The Collapse Equation: Predicting Phase Transitions

Author: Fabio Ghioni Ph.D. Affiliation: Ordinative Sciences Foundation Research Labs DOI: 10.5281/zenodo.19932312 Version: 1.3 — empirically validated through eight micro-junctions License: CC BY 4.0

Companion paper: The 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.

How to Cite

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. 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.

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.