Pith Number

pith:QA6CMPRA

pith:2010:QA6CMPRA735A5LIUTVY37ZFWLJ

not attested not anchored not stored refs pending

Random groups arising as graph products

Michael Farber, Ruth Charney

arxiv:1006.3378 v1 · 2010-06-17 · math.GR · math.AT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{QA6CMPRA735A5LIUTVY37ZFWLJ}

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	2026-05-18T02:41:50.853265Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

803c263e20fefa0ead149d71bfe4b65a4788f385153f62bcc135b9a84f6159f9

Aliases

arxiv: 1006.3378 · arxiv_version: 1006.3378v1 · doi: 10.48550/arxiv.1006.3378 · pith_short_12: QA6CMPRA735A · pith_short_16: QA6CMPRA735A5LIU · pith_short_8: QA6CMPRA

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/QA6CMPRA735A5LIUTVY37ZFWLJ \
  | 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: 803c263e20fefa0ead149d71bfe4b65a4788f385153f62bcc135b9a84f6159f9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8d7a8d9c0a16921bde04c381ee377de36476ac27acd3c826652e653f7999d2e3",
    "cross_cats_sorted": [
      "math.AT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2010-06-17T05:59:07Z",
    "title_canon_sha256": "b7e37cdb4b97bf5ed7d18f75d176df8def416abdf9c57339e4378a81f20c243d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1006.3378",
    "kind": "arxiv",
    "version": 1
  }
}