Quantum gravity is not primarily the quantization of material objects in spacetime. It is the reconstruction of spacetime, matter, causality, and measurement from invariant representation structures.
This repository treats quantum gravity as a modular site of partially overlapping representation regimes rather than one monolithic theory. Twelve regimes each get a precise dictionary entry, an epistemic status label, a rigorous paper, and machine-checked code; a synthesis paper shows how they compose.
- Live site: https://math-qg-representation-library.vercel.app
- Papers: 12 regime studies (≥20 pages each) + 1 synthesis, arXiv-style
- Every mathematical claim is checked twice: runnable Haskell (QuickCheck + equational proofs) and a Lean 4 formalization of the status calculus.
invariant representation structures
│
┌─────────────────────┼─────────────────────┐
classical quantum geometry amplitudes /
geometry & dynamics holography
(I, II) (III, IV) (V–VIII)
└─────────────────────┼─────────────────────┘
│
UV completion & foundations
(IX, X, XI, XII)
│
synthesis: weakest-link
S/H/P status calculus
(a composite is never stronger than its weakest regime)
Read on the site (rendered math, dark theme) or open the PDF.
| Part | Paper | Cat. | pp | ||
|---|---|---|---|---|---|
| — | A Modular Site of Reconstruction Regimes (synthesis) | gr-qc | 25 | read | |
| I | The Solution Stack of General Relativity | gr-qc | 22 | read | |
| II | Observables as Cohomology (BV-BRST) | hep-th | 23 | read | |
| III | Quantum Spatial Geometry as Representation Data (spin networks) | gr-qc | 24 | read | |
| IV | Covariant Quantum Geometry as a State Sum (spin foams) | gr-qc | 25 | read | |
| V | Many Boundary Representatives, One Bulk Operator (tensor networks / QEC) | hep-th | 23 | read | |
| VI | Amplitudes as Canonical Forms (positive geometries) | hep-th | 21 | read | |
| VII | Gravity as the Square of Gauge Theory (double copy) | hep-th | 21 | read | |
| VIII | The Flat-Space S-Matrix as Conformal Data (celestial CFT) | hep-th | 22 | read | |
| IX | A Fixed Point in Theory Space (asymptotic safety) | hep-th | 24 | read | |
| X | Observables from Gluing (factorization algebras) | math-ph | 21 | read | |
| XI | Geometry as a Theorem About an Algebra (noncommutative geometry) | math-ph | 21 | read | |
| XII | Causal Order as Representation Data (quantum causal structures) | quant-ph | 25 | read |
Every dictionary entry carries a label, and composition is monotone — a chain is never stronger than its weakest link:
| Label | Meaning |
|---|---|
S |
Standard mathematical / mathematical-physics correspondence |
H |
Strong heuristic physical representation |
P |
Speculative ontological extension |
The synthesis proves the composite of all twelve regimes lands at P (dragged there by the causal-structure regime), and drops to H if that regime is removed — the modular claim, made precise.
- Haskell (
src/<topic>/): every topic compiles underghc -Wall -Wextra -Werrorwith zero warnings; 213 QuickCheck properties and per-topic equational proofs, all passing. Reviewed by Codex. - Lean 4 (
lean/): a self-contained Lake project (no Mathlib).QGRep/Core.leanandQGRep/Synthesis.leanprove the S/H/P weakest-link calculus and the modular composition theorems with nosorry; the twelve topic modules state faithful theorems, usingsorryonly for four genuinely-open physics problems (each annotated). - Peer review: each paper went through an iterative review loop (Gemini 3.1 Pro) to an ACCEPT / MINOR-REVISIONS verdict, plus a Codex formatting pass. Review transcripts are in
reviews/.
papers/latex/ arXiv-style LaTeX sources (12 regimes + synthesis)
papers/pdf/ compiled PDFs
src/<topic>/ Haskell: Core, Properties (QuickCheck), Proofs (equational), Main
lean/ Lean 4 Lake project (QGRep.Core, QGRep.Synthesis, QGRep/Topics/*)
docs/papers/ HTML conversions docs/research/ deep-research dossiers
reviews/ peer-review + Codex transcripts
website/ Next.js static site (KaTeX server-side render)
posts/ social posts (twitter/linkedin/facebook/bluesky)
context/ the seed research library (mqg_repr Python scaffold, dictionary)
# Haskell checks (per topic)
ghc -Wall -Wextra -Werror src/spin-networks/*.hs -isrc/spin-networks -package QuickCheck -o /tmp/t && /tmp/t
# Lean formalization
cd lean && lake build
# Website
cd website && npm install && npm run build && npx serve outMatthew Long The YonedaAI Collaboration, YonedaAI Research Collective Chicago, IL matthew@yonedaai.com · https://yonedaai.com
See context/math_qg_representation_library/LICENSE. The library is a structured way to record, search, compose, and test representation entries while keeping rigorous mathematics, heuristic physics, and speculative ontology explicitly separated. It is not a claim that quantum gravity is solved.