Pith Number

pith:65GAA7FE

pith:2010:65GAA7FEOGUAVCTHXI4XU6SQ4F

not attested not anchored not stored refs pending

Growth of permutational extensions

Anna G. Erschler, Laurent Bartholdi

arxiv:1011.5266 v2 · 2010-11-24 · math.GR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{65GAA7FEOGUAVCTHXI4XU6SQ4F}

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	2026-05-18T02:28:32.236828Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f74c007ca471a80a8a67ba397a7a50e177ed1285212a66c1c75185155dbdeee0

Aliases

arxiv: 1011.5266 · arxiv_version: 1011.5266v2 · doi: 10.48550/arxiv.1011.5266 · pith_short_12: 65GAA7FEOGUA · pith_short_16: 65GAA7FEOGUAVCTH · pith_short_8: 65GAA7FE

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/65GAA7FEOGUAVCTHXI4XU6SQ4F \
  | 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: f74c007ca471a80a8a67ba397a7a50e177ed1285212a66c1c75185155dbdeee0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "609b689169bf9bba7ed889cba51830e42d6fd2a0e1c8da4073e68edf3ad64e7a",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2010-11-24T01:16:13Z",
    "title_canon_sha256": "7097568120ad501f7baea87f441d09d570c79086c4a3d315b3a3ef53e58060c1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1011.5266",
    "kind": "arxiv",
    "version": 2
  }
}