Pith. sign in

REVIEW 2 cited by

Formalization of physics index notation in Lean 4

Not yet reviewed by Pith; the record is open.

Re-run · record.json Download PDF Read on arXiv ↗

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 2411.07667 v1 pith:5EJIOZAI submitted 2024-11-12 cs.LO hep-phhep-th

Joseph Tooby-Smith This is my paper · ORCID
classification cs.LOhep-phhep-th
keywords notationindexleanphysicsimplementationproveresultstensors
verification ladder T0 review T1 audit T2 compute T3 formal

Signed reviews

No signed human review yet.

0 comments
read the original abstract

The physics community relies on index notation to effectively manipulate types of tensors. This paper introduces the first formally verified implementation of index notation in the interactive theorem prover Lean 4. By integrating index notation into Lean, we bridge the gap between traditional physics notation and formal verification tools, making it more accessible for physicists to write and prove results within Lean. We also open up a new avenue through which AI tools can be used to prove results related to tensors in physics. Behind the scenes our implementation leverages a novel application of category theory.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. LeanTree: Accelerating White-Box Proof Search with Factorized States in Lean 4

    cs.LG 2025-07 conditional novelty 6.0 of 10

    White-box proof search with factorized Lean 4 goals reaches 18.4% on MiniF2F with Llemma-7B, outperforming black-box generation at 9.6%.

  2. Benchmarking Energy Calculations Using Formal Proofs

    cond-mat.stat-mech 2025-05 conditional novelty 6.0 of 10

    LeanLJ computes Lennard-Jones energies and long-range corrections in periodic boundaries using Lean 4, with proofs about the mathematical functions and numerical agreement with NIST SRSW benchmarks.

Pith tools