Pith Number

pith:UBQJA7ZR

pith:2011:UBQJA7ZRAVJBXLALZASZI64D6U

not attested not anchored not stored refs pending

Strictly and non-strictly positive definite functions on spheres

Tilmann Gneiting

arxiv:1111.7077 v5 · 2011-11-30 · math.PR · 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{UBQJA7ZRAVJBXLALZASZI64D6U}

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	2026-05-18T03:11:47.294014Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a060907f3105521bac0bc825947b83f52c034c5817edc4e1b3e86e40f240f178

Aliases

arxiv: 1111.7077 · arxiv_version: 1111.7077v5 · doi: 10.48550/arxiv.1111.7077 · pith_short_12: UBQJA7ZRAVJB · pith_short_16: UBQJA7ZRAVJBXLAL · pith_short_8: UBQJA7ZR

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/UBQJA7ZRAVJBXLALZASZI64D6U \
  | 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: a060907f3105521bac0bc825947b83f52c034c5817edc4e1b3e86e40f240f178

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d55d4f36f53d06675dd423c44a3c6ec305e68ff73fa033e50174f95b242ffd8f",
    "cross_cats_sorted": [
      "math.ST",
      "stat.TH"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2011-11-30T08:13:30Z",
    "title_canon_sha256": "aec2e329f0daa7a8d81d16dd319dc0ab00ef9daa260decc9177eed6d50ad0476"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1111.7077",
    "kind": "arxiv",
    "version": 5
  }
}