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# The Collapse Equation: Predicting Phase Transitions

**Author:** Fabio Ghioni Ph.D.
**Affiliation:** Ordinative Sciences Foundation Research Labs
**DOI:** [10.5281/zenodo.19932312](https://doi.org/10.5281/zenodo.19932312)
**Version:** 1.3 — empirically validated through eight micro-junctions
**License:** [CC BY 4.0](https://creativecommons.org/licenses/by/4.0/)

**Companion paper:** [*The Direction Problem*](../direction_problem/) — the causal argument behind g_j.

## Abstract

First empirical measurement of **g_j**, the ordinative acceleration constant — the universal measure of attractor signal intensity at a given scale. Every determined result in the coherent realm operates as an attractor: it emits a signal that pulls the decoherent system toward it. As the system approaches, the signal intensifies and g_j increases. The path is free; the destination is determined.

The model is grounded in Ordinative Set Theory (OST) and the Technology of Expressions (TE), using a Belousov-Zhabotinsky reaction-diffusion isomorphism. Two empirical validations (μ₁ = 7 April 2026, μ₂ = 29 April/1 May 2026) confirm the model in both timing and structural type.

**Status:** v1.3 — eight micro-junctions observed: six confirmed in timing and structural type, one under review, one window-consistent. Notation aligned with the Ordinative Sciences Symbol Canon v1.2. Under observation and continuous refinement.

## Files

| File | Format | Purpose |
|------|--------|---------|
| `Ghioni_2026_The_Collapse_Equation_v1_3.pdf` | PDF | Human reading |
| `Ghioni_2026_The_Collapse_Equation_v1_3.tex` | LaTeX | Overleaf source / editing |
| `Ghioni_2026_The_Collapse_Equation_v1_3.md` | Markdown | AI parsing |

The v1.2 files are retained in this folder: they are the version archived under DOI [10.5281/zenodo.19932312](https://doi.org/10.5281/zenodo.19932312).

## How to Cite

### BibTeX

```bibtex
@article{ghioni2026collapse,
  author    = {Ghioni, Fabio},
  title     = {The Collapse Equation: Predicting Phase Transitions --- Reaction-Diffusion Dynamics of Civilizational Systems with Triple-Scale Architecture and Structural Controfase},
  year      = {2026},
  version   = {1.3},
  doi       = {10.5281/zenodo.19932312},
  url       = {https://doi.org/10.5281/zenodo.19932312},
  publisher = {Zenodo},
  license   = {CC BY 4.0}
}
```

### APA

Ghioni, F. (2026). *The Collapse Equation: Predicting Phase Transitions — Reaction-Diffusion Dynamics of Civilizational Systems with Triple-Scale Architecture and Structural Controfase* (v1.2-beta). Zenodo. https://doi.org/10.5281/zenodo.19932312

### Plain Text

Fabio Ghioni Ph.D., "The Collapse Equation: Predicting Phase Transitions," Ordinative Sciences Foundation Research Labs, April 2026, v1.2 Beta. DOI: 10.5281/zenodo.19932312

## Part of the Ordinative Sciences Programme

This paper is part of the [Ordinative Sciences Framework](https://github.com/anckhalion/ordinative_sciences_framework). Canonical symbols are aligned with TE Vol 1 and OST Vol 2.

## License

This work is licensed under the [Creative Commons Attribution 4.0 International License](https://creativecommons.org/licenses/by/4.0/).

You are free to share and adapt this material for any purpose, provided you give appropriate credit, provide a link to the license, and indicate if changes were made.