Pith Number

pith:X2PZIDYV

pith:2013:X2PZIDYV6LFR5ZENT2TGJFQMJU

not attested not anchored not stored refs pending

Hahn, Jacobi, and Krawtchouck polynomials of several variables

Yuan Xu

arxiv:1309.1510 v1 · 2013-09-05 · 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{X2PZIDYV6LFR5ZENT2TGJFQMJU}

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	2026-05-18T03:13:59.291194Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

be9f940f15f2cb1ee48d9ea664960c4d34a5cc4666fd1e53f1adb72299f243ed

Aliases

arxiv: 1309.1510 · arxiv_version: 1309.1510v1 · doi: 10.48550/arxiv.1309.1510 · pith_short_12: X2PZIDYV6LFR · pith_short_16: X2PZIDYV6LFR5ZEN · pith_short_8: X2PZIDYV

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/X2PZIDYV6LFR5ZENT2TGJFQMJU \
  | 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: be9f940f15f2cb1ee48d9ea664960c4d34a5cc4666fd1e53f1adb72299f243ed

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a0ac399b968f9993a51b7df4b80cca5952567d96eb121f80763f60d23f2183e0",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2013-09-05T23:33:55Z",
    "title_canon_sha256": "2eafdf5ae00d2724a53a23760613c09722b709f722529f71c18c97c6b9355eab"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1309.1510",
    "kind": "arxiv",
    "version": 1
  }
}