The Direction Problem: On the Causal Origin of Oriented Motion in Complex Systems

Author: Fabio Ghioni Ph.D. Affiliation: Ordinative Sciences Foundation Research Labs Version: Preprint v1.1 (May 2026 · revised September 2026) License: CC BY 4.0 Companion to: The Collapse Equation — DOI 10.5281/zenodo.19932312

Abstract

While constructing a predictive model for phase transitions in complex systems, we encountered a dilemma: the empirically measured acceleration constant g_j required a source that no known mechanism could supply. Starting from a simple observation — that every functional system exhibits a vector oriented toward the future — the paper follows a chain of logical elimination through the available candidate explanations.

The result is formalized as the Principle of Causal Inversion: every determined result occupies a coordinate in a space where time is treated as a navigable dimension, and emits a signal that orients the decoherent system toward it. The principle is applied to five open problems: the origin of genuine novelty, the arrow of time, the source of spontaneous impulses in neuroscience, and the acceleration observed before phase transitions.

Terminological note. Coherent and decoherent are used structurally, not in the quantum-mechanical sense: coherent denotes the domain of determined results, decoherent the domain in which a system moves toward them.

Status

v1.1 — notation aligned with the Ordinative Sciences Symbol Canon v1.2; under observation and continuous refinement.

The v1.1 revision changed no definition, claim or equation. It aligns four glyphs to the canon (𝒜 → 𝔸 attractor, 𝒯 → 𝕋 ordinative space, bare σ → σ_𝔸 attractor signal, ρ → ϱ form resistance), resolving collisions with symbols reserved elsewhere in the programme. Sections 6–7 of v1.0 are preserved verbatim as a pre-registration record of the empirical predictions.

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Citation

Ghioni, F. (2026). The Direction Problem: On the Causal Origin of Oriented Motion in Complex Systems (Preprint v1.1). Ordinative Sciences Foundation Research Labs.

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