Pith Number

pith:4EHXX3OG

pith:2021:4EHXX3OG3VRM2PE2LJZOYLF5VL

not attested not anchored not stored refs pending

Heavy Ball Neural Ordinary Differential Equations

Andrea L. Bertozzi, Bao Wang, Hangjie Ji, Hedi Xia, Stanley J. Osher, Tan M. Nguyen, Vai Suliafu

arxiv:2110.04840 v1 · 2021-10-10 · cs.LG · cs.AI · cs.NA · math.DS · 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{4EHXX3OG3VRM2PE2LJZOYLF5VL}

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	2026-07-05T03:21:21.977257Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e10f7bedc6dd62cd3c9a5a72ec2cbdaac9a5d8fedd3d92c78a79a798c8720567

Aliases

arxiv: 2110.04840 · arxiv_version: 2110.04840v1 · doi: 10.48550/arxiv.2110.04840 · pith_short_12: 4EHXX3OG3VRM · pith_short_16: 4EHXX3OG3VRM2PE2 · pith_short_8: 4EHXX3OG

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/4EHXX3OG3VRM2PE2LJZOYLF5VL \
  | 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: e10f7bedc6dd62cd3c9a5a72ec2cbdaac9a5d8fedd3d92c78a79a798c8720567

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8d03de4c771a828946fa1d03edfb7e67f73c3ba0737df0b6282c8a9a8060b7e6",
    "cross_cats_sorted": [
      "cs.AI",
      "cs.NA",
      "math.DS",
      "math.NA"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2021-10-10T16:11:11Z",
    "title_canon_sha256": "273adc2f54cc1d2525114c5ff3f348fd52fe57308ed15cd0fa4bf563736520ac"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2110.04840",
    "kind": "arxiv",
    "version": 1
  }
}