Pith Number

pith:OCILM4ZA

pith:2011:OCILM4ZAIADTXVHWKMC5ARTIKF

not attested not anchored not stored refs pending

A Markov chain on the symmetric group which is Schubert positive?

Lauren Williams, Thomas Lam

arxiv:1102.4406 v2 · 2011-02-22 · math.CO · 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{OCILM4ZAIADTXVHWKMC5ARTIKF}

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	2026-05-18T04:23:45.202158Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7090b6732040073bd4f65305d0466851520f63df948d231bece453ee84b7a9a4

Aliases

arxiv: 1102.4406 · arxiv_version: 1102.4406v2 · doi: 10.48550/arxiv.1102.4406 · pith_short_12: OCILM4ZAIADT · pith_short_16: OCILM4ZAIADTXVHW · pith_short_8: OCILM4ZA

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/OCILM4ZAIADTXVHWKMC5ARTIKF \
  | 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: 7090b6732040073bd4f65305d0466851520f63df948d231bece453ee84b7a9a4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2ad90462c70fb78fa3094df8f76678833f6171c5e87ea4dacdb60cded5bc51c5",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2011-02-22T04:24:30Z",
    "title_canon_sha256": "fd91ba3807d3ba333924c45753eb63273db944100bf904e0222b7faef139e0ea"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1102.4406",
    "kind": "arxiv",
    "version": 2
  }
}