Artificial F1: Full Computational Model - Selection Hardness, Non-Scalarizability, and Phase Transition in Bounded Evaluative Architectures

Published June 3, 2026 | Version v2

Preprint Open

We introduce a formal framework for bounded evaluative architectures

in which signal admission precedes task specification. The central

object is a gating operator F1: S -> S' that constitutes a

selection-conditioned subspace S' subset S prior to any encoding,

learning, or reward optimisation. We prove three main results. First,

valence-conditioned evaluation over S' is non-scalarizable (Theorem

2A-1): the multi-dimensional preference structure induced by

selection-conditioned access violates the totality condition required

for scalar representation, and selection-conditioning generates

incommensurability — a strictly stronger failure — across distinct

selection-conditioned submanifolds. Second, the evaluative state F2(t)

satisfies a stochastic differential equation whose stationary

distribution and stability properties depend on the selection hardness

H_s(G) and noise variance sigma^2 (Theorems 2A-2, 2A-3). Third, the

action-selection entropy exhibits a phase transition at the gating

threshold: a discontinuity that cannot arise in scalar-reward systems

with smooth policies, and that is architecture-invariant below the

collapse threshold gamma* while architecture-dependent above it. We

introduce Selection Hardness H_s(G) as a measurable quantity connecting

these theoretical results to empirical predictions developed in the

companion paper. This paper makes no empirical claims; all experimental

validation is deferred to the companion empirical paper.

Companion Papers:

**Saka, H. (2026a).** Toward a Reframing of the Hard Problem of Consciousness: Subjective Reality, Feeling, and
the Origins of the Conceptual World. Version 7.19. PhilPapers. https://philpapers.org/rec/SAKTAR
**Saka, H. (2026b).** Organizational Phenomenology: Artificial F1 and the Geometry of Coherent Agency. https://doi.org/10.5281/zenodo.20555024
**Saka, H. (2026d-Emperical).** Hard-Gating Collapse Dynamics: Selection Hardness as the Organizing Parameter for Robust Sparse Routing. https://doi.org/10.5281/zenodo.20523503

Keywords:

selection-conditioned representation, non-scalarizability, selection hardness,

phase transition, gating architecture, bounded evaluation, RLHF, dynamical systems

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