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 five and a half minutes · ⚡ Run the verifier · 📄 Read the theory
This repository contains the complete TFPT compiler-closure document set, 27 status-graded, falsifiable test surfaces (the 16-entry core registry frozen before the data), three independent verification engines (Python + Wolfram + Lean), and a versioned status ledger that types every claim — including its explicit open problems and falsification criteria.
The new consolidated research map connects the post-Round27 archive to the updated papers and public overview. The original filled QWZ strip now supports a source-based charged CAR field limit with both adjoints and energy control. A separate compact-U(1) test parent has all-time lattice dynamics and neutral physical ground-state representations. Clock, cocycle and parent-selection audits identify the remaining source-to-E8 bridge. These constructions are not yet one derived microscopic theory; all physical T1–T8 gates remain open.
Earlier records keep their source-pinned historical wording. Related double-cover, inter-sheet and prime-event investigations are shipped with their own scope and negative controls, not as TOE or RH solutions.
The research contracts through Round27 now accompany the updated papers and public research overview. The latest finite-regulator result removes an artificial charge factor from the signed-history error bounds, improves certified charge/hop cutoffs, and supplies a nonzero quadratic-memory cutoff after the signed sum. It does not evaluate the complete interacting partition or close the physical T1–T8 gates. Earlier round records retain their original local-only wording as historical provenance; this integration ships the archive without rewriting those source-pinned snapshots.
The 5½-minute film — updated 2026-08-31: compiler, alpha fixed point, dual status card, the August structural wave, falsification discipline, live predictions.
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 5½-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 # ~4-5h : the entire Python suite, 1028 modules (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.
Strict TOE status (2026-09-05): v1026–v1030 narrow only TEL-B/T2, T4 and T6–T8
subgates. The relaxed TEL-B norm theorem is uniform for even N≥16, but every T1–T8
gate remains [O], and a shared 3+1D parent is still missing.
Round 7 (v1031–v1035, including the round-6 quantum prerequisite) adds
233 typed checks and full proofs in the contracts paper: a zero-mean free
Weyl/Fock curvature field with helicities ±2; auxiliary Z4 flux-register corners
with a twist-weight/parity obstruction; the factorized mirror lower gap
1+sqrt(3)/2; and physical-Fourier Ward propagation for prescribed sources.
These are not a common-parent derivation, microscopic MMST, an interacting
mirror-gap theorem or universal nonlinear gravity. Every T1–T8 gate stays [O].
Run each verification/v1031_*.py through v1035_*.py locally with the repository
dependencies. The source-auditing v1033/v1034 require a full checkout, not Pyodide.
Portability amendment (2026-09-06): v1033 now treats the degenerate QWZ zero space without an eigensolver-selected vacuum. It reports a fixed-particle ground-space mixture and bounds over all pure fillings; the corrected numeric interpretation is explicit in the contracts paper. The 233-check count and open gates do not change. A separate free 3D scalar theory contract gives the complete local symmetric-stress derivation and 68 exact checks, including its finite-volume Weyl operator lift. It is unpromoted and does not solve interacting matter or nonlinear gravity.
For the full native certificate chain (including the interval inputs), run
v1022_telb_round3_certificates.py, v1025_telb_c1_c2a_certificates.py and
v1026_telb_round4_closure.py from verification/ in the environment installed
from requirements.txt (python-flint==0.9.0). The browser reproducer explicitly
excludes these three modules; it does not replace their native certificates.
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 — the MMST route is closed modulo a cited theorem (SEAM.EQUIV.MMST.01 [C]); the parent claim is 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]). Within that compiler lane, the historical
residual is three named interface problems (the seam interface carries two routes):
| Interface | Question | Status |
|---|---|---|
v_geo |
the one metrology unit (= 1/√G); No-Unit Thm: a scale-invariant seam has no compiler scale; interface structurally closed as an R+ scale torsor in calibration form (v725) |
primitive [O] |
SEAM.EQUIV.01 |
the raw seam is the holomorphic (E8)₁ net (parent target; closed if either route closes) |
[O] as an unconditional claim |
SEAM.EQUIV.MMST.01 |
the MMST route: lattice + S3 stack + Lean, scaling limit cited | [C] — closed modulo cited theorems |
SEAM.EQUIV.TWISTOR.01 |
the twistor route: the open Costello–Li construction (prepared by CELEST.SEAM.01) |
[O] |
F_transfer |
one functor, four typed interfaces (Koide, η_B, axion, m_p/m_e) |
[C] |
(Route split 2026-07-22 — an ID restructuring, no status change in substance: the statements
previously attached to "SEAM.EQUIV.01 closed modulo a cited theorem" now live on the MMST route ID.)
This compiler accounting is not the physical TOE accounting. TFPT.TOE.COMPLETE.01 is the AND of
eight independent gates T1–T8; all eight remain [O]. Round 4 proves the relaxed uniform TEL-B
norm and adds scoped algebraic/constraint results, but makes no aggregate marker move.
No single shared 3+1D parent currently satisfies T3–T8.
The complete gate matrix and remaining obligations are in
tfpt_research_contracts.tex and
docs/OPEN_PROBLEMS.md.
The predictions are frozen (predictions_frozen.json,
2026-06-09) and locked to their formulas on every run — the freeze protects future
measurements; for historically known observables the honest statistics caveat is in
docs/FALSIFICATION.md (contract PRED.JOINTLIKELIHOOD.01). 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 — under its
declared null model; see the statistics caveat there), 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 compiler interface or one T1–T8 completeness gate.
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/ # 1028 registered 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)
├── rh/ # the consolidated RH-program workspace (inventory, Lean pilot, paper,
│ # run_rh.py suite — gated by build.sh audit; no RH claim)
├── website/ # the public mirror (fixpoint-theory.com), kept byte-identical by the audit
├── *.tex # the 12 published theory documents + the repo-only prime-front
│ # research documentation (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.21128999},
url = {https://doi.org/10.5281/zenodo.21128999}
}- 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.21128999 (Zenodo, v5.4); concept DOI for all versions: https://doi.org/10.5281/zenodo.18328333.
- 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.