Pith Number

pith:A5ODDMCE

pith:2011:A5ODDMCEHRUVBJGZAKED6HZAMK

not attested not anchored not stored refs pending

A pattern theorem for random sorting networks

Alexander E. Holroyd, Omer Angel, Vadim Gorin

arxiv:1110.0160 v2 · 2011-10-02 · math.PR · 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{A5ODDMCEHRUVBJGZAKED6HZAMK}

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	2026-05-18T03:40:25.791384Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

075c31b0443c6950a4d902883f1f2062b1b37c7664772b90b22121a5c566d39d

Aliases

arxiv: 1110.0160 · arxiv_version: 1110.0160v2 · doi: 10.48550/arxiv.1110.0160 · pith_short_12: A5ODDMCEHRUV · pith_short_16: A5ODDMCEHRUVBJGZ · pith_short_8: A5ODDMCE

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/A5ODDMCEHRUVBJGZAKED6HZAMK \
  | 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: 075c31b0443c6950a4d902883f1f2062b1b37c7664772b90b22121a5c566d39d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cf8131549c80a6acf0884e07d35e1c3e17e4f9dc5856575b4ef327c855797602",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2011-10-02T09:05:47Z",
    "title_canon_sha256": "f262c76653e42be7ae166bfa9fcfbb8540febc13e5e902accb3de6a23dc83eb3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1110.0160",
    "kind": "arxiv",
    "version": 2
  }
}