# 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](https://creativecommons.org/licenses/by/4.0/)
**Companion to:** [*The Collapse Equation*](../collapse_equation/) — DOI [10.5281/zenodo.19932312](https://doi.org/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.

## Files

| File | Format | Purpose |
|------|--------|---------|
| `Ghioni_2026_The_Direction_Problem_v1_1.pdf` | PDF | Human reading (25 pp.) |
| `Ghioni_2026_The_Direction_Problem_v1_1.tex` | LaTeX | Source |
| `Ghioni_2026_The_Direction_Problem_v1_1.md` | Markdown | AI parsing |

## 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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