Pith Number

pith:A6UT4KEG

pith:2011:A6UT4KEGVKCHRQOLJ6XFVVSYIH

not attested not anchored not stored refs pending

On the divisibility of $#\Hom(\Gamma,G)$ by $|G|

Cameron Gordon, Fernando Rodriguez Villegas

arxiv:1105.6066 v1 · 2011-05-30 · math.GR · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{A6UT4KEGVKCHRQOLJ6XFVVSYIH}

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	2026-05-18T00:19:49.363476Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

07a93e2886aa8478c1cb4fae5ad65841f82507d39d6b296dd94c27372b69b2c8

Aliases

arxiv: 1105.6066 · arxiv_version: 1105.6066v1 · doi: 10.48550/arxiv.1105.6066 · pith_short_12: A6UT4KEGVKCH · pith_short_16: A6UT4KEGVKCHRQOL · pith_short_8: A6UT4KEG

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/A6UT4KEGVKCHRQOLJ6XFVVSYIH \
  | 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: 07a93e2886aa8478c1cb4fae5ad65841f82507d39d6b296dd94c27372b69b2c8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0218f43086e9515d7f5b91d8bb9d342332845bfd3124d4c3d231f1fa90a5890e",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2011-05-30T18:49:36Z",
    "title_canon_sha256": "466b535360276ba2a4f9ac0f4f506c0ec56069a9dc675be1b5dd31eb2a2df489"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1105.6066",
    "kind": "arxiv",
    "version": 1
  }
}