Pith Number

pith:AWC3WBWZ

pith:2012:AWC3WBWZAPWM464I554XZQMJMU

not attested not anchored not stored refs pending

Word length statistics for Teichm\"uller geodesics and singularity of harmonic measure

Giulio Tiozzo, Joseph Maher, Vaibhav Gadre

arxiv:1212.1481 v3 · 2012-12-06 · math.GT · math.DS · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{AWC3WBWZAPWM464I554XZQMJMU}

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	2026-05-18T02:39:54.377557Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0585bb06d903ecce7b88ef797cc189652ae76cea79985b32d5665b3b0b604e9f

Aliases

arxiv: 1212.1481 · arxiv_version: 1212.1481v3 · doi: 10.48550/arxiv.1212.1481 · pith_short_12: AWC3WBWZAPWM · pith_short_16: AWC3WBWZAPWM464I · pith_short_8: AWC3WBWZ

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/AWC3WBWZAPWM464I554XZQMJMU \
  | 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: 0585bb06d903ecce7b88ef797cc189652ae76cea79985b32d5665b3b0b604e9f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a075d8bcaf7bd0e7584d5a706554233ac48c24057e54bed75e91a087efacbfe3",
    "cross_cats_sorted": [
      "math.DS",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2012-12-06T21:36:52Z",
    "title_canon_sha256": "c481502f0bbe6f28a7530e19ccd6fc608b270c8c74abc92c17a14bef4fb9e950"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1212.1481",
    "kind": "arxiv",
    "version": 3
  }
}