Pith Number

pith:CQN2OYB7

pith:2009:CQN2OYB7QVHFWM2C7E5SDX2XRC

not attested not anchored not stored refs pending

JSJ decompositions: definitions, existence, uniqueness. I: The JSJ deformation space

Gilbert Levitt, Vincent Guirardel

arxiv:0911.3173 v3 · 2009-11-16 · 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{CQN2OYB7QVHFWM2C7E5SDX2XRC}

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	2026-05-18T01:18:18.699853Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

141ba7603f854e5b3342f93b21df5788bca205d25640f759e80e5c9c31a8b667

Aliases

arxiv: 0911.3173 · arxiv_version: 0911.3173v3 · doi: 10.48550/arxiv.0911.3173 · pith_short_12: CQN2OYB7QVHF · pith_short_16: CQN2OYB7QVHFWM2C · pith_short_8: CQN2OYB7

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/CQN2OYB7QVHFWM2C7E5SDX2XRC \
  | 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: 141ba7603f854e5b3342f93b21df5788bca205d25640f759e80e5c9c31a8b667

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b5d999764c7545c705c49bbc1ca222871d045b66422cb71bac44235fb4c97da6",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2009-11-16T22:06:10Z",
    "title_canon_sha256": "231439460be593330216bc554e560c4392269715ef3b8906854d86e0d50e74a2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0911.3173",
    "kind": "arxiv",
    "version": 3
  }
}