Pith Number

pith:FG3YLWI3

pith:2012:FG3YLWI3BMQO4YO2CGCW6BVYGL

not attested not anchored not stored refs pending

Lipschitz constants to curve complexes

Christopher J. Leininger, Eriko Hironaka, Richard P. Kent IV, Vaibhav Gadre

arxiv:1212.4432 v1 · 2012-12-18 · 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{FG3YLWI3BMQO4YO2CGCW6BVYGL}

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	2026-05-18T03:38:13.029566Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

29b785d91b0b20ee61da11856f06b832e7b2c2159d46dc0ab2dfa49d0bf18e66

Aliases

arxiv: 1212.4432 · arxiv_version: 1212.4432v1 · doi: 10.48550/arxiv.1212.4432 · pith_short_12: FG3YLWI3BMQO · pith_short_16: FG3YLWI3BMQO4YO2 · pith_short_8: FG3YLWI3

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/FG3YLWI3BMQO4YO2CGCW6BVYGL \
  | 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: 29b785d91b0b20ee61da11856f06b832e7b2c2159d46dc0ab2dfa49d0bf18e66

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "08a3b22397166fab1d36346a59f4f073a239eb4dda90bb0a4112639b84756e4c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2012-12-18T17:14:18Z",
    "title_canon_sha256": "d9a372306a5f9c4264417224b37a0091e5def89e9e7e184e2764b6f3bfbfcdf0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1212.4432",
    "kind": "arxiv",
    "version": 1
  }
}