Pith Number

pith:5OHC2VKA

pith:2012:5OHC2VKALLBX7LGVMMJGSS4RRU

not attested not anchored not stored refs pending

Separation probabilities for products of permutations

Alejandro H. Morales (MIT), Olivier Bernardi (MIT), Richard P. Stanley (MIT), Rosena R. X. Du

arxiv:1202.6471 v1 · 2012-02-29 · 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{5OHC2VKALLBX7LGVMMJGSS4RRU}

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	2026-05-17T23:53:18.910403Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

eb8e2d55405ac37facd56312694b918d276899975deb28446f089ed3bce81956

Aliases

arxiv: 1202.6471 · arxiv_version: 1202.6471v1 · doi: 10.48550/arxiv.1202.6471 · pith_short_12: 5OHC2VKALLBX · pith_short_16: 5OHC2VKALLBX7LGV · pith_short_8: 5OHC2VKA

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/5OHC2VKALLBX7LGVMMJGSS4RRU \
  | 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: eb8e2d55405ac37facd56312694b918d276899975deb28446f089ed3bce81956

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "96f0cd2810e28dd70763cc79b4ceced62fe4843bf156eec9b2c9f2895a230967",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2012-02-29T07:49:22Z",
    "title_canon_sha256": "d5f40a183d0f7f1a2db03acbce023abb5e2b8e3a01efe6c2cd93bb7a0fc19338"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1202.6471",
    "kind": "arxiv",
    "version": 1
  }
}