Pith Number

pith:ZJQ3BJR7

pith:2006:ZJQ3BJR7I44K375UYQTE6NMLUJ

not attested not anchored not stored refs pending

Cycles of free words in several independent random permutations with restricted cycle lengths

CMAP), Florent Benaych-Georges (PMA

arxiv:math/0611500 v7 · 2006-11-16 · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ZJQ3BJR7I44K375UYQTE6NMLUJ}

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	2026-05-18T04:36:51.582371Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ca61b0a63f4738adffb4c4264f358ba27264d4f5f6072cace41ece8b669b193d

Aliases

arxiv: math/0611500 · arxiv_version: math/0611500v7 · doi: 10.48550/arxiv.math/0611500 · pith_short_12: ZJQ3BJR7I44K · pith_short_16: ZJQ3BJR7I44K375U · pith_short_8: ZJQ3BJR7

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/ZJQ3BJR7I44K375UYQTE6NMLUJ \
  | 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: ca61b0a63f4738adffb4c4264f358ba27264d4f5f6072cace41ece8b669b193d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f69e34069e0477734b6c6a8ede904c65c3a9f9e0afd783b7af9a50065cb2d89e",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2006-11-16T15:01:22Z",
    "title_canon_sha256": "bbde7e98d44f5a3ea2df85c596c2cd73241ca9493c37953c30bce070063ad302"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0611500",
    "kind": "arxiv",
    "version": 7
  }
}