Pith Number

pith:FB53JAZV

pith:2016:FB53JAZVWYRJITIHOO7Y7D6OXK

not attested not anchored not stored refs pending

JSJ decompositions of groups

Gilbert Levitt, Vincent Guirardel

arxiv:1602.05139 v2 · 2016-02-16 · math.GR · 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{FB53JAZVWYRJITIHOO7Y7D6OXK}

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.

Cited by

1 paper in Pith

Accessibility, planar graphs, and quasi-isometries

Receipt and verification

First computed	2026-05-17T23:44:04.961993Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

287bb48335b622944d0773bf8f8fceba9ec03f8c143f897a2525a7b67d201661

Aliases

arxiv: 1602.05139 · arxiv_version: 1602.05139v2 · doi: 10.48550/arxiv.1602.05139 · pith_short_12: FB53JAZVWYRJ · pith_short_16: FB53JAZVWYRJITIH · pith_short_8: FB53JAZV

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/FB53JAZVWYRJITIHOO7Y7D6OXK \
  | 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: 287bb48335b622944d0773bf8f8fceba9ec03f8c143f897a2525a7b67d201661

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "614b95ba97f4f05a7117ec1db0865d6dedcec0045cffedbad6eda6249f7a895e",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2016-02-16T18:55:20Z",
    "title_canon_sha256": "a7bb034e81b8edfbd82d0c2cf0a10d15c8a82d71d1d3545099925a993f76698b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1602.05139",
    "kind": "arxiv",
    "version": 2
  }
}