Pith Number

pith:JSNR2PGP

pith:2019:JSNR2PGPG3OMW7MYDSWXJR44C6

not attested not anchored not stored refs pending

Liouville properties

Tobias Holck Colding, William P. Minicozzi II

arxiv:1902.09366 v1 · 2019-02-25 · math.DG · math.AP · math.CA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{JSNR2PGPG3OMW7MYDSWXJR44C6}

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	2026-05-17T23:52:45.960806Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4c9b1d3ccf36dccb7d981cad74c79c17981e6230425cb6bfd672e7d475ebe9b5

Aliases

arxiv: 1902.09366 · arxiv_version: 1902.09366v1 · doi: 10.48550/arxiv.1902.09366 · pith_short_12: JSNR2PGPG3OM · pith_short_16: JSNR2PGPG3OMW7MY · pith_short_8: JSNR2PGP

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/JSNR2PGPG3OMW7MYDSWXJR44C6 \
  | 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: 4c9b1d3ccf36dccb7d981cad74c79c17981e6230425cb6bfd672e7d475ebe9b5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1f3de4c4d79261143951c491a934493f0f3e45d81adaff0bc1be91ab726f0ae3",
    "cross_cats_sorted": [
      "math.AP",
      "math.CA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2019-02-25T15:30:11Z",
    "title_canon_sha256": "dbbc6eff5a2df5e1c9afbef341f959c69ea73c3092f7cdba2ab2a917b4b71f65"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1902.09366",
    "kind": "arxiv",
    "version": 1
  }
}