Pith Number

pith:UNPYL7JJ

pith:2007:UNPYL7JJHL2AELX5PLF7PDPWUP

not attested not anchored not stored refs pending

Liouville energy on a topological two sphere

Meijun Zhu, Xiuxiong Chen

arxiv:0710.4320 v1 · 2007-10-23 · math.AP · math.DG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{UNPYL7JJHL2AELX5PLF7PDPWUP}

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	2026-07-04T15:05:08.271251Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a35f85fd293af4022efd7acbf78df6a3ff7d6506c7723f0e2c121f3111a97742

Aliases

arxiv: 0710.4320 · arxiv_version: 0710.4320v1 · doi: 10.48550/arxiv.0710.4320 · pith_short_12: UNPYL7JJHL2A · pith_short_16: UNPYL7JJHL2AELX5 · pith_short_8: UNPYL7JJ

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/UNPYL7JJHL2AELX5PLF7PDPWUP \
  | 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: a35f85fd293af4022efd7acbf78df6a3ff7d6506c7723f0e2c121f3111a97742

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "177dd3f83c2a3595468ec0251c39416bec9b8682410fc5a00856fc3d8ba19dff",
    "cross_cats_sorted": [
      "math.DG"
    ],
    "license": "",
    "primary_cat": "math.AP",
    "submitted_at": "2007-10-23T19:26:17Z",
    "title_canon_sha256": "8ed072294e0eebe33b6be7fb723969c4b08293dc5ac572cdff1ed1c45f6d9981"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0710.4320",
    "kind": "arxiv",
    "version": 1
  }
}