davidichalfyorov-wq/sct-theory

Summary

SCT Theory is a solo research workspace implementing 'Spectral Causal Theory', a theoretical physics program attempting to derive quantum gravity corrections from the spectral data of the Dirac operator. The Python code performs high-precision numerical verification of heat kernel expansions, Seeley-DeWitt coefficients, and form factors for the spectral action principle, with the goal of producing testable predictions for deviations from Newtonian gravity. It is a computational companion to a set of Zenodo-hosted physics preprints.

Great for

people interested in computational mathematical physics, specifically heat kernel methods, spectral geometry, and numerical verification of quantum field theory calculations in curved spacetime

Easy wins

• +Add a CONTRIBUTING.md explaining what parts of the research roadmap are open questions vs. settled, so a physicist could identify where to plug in
• +Add a CI workflow (GitHub Actions) to actually run the promised test suite on push, since has_ci=false despite the README advertising an 8-layer verification pipeline
• +The requirements.txt specifies minimum versions but has no lockfile (no poetry.lock or requirements-lock.txt), making environment reproduction fragile — add a pinned lockfile or pyproject.toml with locked deps
• +Many scripts (e.g. mr5b_two_loop.py, a8_avramidi_recursion.py) have large comment blocks describing planned work or alternative approaches that are never implemented — consolidating these into GitHub Issues would make the open research questions visible and actionable

Red flags

• !a8_avramidi_recursion.py terminates mid-implementation — the core computation it promises (extracting c_S3 from the Avramidi recursion) is never actually executed; the file contains ~400 lines of setup and commentary followed by an incomplete function body, meaning this verification layer is not actually implemented despite being implied by the README
• !README claims '4000+ tests' but has_ci=false — there is no automated test run, so these tests may be passing locally but cannot be verified by a contributor
• !Single commit, single contributor, 2 stars — this is effectively a personal research notebook uploaded to GitHub, not a collaborative project; the framing as a 'collaboration platform' target is aspirational
• !The Zenodo DOIs (published papers) predate what appears to be the repository's initial commit, suggesting the code may be a post-hoc reconstruction of computations rather than the live development environment
• !requirements.txt lists 'aristotlelib>=0.7' — this is a non-standard package not on PyPI (likely a custom internal library), which would break any contributor attempting a clean install

Code quality

The code is genuinely sophisticated and well-commented for a physics research context — docstrings cite primary literature (Vassilevich, Gilkey, Avramidi) and explicitly flag sign conventions and normalization choices, which is unusually rigorous. However, there are structural issues: a8_avramidi_recursion.py is largely unfinished, with multi-page comment blocks describing computation strategies that trail off without implementation (the file ends mid-function with `a_2 = (1/12) Omega_sq + ...` as a comment). Several scripts like mr5b_two_loop.py contain long comment sections acknowledging open uncertainties ('DISCREPANCY: The MR-4 memory file quote appears to refer to a different invariant') that indicate work in progress. Error handling is absent throughout — scripts assume all imports succeed and all numerical computations converge. The sct_tools package (13 modules) is not sampled but the scripts importing from it suggest it's real infrastructure.

What makes it unique

There is no direct analogue on GitHub — open-source computational frameworks for noncommutative geometry and spectral action physics are extremely rare. The closest analogues are specialized HEP tools like FeynCalc or xAct, but those serve established formalisms. SCT is a novel theoretical program, so this repo is unique by definition. Whether the physics itself is sound is a separate question that requires expert peer review — the README is careful to note it is 'not a replacement for peer review'.