Pith Number

pith:Y3KJB6FK

pith:2010:Y3KJB6FKSGAXYWG5PA5T4C75ZQ

not attested not anchored not stored refs pending

Expansions of one density via polynomials orthogonal with respect to the other

Pawe{\l} J. Szab{\l}owski

arxiv:1011.1492 v5 · 2010-11-05 · math.CA · 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{Y3KJB6FKSGAXYWG5PA5T4C75ZQ}

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	2026-05-18T03:49:01.255370Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c6d490f8aa91817c58dd783b3e0bfdcc05b268ad4faac9c0a55223062292367a

Aliases

arxiv: 1011.1492 · arxiv_version: 1011.1492v5 · doi: 10.48550/arxiv.1011.1492 · pith_short_12: Y3KJB6FKSGAX · pith_short_16: Y3KJB6FKSGAXYWG5 · pith_short_8: Y3KJB6FK

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/Y3KJB6FKSGAXYWG5PA5T4C75ZQ \
  | 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: c6d490f8aa91817c58dd783b3e0bfdcc05b268ad4faac9c0a55223062292367a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2f8300e1d8859860ac2d5b06eeec6d0fb5e115c5a26c29c8b00e6885dd21cc11",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2010-11-05T19:46:46Z",
    "title_canon_sha256": "82302d904d7963bf4c682d486cc49c3f6c536d72cda344b759ad6b7295435eba"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1011.1492",
    "kind": "arxiv",
    "version": 5
  }
}