Pith Number

pith:ZYX4A7WZ

pith:2023:ZYX4A7WZQAVYHBZXIUPOFMW5KR

not attested not anchored not stored refs pending

Self-Supervised Learning with Lie Symmetries for Partial Differential Equations

Bobak T. Kiani, Danyal Rehman, Gr\'egoire Mialon, Hannah Lawrence, Quentin Garrido, Yann LeCun

arxiv:2307.05432 v2 · 2023-07-11 · cs.LG · cs.NA · math.NA

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ZYX4A7WZQAVYHBZXIUPOFMW5KR}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Receipt and verification

First computed	2026-07-05T07:44:54.983965Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ce2fc07ed9802b838737451ee2b2dd544ea79c372227214facf0642b35552a19

Aliases

arxiv: 2307.05432 · arxiv_version: 2307.05432v2 · doi: 10.48550/arxiv.2307.05432 · pith_short_12: ZYX4A7WZQAVY · pith_short_16: ZYX4A7WZQAVYHBZX · pith_short_8: ZYX4A7WZ

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/ZYX4A7WZQAVYHBZXIUPOFMW5KR \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: ce2fc07ed9802b838737451ee2b2dd544ea79c372227214facf0642b35552a19

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d9b222bf73959a46f2fff6fa658a3947b639679f11614f10deea08c5df0fe39e",
    "cross_cats_sorted": [
      "cs.NA",
      "math.NA"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2023-07-11T16:52:22Z",
    "title_canon_sha256": "140a7341c44a6b118da136c26492bafcf5a6617c042ee7b3f30a7bb7c7727afd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2307.05432",
    "kind": "arxiv",
    "version": 2
  }
}