This repository contains the source of the Cosmochrony paper.

Cosmochrony is a pre-geometric theoretical framework in which time ordering, spacetime geometry, dynamics, and matter emerge from the irreversible relaxation of a single relational substrate, denoted $\chi$.

The framework does not assume a pre-existing spacetime manifold, metric, or fundamental quantization. Instead, familiar physical structures are recovered as regime-dependent effective descriptions arising through projection and coarse-graining of the underlying $\chi$ dynamics.

Core Thesis

Cosmochrony is based on the following central statements:

1. Time is not fundamental
   Time corresponds to the intrinsically directed (irreversible) relaxation or ordering of $\chi$, rather than to an external parameter.

2. Spacetime is emergent
   Spacetime geometry arises as an effective, continuum encoding of microscopic relational connectivity, reconstructed through spectral methods in appropriate limits.

3. Observables are projected quantities
   Physical observables belong to an effective spacetime-level descriptor $\chi_{eff}$, obtained through a generally non-injective projection from $\chi$. As a result, effective descriptions can underdetermine the underlying configuration.

4. Dynamics are derived, not postulated
   The dynamical law governing $\chi$ and the effective Born–Infeld-like action are obtained ab initio from structural constraints on relaxation and causal saturation of fluxes.

The $\chi$ Substrate

• $\chi$ is not a scalar field defined on spacetime
• it is a pre-geometric, relational substrate
• it does not carry values in space or time
• spacetime notions arise only in projectable regimes

A key distinction is made between:

• $\chi$, the fundamental relational substrate
• $\chi_{eff}$, an effective scalar descriptor used once a stable geometric regime exists

The mapping $\chi → \chi_{eff}$ is generally non-injective, which constrains reconstruction and plays a central role in the emergence of effective indeterminacy.

Causality and Bounds

Cosmochrony distinguishes between:

• $c_{\chi}$: a structural bound governing pre-temporal relaxation fluxes
• $c$: the emergent causal constraint within effective spacetime descriptions

This distinction resolves apparent circularities between dynamics and geometry and underlies the recovery of relativistic causality as an effective limit.

Matter, Gravitation, and Spectra

Within Cosmochrony:

• Localized, stable configurations of $\chi$ correspond to matter-like excitations
• Stability is characterized by spectral signatures, rather than fundamental couplings
• Mass arises from resistance to relaxation, not from a Higgs-type mechanism
• Gravitation emerges from sustained constraints on $\chi$ relaxation, recovered as an effective geometric description

Spacetime curvature, time dilation, and gravitational dynamics are obtained as thermodynamic or continuum limits of relational structure.

Quantum-like Phenomena

Quantum behavior is not postulated as fundamental.

Instead:

• quantization arises at the effective level
• quantum correlations emerge from shared $\chi$ configurations and projection structure
• nonlocal correlations do not require fundamental superluminal influence
• the wavefunction is an effective descriptor, not an ontological object

Cosmology and Strong-Gravity Regimes

Cosmological and strong-gravity behavior follow from the same underlying relaxation dynamics:

• large-scale expansion arises from global relaxation structure
• apparent acceleration is cumulative and regime-dependent
• horizon-like thresholds correspond to deprojection regimes where effective descriptions become fragile
• black-hole-like behavior is reinterpreted in terms of relaxation saturation and reprojection dynamics

Status of the Framework

Cosmochrony is:

• foundational and pre-geometric
• conceptually closed at the dynamical level
• incomplete at the phenomenological and experimental level

It does not claim:

• experimental validation
• full derivation of all Standard Model phenomenology
• final unification

It does provide:

• a derived dynamical core
• a coherent ontological structure
• explicit effective limits
• avenues for falsifiable development

Repository Contents

paper/
├── pdf/ # Compiled Cosmochrony PDF
├── tex/ # LaTeX sources
├── figures/ # Diagrams and illustrations
└── README.md

Links

• 📄 Paper PDF: https://github.com/Cosmochrony/paper
• 🌐 Website: https://cosmochrony.org
• 💻 GitHub organization: https://github.com/Cosmochrony

Citation

If you reference this work, please cite:

J. Beau, Cosmochrony: A Pre-geometric Framework for Emergent Spacetime,
Dynamics, and Matter, Zenodo, 2025.

Acknowledgements

Portions of the conceptual development, formal clarification, and editorial refinement of Cosmochrony benefited from iterative interactions with large language models. These tools were used as analytical assistants for exploring alternative formulations, testing internal consistency, and improving clarity of presentation. All theoretical claims, structural choices, and final formulations remain the sole responsibility of the author.

Contributions

This repository is intended as a research reference.

Critical feedback, independent analyses, and theoretical scrutiny are welcome. Please open an issue to discuss conceptual points or potential extensions.