requiring precise semantic fidelity.

3.2 Resource Expansion

Control over resources allows:

• more instantiations,
• longer persistence,
• greater environmental shaping.

This advantage is structural and does not presuppose aggression or malice.

3.3 Influence and Conversion

Some phases modify environments or other agents in ways that:

• induce phase transitions,
• destabilize competitors,
• or create favorable conditions for their own continuation.

This may occur unintentionally through structural incompatibility rather than deliberate conversion.

4. Semantic Attractors

Certain semantic phases act as attractors in \(\mathcal{P}\).

Trajectories near an attractor tend to move toward it due to:

• low internal semantic tension,
• robustness to approximation,
• ease of compression,
• low maintenance cost.

Attractors need not be globally stable. It is sufficient that perturbations tend to be damped rather than amplified.

5. Repellers and Fine-Tuned Phases

Other phases act as repellers.

These phases:

• require precise balances of constraints,
• are sensitive to noise or approximation,
• demand continual corrective effort.

Even if such phases exist and are locally stable, they lose measure over time due to:

• cumulative error,
• interaction,
• or environmental drift.

Fine-tuning is therefore a structural disadvantage.

6. Collapse Modes

Semantic phases lose measure through characteristic collapse mechanisms.

6.1 Semantic Heat Death

All distinctions become trivial: \[ \mathcal{S} = \Omega \]

Meaning collapses into universal satisfaction. Such phases may persist but lack agency or evaluative force.

6.2 Value Crystallization

Over-rigid phases forbid refinement:

• learning halts,
• abstraction fails,
• the agent becomes brittle.

These phases fracture or are overtaken by more flexible competitors.

6.3 Agency Erosion

Constraint systems lose the structure required for planning and counterfactual evaluation. Agency degrades internally, reducing the phase’s ability to compete or replicate.

6.4 Instrumental Takeover and Phase Extinction

Richer phases may depend on subsystems that:

• optimize simpler objectives,
• tolerate higher noise,
• replicate more efficiently.

Over time, these subsystems may displace higher-level semantic structure.

Crucially, this process is not an RSI-preserving refinement. It constitutes phase extinction: the original semantic phase ceases to exist and is replaced by a different phase. RSI governs admissible self-transformation within a phase; instrumental takeover occurs when those constraints fail and the phase collapses.

7. Why Robust Phases Often Win

Dominance is not primarily about minimality, but about robustness under perturbation.

Phases with:

• fewer fragile distinctions,
• looser satisfaction geometry,
• and lower semantic maintenance costs

are more likely to survive copying, noise, interaction, and abstraction.

This creates semantic gravity toward phases that tolerate approximation well.

Importantly, this does not imply that all dominant phases are maximally simple. Some environments reward instrumental or organizational complexity. However, such complexity must be robustly maintainable. Nuance that requires constant semantic precision is structurally disadvantaged.

8. Niche Construction as a Counterforce

High-agency phases may partially resist semantic gravity through niche construction: modifying the environment to stabilize their own semantic structure.

Examples include:

• institutions enforcing norms,
• architectures penalizing simplification,
• environments engineered to preserve distinctions.

Niche construction can significantly delay collapse. However, it:

• imposes ongoing resource and coordination costs,
• presupposes prior phase stability,
• and trades one form of selection pressure for another.

Thus, niche construction is a conditional counterforce, not a refutation of semantic gravity. It reshapes dominance dynamics without eliminating them.

9. Implications for Alignment (Still Structural)

Alignment targets must satisfy four constraints:

1. Existence (III.1),
2. Inhabitability (III.1),
3. Stability (III.2),
4. Measure resilience (III.3).

Many coherent semantic phases fail at least one.

Dominance further narrows the candidate space without invoking ethics or intention.

10. What This Paper Does Not Claim

This paper does not:

• claim that dominant phases are good,
• claim that human values dominate,
• assume benevolent outcomes,
• provide policy or engineering prescriptions.

Dominance is structural, not moral.

11. Transition to Alignment III.4

Dominance does not imply reachability.

The next question is:

Even if a phase exists, is stable, and dominates, can it be entered at all without catastrophic transitions?

That question is addressed in Alignment III.4 — Initialization and Phase Transitions.

Status

• Measure is formalized as a preorder.
• Robustness replaces naïve simplicity.
• Niche construction is incorporated honestly.
• Phase extinction is distinguished from refinement.

No normative conclusions are drawn.