Pith Number

pith:3VHYOYA6

pith:2010:3VHYOYA6LSYVNMG26NHFS6AW2G

not attested not anchored not stored refs pending

Minimization of the Probabilistic p-frame Potential

Kasso A. Okoudjou, Martin Ehler

arxiv:1101.0140 v2 · 2010-12-30 · math.FA · math.ST · 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{3VHYOYA6LSYVNMG26NHFS6AW2G}

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.

Cited by

1 paper in Pith

Energy on spheres and discreteness of minimizing measures

Receipt and verification

First computed	2026-05-18T00:36:14.790846Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

dd4f87601e5cb156b0daf34e597816d1a73e7e67f9251e93514ff99260f81899

Aliases

arxiv: 1101.0140 · arxiv_version: 1101.0140v2 · doi: 10.48550/arxiv.1101.0140 · pith_short_12: 3VHYOYA6LSYV · pith_short_16: 3VHYOYA6LSYVNMG2 · pith_short_8: 3VHYOYA6

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/3VHYOYA6LSYVNMG26NHFS6AW2G \
  | 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: dd4f87601e5cb156b0daf34e597816d1a73e7e67f9251e93514ff99260f81899

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e65d6782699268e7afe6acd2db647190b4303a28c91add2243caeba878d40fd9",
    "cross_cats_sorted": [
      "math.ST",
      "stat.TH"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2010-12-30T19:29:42Z",
    "title_canon_sha256": "d55e3cd36b9cd06f9c780da6a78a591f50e22a8565ae3ee2d70d0c52945accac"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1101.0140",
    "kind": "arxiv",
    "version": 2
  }
}