Pith Number

pith:5QXIPSRZ

pith:2018:5QXIPSRZXNH6J53JBNGWRGW73D

not attested not anchored not stored refs pending

Divergent on average directions of Teichmuller geodesic flow

Howard Masur, Paul Apisa

arxiv:1803.00093 v2 · 2018-02-28 · 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{5QXIPSRZXNH6J53JBNGWRGW73D}

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	2026-05-18T00:03:49.493262Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ec2e87ca39bb4fe4f7690b4d689adfd8dbab46eba41366e2c694928116e9a5de

Aliases

arxiv: 1803.00093 · arxiv_version: 1803.00093v2 · doi: 10.48550/arxiv.1803.00093 · pith_short_12: 5QXIPSRZXNH6 · pith_short_16: 5QXIPSRZXNH6J53J · pith_short_8: 5QXIPSRZ

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/5QXIPSRZXNH6J53JBNGWRGW73D \
  | 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: ec2e87ca39bb4fe4f7690b4d689adfd8dbab46eba41366e2c694928116e9a5de

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e8d5219ee87b841c868e5e72d48b3a5f4cc2d9094fe4f45605bf41fb112d3f63",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2018-02-28T21:24:46Z",
    "title_canon_sha256": "b5b06ebd63118e932e6ea30bac5a2ef385649fe1c72fd300ca96f05f29f6406b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1803.00093",
    "kind": "arxiv",
    "version": 2
  }
}