Pith Number

pith:6KREXHAE

pith:2010:6KREXHAEHVP7X2KD3RSQ3D2NRM

not attested not anchored not stored refs pending

Orthogonal polynomials and expansions for a family of weight functions in two variables

Yuan Xu

arxiv:1012.5268 v2 · 2010-12-23 · math.CA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{6KREXHAEHVP7X2KD3RSQ3D2NRM}

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	2026-05-18T04:21:00.508710Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f2a24b9c043d5ffbe943dc650d8f4d8b213e58d8841f33af21b4a253805cd7bc

Aliases

arxiv: 1012.5268 · arxiv_version: 1012.5268v2 · doi: 10.48550/arxiv.1012.5268 · pith_short_12: 6KREXHAEHVP7 · pith_short_16: 6KREXHAEHVP7X2KD · pith_short_8: 6KREXHAE

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/6KREXHAEHVP7X2KD3RSQ3D2NRM \
  | 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: f2a24b9c043d5ffbe943dc650d8f4d8b213e58d8841f33af21b4a253805cd7bc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fd7a599ab9547d2542cbb91979e60d3ebf06e480646f192809a58a8e7d14b381",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2010-12-23T18:08:55Z",
    "title_canon_sha256": "b12036e00b7e2292ef820ae842c2d4d8eccae86456cac5497f2cc07155abfbf8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1012.5268",
    "kind": "arxiv",
    "version": 2
  }
}