A twenty-two-paper series (with epilogue) building a unified cohomological theory of quantum contextuality.
Author: Zhou-Li Chen (co-nlang Research)
Quantum observation forces an observer to view a system through incompatible contexts — complementary measurement setups, each locally classical, that refuse to glue into a global picture. This series builds the algebraic machinery that measures that refusal: an obstruction ladder graded by group cohomology, where
The series has three arcs. Papers I–VI construct the ladder from scratch — Bohrification, spectral sequences, and the necessity of
The endpoint: the framework's deepest invariant (
→ READING_GUIDE.md — per-paper summaries and recommended reading orders.
→ RESEARCH_FRONTIER.md — mathematical toolbox and open problems.
→ insight/ — post-series exploration notes (QEC substrate identity, BHQC, AdS/CFT holographic codes, Klein quartic, and others).
→ worknotes/ — selected internal working documents, published verbatim: how the human + LLM collaboration actually ran (planning menus, paper seeds, cross-reviews, session logs, dead ends, self-caught errors — including the full idea→draft→review chain of Paper XXII and the connect-the-dots session that seeded Paper VII; with a decoder for the internal jargon).
→ Paper N — the n/ whitepaper: the bridge from this series to the n/ language specification (CAID, forced quantization → Bohrification, the
| # | Title | Key Result |
|---|---|---|
| N | The n/ Program: Forced Quantization, Bohrification, and the Contextuality Ceiling (whitepaper) | spec ↔ series bridge: CAID, forced |
| I | From Contextuality to Phase Cohomology |
|
| II | Semiclassical Reconstruction of Riemann Surfaces from Bohrification | Bohr-Sommerfeld orbits as divisors on spectral curves |
| III | Kochen–Specker Contextuality as Central Extension | KS obstruction = |
| IV | LHS Transgression and the $H^3$ Frontier |
|
| Epilogue | The Algebraic Logic of Geometry |
|
| V | Observation as Functor | LHS spectral sequence unifies all obstructions |
| VI | Deriving QM from the Logic of Observation |
|
| VII | Twistor Theory from the Obstruction Ladder | Googly problem = |
| VIII | The $\Phi$ Functor |
|
| IX | The 3-Qubit Obstruction Ladder |
|
| X | Equiangular Characterization of Mermin Pentagrams |
|
| XI | Quadratic Refinement and Parity |
|
| XII | The T-Vector Theorem |
|
| XIII | Maslov Index and the KS Obstruction | Kashiwara ≠ |
| XIV | Stabilizer Algebra and $k$-Profile |
|
| XV | Weil Representation and $S_3$ Lifting | Split / non-split classification; |
| XVI | The Weyl Product Identity |
|
| XVII | Cross-Context Anticommutation Theorem |
|
| XVIII | Mermin Pentagrams in $\mathrm{Sp}(8,\mathbb{F}_2)$ |
|
| XIX | $n \ge 5$: Modulus Phenomenon | No arity-$\le 4$ invariant classifies the fiber |
| XX | $H^3$ Opens at $n \ge 5$ |
|
| XXI | Master Theorem |
|
| XXII | Arity–Resonance Ceiling |
|
| L-S I–III | Contraction Appendices | Dynamical reinterpretation of |
Level 0 (Foundation): H¹ — E_∞^{1,0} survivors — Geometric phases (Aharonov–Bohm, Berry)
Level 1 (Obstruction): H² — d₂ transgression — Kochen–Specker contextuality
Level 2 (Obstruction): H³ — d₃ higher differential — Borromean non-associativity
(truncates: H⁴ = 0, Paper XXII)
Geometric phases are stable features surviving the entire spectral sequence (
research/
├── README.md
├── READING_GUIDE.md # Per-paper summaries & reading orders
├── RESEARCH_FRONTIER.md # Toolbox & open problems
├── LICENSE # CC BY 4.0
├── insight/ # Post-series exploration notes (+ the archived timescape .tex)
├── worknotes/ # Internal working documents, published verbatim (with decoder README)
├── papers/
│ ├── Paper0_nlang_whitepaper.tex # Paper N — the n/ whitepaper (spec↔series bridge)
│ ├── Paper1_contextuality_phase.tex
│ ├── ...
│ ├── Paper22_resonance_ceiling.tex
│ ├── Epilogue_algebraic_logic.tex
│ └── LsNote_*.tex # L-S contraction appendices (3)
└── supplementary/
├── construct_16cell/ # Z3 SAT, 16-cell nerve (Paper IV)
├── paper7_conj42/ # Φ* pullback verification (Paper VII)
├── paper10/ – paper22/ # Per-paper computational scripts
├── klein/ # Klein quartic / PSL(2,7) bridge
├── adscft/ # HaPPY holographic codes (insight)
├── mbqc/ # l2-MBQC computational degree (insight)
├── bockstein/ # Z/4-Bockstein / Sq¹-acyclicity (insight)
├── twistor_cp/ # item 13: CP^{2^n-1} realization is family-B only
├── familyB_resonance/ # item 22: family B is family A's omega=2 floor
├── k4_h2_opening/ # K4/H2 Maslov rung: opening witnesses + flip reduction
└── timescape/ # SN × void-fraction cross-validation
| Directory | Paper | Description |
|---|---|---|
construct_16cell/ |
IV | Z3 SAT construction of the 16-cell nerve |
paper7_conj42/ |
VII |
|
paper10/ |
X | 12,096 pentagrams, equiangular characterization, |
paper11/ |
XI |
|
paper12/ |
XII | T-vector, Arf search, |
paper13/ |
XIII | Kashiwara index, |
paper14/ |
XIV | Stabilizer classification, |
paper15/ |
XV | Metaplectic lifting, |
paper16/ |
XVI | Weyl product identity verification |
paper17/ |
XVII | Cross-context anticommutation (12,096) |
paper18/ |
XVIII | B0/B1/B2 recheck, landscape table, Key Lemma |
paper19/ |
XIX | Upper-bound ladder, modulus witness, Arf ruling-out |
paper20/ |
XX |
|
paper21/ |
XXI | Master theorem, spread-stabilisation witnesses |
paper22/ |
XXII | Arity–resonance, truncation, clique criterion, |
klein/ |
IX | 168-action, bitangent bijection, theta/spin spiral |
adscft/ |
insight | HaPPY holographic codes; reconstruction is blind to contextuality |
mbqc/ |
insight | l2-MBQC: computational degree |
bockstein/ |
insight |
|
twistor_cp/ |
VIII | item 13: the |
familyB_resonance/ |
XXII | item 22: no family-B resonance — it is the |
k4_h2_opening/ |
XXII | the |
timescape/ |
insight | SN Hubble-residual insight/timescape_cross_validation.tex) |
All components are archived on Zenodo:
This research project integrated various Large Language Models (LLMs) across multiple stages to enhance rigor and clarity. The author(s) maintain full accountability for the final content.
- Theoretical Derivation: AI was used to assist in symbolic manipulation, cross-verifying mathematical proofs, and identifying potential edge cases in formulas.
- Development & Typesetting: Code implementation and LaTeX structural optimization were supported by AI-assisted pair programming.
- Language & Refinement: Sentences were polished for academic flow and grammatical precision.
- Simulated Peer Review: AI agents were tasked to act as independent reviewers to provide critical feedback and identify logical gaps prior to publication.
Models used: Gemini 3 Pro/3.1 Pro, GPT-5.3, Claude Sonnet 4.6/Opus 4.6&4.8, Kimi K2.5/K2.6, GLM-5.0, QWen 3.5 Plus, DeepSeek V4 Pro/Flash.
Each paper is a standalone LaTeX document. Compile with:
pdflatex Paper1_contextuality_phase.tex
pdflatex Paper1_contextuality_phase.tex
pdflatex Paper1_contextuality_phase.texRequirements: TeX Live 2023+ with amsmath, amssymb, amsthm, tikz-cd, booktabs, hyperref.
To cite the series, please reference the individual paper(s) by DOI (see above). For the series as a whole:
@misc{chen2026cohomological,
author = {Chen, Zhou-Li},
title = {The Logic of Observation: A Unified Cohomological Theory of Quantum Contextuality},
year = {2026},
note = {Twenty-two-paper series with epilogue},
url = {https://github.com/co-nlang/research}
}