Pith Number

pith:64VLQ7SB

pith:2010:64VLQ7SBNUFUWANMXML7GU2W7L

not attested not anchored not stored refs pending

The Weil-Petersson geodesic flow is ergodic

Amie Wilkinson, Howard Masur, Keith Burns

arxiv:1004.5343 v3 · 2010-04-29 · math.DS · math.GT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{64VLQ7SBNUFUWANMXML7GU2W7L}

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	2026-05-18T04:11:18.062641Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f72ab87e416d0b4b01acbb17f35356faf70146b01090b5b9399c6dc05ebdd7bc

Aliases

arxiv: 1004.5343 · arxiv_version: 1004.5343v3 · doi: 10.48550/arxiv.1004.5343 · pith_short_12: 64VLQ7SBNUFU · pith_short_16: 64VLQ7SBNUFUWANM · pith_short_8: 64VLQ7SB

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/64VLQ7SBNUFUWANMXML7GU2W7L \
  | 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: f72ab87e416d0b4b01acbb17f35356faf70146b01090b5b9399c6dc05ebdd7bc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "81748095d86b6218981a89dde8a3c002937f45810e7bb11cea0807f2bc9fc842",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2010-04-29T17:09:32Z",
    "title_canon_sha256": "88d3af6b40d4e5f7988a38b2a503895de7ff42cf9ddb920ba9bfb26c6200149e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1004.5343",
    "kind": "arxiv",
    "version": 3
  }
}