Pith Number

pith:XNOJ6IZF

pith:2013:XNOJ6IZFK4O44IROJ4OJOUUM7M

not attested not anchored not stored refs pending

Subgroup Majorization

Andrew R. Francis, Henry P. Wynn

arxiv:1303.2707 v4 · 2013-03-11 · math.ST · math.GR · stat.TH

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{XNOJ6IZFK4O44IROJ4OJOUUM7M}

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	2026-05-18T02:41:42.501401Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bb5c9f2325571dce222e4f1c97528cfb3f245bc3ec0d444d684f3ce49957ea8e

Aliases

arxiv: 1303.2707 · arxiv_version: 1303.2707v4 · doi: 10.48550/arxiv.1303.2707 · pith_short_12: XNOJ6IZFK4O4 · pith_short_16: XNOJ6IZFK4O44IRO · pith_short_8: XNOJ6IZF

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/XNOJ6IZFK4O44IROJ4OJOUUM7M \
  | 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: bb5c9f2325571dce222e4f1c97528cfb3f245bc3ec0d444d684f3ce49957ea8e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a990186fdbebf7dcc4e097bcbc1159096361c243f9e553f209f47bc695b08cf9",
    "cross_cats_sorted": [
      "math.GR",
      "stat.TH"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.ST",
    "submitted_at": "2013-03-11T22:53:25Z",
    "title_canon_sha256": "8ed8b9924be0540adb490211722f9f93e06e88dd5d71338ef69342e96d4e83d9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1303.2707",
    "kind": "arxiv",
    "version": 4
  }
}