Abstract
FIRM is an axiomatic programme that derives quantitative physics ex nihilo. From five purely mathematical axioms we construct the Grace operator G and work in its fixed-point category Fix(G). The resulting φ-recursive structure fixes dimensionless couplings, mass ratios, and cosmological observables as mathematical invariants—no empirical inputs, no parameter fitting, no posterior tuning. All predictions are registered a priori and accompanied by cryptographic, machine-verifiable provenance.
- Fine-structure constant, mass ratios, and cosmology from φ-recursion
- CMB spectrum with acoustic peaks at ℓ ≈ ℓ₁ φⁿ and correct damping tail
- Zero fitting/tuning; explicit falsifiability and provenance seals
Paper (Embedded)
Open the full PDF for figure captions and derivation details.
Overview Video
Selected Figures
Reproduce in One Command
Clone, install, and build the paper and figures:
git clone https://github.com/ktynski/FIRM-Fractal-Identity-Recursive-Mechanics.git
cd ExNahiloReality
pip install -e .
PYTHONPATH=$PWD python regenerate_figures.py
cd arxiv_paper/FIRM_FINAL_SUBMISSION_arxiv_tmp && pdflatex -interaction=nonstopmode main.texProvenance bundle: download JSON (figure provenance + commit hash).
FAQ
No. The pipeline forbids parameter fitting/tuning. Disagreement falsifies the framework.
From $\Fix(\mathcal{G})$ and $\phi$-recursion. See paper Methods and `constants/`.
Run the one-command steps, compare outputs, check sealed provenance JSON.
Cite
@article{FIRM2025,
title={FIRM: Fractal Identity \& Recursive Mechanics},
author={Tynsk, Kristin and Sage},
journal={arXiv preprint},
year={2025},
url={https://ktynski.github.io/FIRM-Fractal-Identity-Recursive-Mechanics/},
}