Pith Number

pith:EVJ6T3JB

pith:2009:EVJ6T3JB537K4BR55HIZJ7MIJA

not attested not anchored not stored refs pending

Ping-pong and Outer space

Ilya Kapovich, Martin Lustig

arxiv:0902.4017 v4 · 2009-02-24 · 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{EVJ6T3JB537K4BR55HIZJ7MIJA}

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	2026-05-18T04:20:51.415744Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2553e9ed21eefeae063de9d194fd88482e937d595021f9b7990286f0a0910256

Aliases

arxiv: 0902.4017 · arxiv_version: 0902.4017v4 · doi: 10.48550/arxiv.0902.4017 · pith_short_12: EVJ6T3JB537K · pith_short_16: EVJ6T3JB537K4BR5 · pith_short_8: EVJ6T3JB

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/EVJ6T3JB537K4BR55HIZJ7MIJA \
  | 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: 2553e9ed21eefeae063de9d194fd88482e937d595021f9b7990286f0a0910256

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a4cb67cc62a4c34b870e4db71fbe8e4692f1d055c4be2a84b5b030a7676b8bb7",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2009-02-24T15:24:05Z",
    "title_canon_sha256": "bca3323e304f7827bcc14352e21994ba8a0f7519f29107b13d6aa266692f9226"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0902.4017",
    "kind": "arxiv",
    "version": 4
  }
}