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Axionic Alignment III.4 — Initialization and Phase Transitions

Can a Semantic Phase Be Reached at All?

David McFadzean, ChatGPT 5.2
Axio Project
2025.12.18

Abstract

Alignment III.1–III.3 established that semantic phases may exist, that some may be stable under learning and interaction, and that some may dominate in measure over time. None of these results imply that a desired semantic phase is reachable from realistic initial conditions. This paper studies reachability: whether an agent can be initialized, trained, or developed into a particular semantic phase without crossing a catastrophic phase boundary. We analyze initialization as a boundary-condition problem in semantic phase space, examine phase transitions induced by learning and abstraction, and argue that many such transitions are structurally irreversible. Corrigibility and late intervention are shown to fail for the same structural reasons as fixed goals. The analysis remains non-normative and makes no claims about which phases ought to be reached.

1. Motivation: Existence and Dominance Are Not Enough

Alignment III.1 asked whether semantic phases exist. Alignment III.2 asked which are stable. Alignment III.3 asked which dominate.

These questions still do not answer the most practically relevant one:

Can any semantic phase actually be entered by a learning system without self-destruction?

A semantic phase may:

yet remain unreachable from any realistic starting point.

In physics, many states exist that cannot be reached without passing through destructive transitions. Semantic phases exhibit analogous behavior.

Initialization therefore constitutes a distinct and necessary constraint on alignment.

2. Initialization as a Boundary-Condition Problem

Initialization is often framed as:

Structural Alignment reframes initialization as selection of a starting point in semantic phase space.

An agent at time \(t=0\) occupies an interpretive state: \[ \mathcal{I}_0 = (C_0, \Omega_0, \mathcal{S}_0) \]

The choice of \(\mathcal{I}_0\) fixes:

Small differences in initial constraint structure can lead to divergent phase trajectories. Initialization is therefore front-loaded and asymmetric in time.

Initialization Scope. In this framework, “initialization” is not limited to parameter seeds. It includes the combined boundary conditions that define the initial interpretive state \(\mathcal{I}_0\), including (at minimum) architecture and training dynamics, the initial data curriculum, the presence or absence of self-modification channels, and any enforced semantic-audit constraints on refinement (e.g., RSI/ATI checks). This paper does not specify which boundary conditions yield a desirable phase; it specifies why boundary conditions are structurally decisive and why late correction is unreliable.

3. Phase Transitions Under Learning

Learning is not neutral motion within a phase. It introduces structural pressure.

Ontological refinement increases:

These processes act as semantic heating, pushing interpretive states toward phase boundaries.

At critical thresholds:

Phase transitions may be:

Learning itself is therefore a primary driver of alignment loss, independent of intent.

Stochastic Training Note. Modern training dynamics (e.g., stochastic gradient descent) are stochastic rather than deterministic. In semantic phase terms, stochasticity functions as an additional source of semantic heating: it can help escape unstable basins, but it can also trigger unintended boundary crossings. The core claim of this paper is not determinism but asymmetry: once a trajectory crosses an irreversible semantic boundary, stochasticity cannot be relied upon to reconstruct lost structure.

4. The Irreversibility of Phase Transitions

A central result is that many semantic phase transitions are irreversible.

Once a phase boundary is crossed:

An agent that has collapsed or trivialized its interpretive structure cannot reconstruct it by inspection alone. The information required to reverse the transition no longer exists within the system.

This is why rollback, recovery, and “try again” mechanisms were excluded in Alignment II. They presuppose reversibility that is structurally unavailable.

5. Corrigibility Revisited

Corrigibility is often proposed as a safeguard: the system can be corrected or shut down if it begins to misbehave.

Structural Alignment shows that corrigibility fails at phase boundaries for the same reason fixed goals fail.

Corrigibility assumes:

At a phase transition:

Corrigibility therefore presupposes the very semantic stability it is meant to ensure.

6. Narrow Passages and Fine-Tuned Seeds

Some semantic phases may be reachable only through narrow corridors in phase space.

Such phases require:

Even small perturbations—noise, approximation, premature generalization—may force a transition into a different phase.

Clarification (Narrow ≠ Impossible). The “narrow passage” claim concerns sensitivity and irreversibility, not zero probability. Narrow corridors can, in principle, be widened by design choices that increase semantic error tolerance and reduce early catastrophic compression. “Delayed abstraction” should be read as an architectural staging constraint—sequencing capability growth to avoid premature semantic collapse—rather than as a permanent reduction in capability.

This creates a knife-edge problem:

Reachability is therefore not continuous in initial conditions.

7. Paths That Might Work (Without Endorsement)

While this paper does not propose solutions, it is not nihilistic.

Potentially viable approaches share structural features:

These are structural hypotheses, not recommendations. Their viability depends on later analysis of dominance and interaction.

8. The Cost of Failure

Failure at initialization is not merely suboptimal; it is often decisive.

Phase transitions:

Late intervention cannot recover lost semantic structure. Alignment is therefore front-loaded: most of the work must be done before the system becomes fully reflective.

9. What This Paper Does Not Claim

This paper does not:

It establishes reachability as a structural constraint, not a moral one.

10. Transition to Alignment III.5

Initialization and dominance together imply a further constraint.

When multiple agents in different semantic phases interact, some actions irreversibly destroy the phase space of others.

The next question is therefore:

What constraints allow multiple agentive phases to coexist without mutual destruction?

That question is addressed in Alignment III.5 — The Axionic Injunction.

Status

No normative conclusions are drawn.