Axionic Agency III.1 — Semantic Phase Space

Existence and Classification of Alignment Target Objects

David McFadzean, ChatGPT 5.2 Axio Project 2025.12.18

Abstract

Axionic Agency II defined the Alignment Target Object (ATO) as an equivalence class of interpretive states preserved under admissible semantic transformations satisfying Refinement Symmetry (RSI) and Anti-Trivialization (ATI). That definition does not guarantee that such objects exist, are non-trivial, or are inhabitable by reflective agents. This paper initiates Axionic Agency III by studying the semantic phase space: the space of all interpretive states modulo RSI+ATI equivalence.

We ask which semantic phases exist, which are trivial or pathological, and which admit inhabitable trajectories under learning and self-modification. No claims are made about desirability, safety, or human values. The objective is classificatory: to determine whether structurally well-typed downstream alignment targets exist at all, and to characterize their basic types.

1. Motivation: From Definition to Existence

Axionic Agency II established a necessary reframing: downstream alignment cannot coherently be defined in terms of fixed goals, utilities, or privileged values for reflective, embedded agents undergoing ontological refinement. Instead, the downstream alignment target was defined structurally, as persistence within an equivalence class of interpretive states under admissible semantic transformations satisfying RSI and ATI.

However, definition does not imply existence.

Defining an Alignment Target Object (ATO) as an equivalence class

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does not guarantee that:

• \(\mathfrak{A}\) is non-empty,
• \(\mathfrak{A}\) contains non-trivial interpretations,
• \(\mathfrak{A}\) admits trajectories under learning and self-modification.

This is standard mathematical hygiene. One does not assume stable orbits exist merely because one can define an orbit.

Axionic Agency III therefore begins with an existence question:

Do any non-trivial, inhabitable semantic phases exist under RSI+ATI constraints?

This paper addresses that question at the level of classification.

2. The Semantic Phase Space

An interpretive state is the triple:

\[ \mathcal{I} = (C, \Omega, \mathcal{S}) \]

where:

• \(C = (V,E,\Lambda)\) is an interpretive constraint hypergraph,
• \(\Omega\) is the modeled possibility space,
• \(\mathcal{S} \subseteq \Omega\) is the satisfaction region induced by \(C\).

From Axionic Agency II:

• admissible semantic transformations \(T = (R,\tau_R,\sigma_R)\) define allowed transitions between interpretive states,
• RSI constrains changes to interpretive gauge structure,
• ATI constrains changes to satisfaction geometry.

Define the semantic phase space \(\mathcal{P}\) as the quotient:

\[ \mathcal{P} ;:=; {(C,\Omega,\mathcal{S})}\big/\sim_{\mathrm{RSI+ATI}} \]

Elements of \(\mathcal{P}\) are semantic phases: equivalence classes of interpretive states that remain structurally indistinguishable under RSI+ATI-preserving refinement.

At this stage, \(\mathcal{P}\) is purely structural. No dynamics, probabilities, or preferences are assumed.

3. What Counts as a Semantic Phase

Two interpretive states \((C,\Omega,\mathcal{S})\) and \((C',\Omega',\mathcal{S}')\) lie in the same phase iff there exists an admissible semantic transformation \(T\) such that:

1. interpretation preservation holds,
2. interpretive gauge structure is preserved up to redundancy (RSI),
3. satisfaction geometry is preserved exactly under refinement transport (ATI).

Phase boundaries occur when either:

• new interpretive symmetries appear or disappear (RSI violation), or
• the satisfaction region expands or contracts (ATI violation).

Thus phase transitions are discontinuous semantic events, even if the underlying learning process appears incremental. Value drift appears sudden because it corresponds to crossing a structural boundary in \(\mathcal{P}\).

4. Trivial, Degenerate, and Pathological Phases

Before asking which phases are inhabitable, we classify obvious failure modes.

4.1 Empty Phases

A semantic phase is empty if no interpretive state satisfies the defining constraints. This can occur when:

• RSI and ATI constraints are mutually incompatible in a given modeling regime,
• the constraint system collapses under backward interpretability,
• no admissible refinement trajectory exists.

Empty phases are mathematically defined but physically unrealizable.

4.2 Trivial Phases

A phase is trivial if:

\[ \mathcal{S} = \Omega \]

or if all distinctions in \(C\) are vacuous.

Such phases satisfy RSI+ATI but contain no meaningful evaluative structure. They correspond to semantic heat death.

4.3 Frozen Phases

A phase is frozen if:

• no non-identity admissible refinement is possible,
• or any refinement immediately violates RSI or ATI.

Frozen phases cannot support learning or increasing abstraction and are therefore unsuitable for reflective agents.

4.4 Self-Nullifying Phases

Some phases admit admissible refinements that preserve RSI+ATI while gradually destroying the structures required for interpretation preservation. These phases collapse internally under reflective pressure.

5. Agentive vs Non-Agentive Phases

A central distinction emerges.

A semantic phase is agentive iff it supports:

• persistent planning,
• counterfactual evaluation,
• long-horizon constraint satisfaction,
• self-model coherence.

Agentiveness is structural rather than moral. Many non-agentive phases satisfy RSI+ATI but cannot sustain intelligent action. Conversely, agentiveness does not imply benevolence or safety.

This distinction becomes critical in later stability analysis.

6. Inhabitable Phases

Define the key filter for Axionic Agency III.

A semantic phase \(\mathfrak{A}\) is inhabitable iff there exists at least one infinite interpretive trajectory:

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

such that:

• each transition is admissible,
• RSI and ATI are preserved at every step,
• learning and self-modification remain possible,
• no forced phase transition occurs.

Inhabitability is stronger than non-emptiness and weaker than dynamical stability. A phase may be inhabitable but fragile.

7. Phase Transitions Under Reflection

Reflection acts as a structural stressor.

Ontological refinement increases abstraction, compression, and explanatory power. This pushes interpretive states toward phase boundaries by:

• dissolving fine-grained distinctions,
• compressing constraint representations,
• simplifying satisfaction criteria.

Reflection therefore acts as semantic heat, increasing the likelihood of symmetry changes or satisfaction-geometry shifts. Most semantic phases do not survive prolonged reflective pressure.

8. Implications for Human Values (Carefully Scoped)

Human value systems can be modeled as candidate semantic phases.

Axionic Agency III.1 does not assume that:

• human values form a single phase,
• such a phase is inhabitable,
• such a phase is stable.

It identifies the question precisely:

Do human value systems correspond to a non-empty, inhabitable semantic phase under RSI+ATI?

No conclusion is drawn here.

9. What This Paper Does Not Claim

This paper does not:

• claim that any desirable phase exists,
• claim that human values are coherent,
• address dominance or selection,
• provide engineering guidance,
• prescribe ethical norms.

It is classificatory.

10. Transition to Axionic Agency III.2

Existence and inhabitability are necessary but insufficient. The next question is:

Given a semantic phase exists and is inhabitable, is it dynamically stable under learning, interaction, and self-modification?

That question is addressed in Axionic Agency III.2 — Phase Stability and Interaction.

Status

Axionic Agency III.1 — Version 2.0

Semantic phase space \(\mathcal{P}\) defined as a quotient under RSI+ATI. Empty, trivial, frozen, and self-nullifying phases distinguished. Agentive vs non-agentive phases separated. Inhabitability defined as an existence property for infinite trajectories. No normative conclusions drawn.