Pith Number

pith:V7JMNLLQ

pith:2010:V7JMNLLQXCUHV7O4T4SCRNSPRD

not attested not anchored not stored refs pending

Statistical properties of subgroups of free groups

Armando Martino, Cyril Nicaud (LIGM), Enric Ventura, Fr\'ed\'erique Bassino (LIPN), Pascal Weil (LaBRI)

arxiv:1001.4472 v3 · 2010-01-25 · math.GR · cs.DM · 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{V7JMNLLQXCUHV7O4T4SCRNSPRD}

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	2026-05-18T03:30:26.218794Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

afd2c6ad70b8a87afddc9f2428b64f88d328a79a44049f143f422a0e6ce04c38

Aliases

arxiv: 1001.4472 · arxiv_version: 1001.4472v3 · doi: 10.48550/arxiv.1001.4472 · pith_short_12: V7JMNLLQXCUH · pith_short_16: V7JMNLLQXCUHV7O4 · pith_short_8: V7JMNLLQ

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/V7JMNLLQXCUHV7O4T4SCRNSPRD \
  | 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: afd2c6ad70b8a87afddc9f2428b64f88d328a79a44049f143f422a0e6ce04c38

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "92f638e578fdb3d4d0ab0784faaab43c9616535b977ac0d287fc401132bd873c",
    "cross_cats_sorted": [
      "cs.DM",
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2010-01-25T16:13:46Z",
    "title_canon_sha256": "e87fedc5993a7dc5262615407cc95d6452e3da87a90d48fe6d75857cbcfde529"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1001.4472",
    "kind": "arxiv",
    "version": 3
  }
}