TFPT is a falsifiable, machine-checked framework that reconstructs major dimensionless structures
of particle physics, gravity and cosmology from a = (1, 1, 2) and π — a candidate
parameter-free compiler for the dimensionless skeleton of fundamental physics.
▶︎ Understand it in 5 minutes · ⚡ Run the verifier · 📄 Read the theory
This repository contains the complete theory, 23 frozen predictions, three independent verification engines (Python + Wolfram + Lean), and a versioned status ledger that types every claim — including its explicit open problems and falsification criteria.
Different readers want different proof. Pick your route:
| I am… | Start with |
|---|---|
| a physicist | docs/FOR_PHYSICISTS.md — the assumptions, the derivation, the open interfaces |
| a mathematician | docs/FOR_MATHEMATICIANS.md — the E8 closure and the formal certificates |
| here to verify the claims | Run the 30-second verifier, then docs/VERIFICATION.md |
| here for the intuition | the 5-minute film |
| here to falsify it | docs/FALSIFICATION.md — the kill tests |
Re-derive TFPT's headline claims from the two axioms, in about a second:
git clone https://github.com/sthamann/tfpt && cd tfpt
pip install -r requirements.txt
./verify # ~1s : the core claim, re-derived from the axioms
./verify --full # ~4min : the entire Python suite (ALL CHECKS PASSED)
./verify --release # : documents + suite + website + sync auditNo local toolchain? docker run --rm ghcr.io/sthamann/tfpt:latest. The three independent engines
are one flag away: ./verify --wolfram, ./verify --lean, ./verify --audit. Full detail in
docs/VERIFICATION.md.
Not everything below has the same epistemic status, and saying so is the point:
| Claim | Result | Status |
|---|---|---|
E8 closure |
(D5 ⊕ A3) + μ4 ≅ E8, 240 roots, glue index 4 |
Exact — machine-proven lattice identity [E] |
| Number of generations | N_fam = 3 |
Exact within the compiler [E] |
| Fine-structure constant | α⁻¹ = 137.0359992 |
Exact numerical identity — unique Ward root, interval-verified [E] (1.9σ from CODATA-2022) |
| Physical origin of the seam | SEAM.EQUIV.01 |
Open — closed modulo a cited theorem, not proven end-to-end [O] |
| Cosmic birefringence | β = φ₀/(4π) ≈ 0.2424° |
Falsifiable prediction — decided by CMB polarimetry [X] |
Markers: [E] exact/machine-proven · [C] conditional · [O] open/axiom · [X] kill test. The
authoritative per-claim status is verification/status_ledger.csv
— the ledger wins. Full matrix and marker system in docs/CLAIMS.md.
The discrete/algebraic compiler is closed ([E]). The honest residual is three named interface
problems, not a diffuse list:
| Interface | Question | Status |
|---|---|---|
v_geo |
the one metrology unit (= 1/√G); No-Unit Thm: a scale-invariant seam has no compiler scale |
primitive [O] |
SEAM.EQUIV.01 |
the raw seam is the holomorphic (E8)₁ net |
[C] — closed modulo a cited theorem |
F_transfer |
one functor, four typed interfaces (Koide, η_B, axion, m_p/m_e) |
[C] |
TFPT does not claim a certified Theory of Everything — the full treatment (parameter-free
gravity, the all-orders perturbative leg, the SEAM.EQUIV.01 status) is in
docs/OPEN_PROBLEMS.md.
The predictions are frozen before the data (predictions_frozen.json,
2026-06-09) and locked to their formulas on every run. A confirmed measurement outside a window
kills the claim:
| Observable | TFPT frozen value | Decided by |
|---|---|---|
| Leptonic CP phase | δ_PMNS = 240° (Galois-locked) |
DUNE, Hyper-K |
| Cosmic birefringence | β ≈ 0.2424° |
CMB polarimetry |
| Reactor angle | sin²θ₁₃ = 0.02311 (now ~2.0σ tension) |
JUNO |
All kill tests, the null model (200,000 look-alikes score ≤ 5/13; TFPT 13/13), and the live
scorecard: docs/FALSIFICATION.md ·
fixpoint-theory.com/falsification.
For a fundamental-physics theory, openly invited criticism is a trust signal. The most valuable contributions, in order of impact:
- Reproduce or falsify a frozen prediction.
- Find a circular dependency — a "derived" quantity that used its own target.
- Identify an unstated physical assumption doing load-bearing work.
- Challenge a claimed uniqueness result (the
E8glue, theα⁻¹root). - Close or kill one of the three open interfaces.
Ready-made issue templates exist for exactly these: claim challenge, reproduction failure, mathematical counterexample, physical interpretation, prediction update, and documentation. This repository is meant to be a scientific discussion space, not just an archive.
├── verify # the one-command verifier (quick / --full / --release)
├── README.md # you are here
├── docs/ # THEORY · CLAIMS · OPEN_PROBLEMS · FALSIFICATION
│ # VERIFICATION · FOR_PHYSICISTS · FOR_MATHEMATICIANS
├── verification/ # 491 machine-checked modules, run_all.py, the status ledger,
│ # the Wolfram second path, the red-team layer
├── experiments/ # research explorations + the Lean 4 proofs (not claims until promoted)
├── website/ # the public mirror (fixpoint-theory.com), kept byte-identical by the audit
├── *.tex # the 9 active theory documents (see docs/THEORY.md)
└── build.sh # the build + sync pipeline (notes · gen · website · audit · release)
Disambiguation: this is the physics theory TFPT (a compiler closure for the Standard Model). It is not the unrelated Brouwer–Lefschetz "topological fixed point theory" of mathematics.
@misc{hamann2026tfpt,
title = {Topological Fixed-Point Theory (TFPT): Two Axioms, One Compiler,
the Standard-Model Skeleton Derived},
author = {Hamann, Stefan and Rizzo, Alessandro},
year = {2026},
note = {Version 5.4},
doi = {10.5281/zenodo.20846087},
url = {https://doi.org/10.5281/zenodo.20846087}
}- Website (interactive): https://www.fixpoint-theory.com — reading guide, compiler walkthrough, in-browser reproducer for every script.
- Archived deposit (DOI): https://doi.org/10.5281/zenodo.20846087 (Zenodo, v5.4).
- AI/agent context: https://www.fixpoint-theory.com/llms.txt
Claim discipline: nothing in this repository is marked closed that is not machine-verified, and no dimensionful quantity is claimed as a derivation from pure numbers.