Pith Number

pith:4YQOF435

pith:2012:4YQOF435UAOER4KIWAEGXE4PDS

not attested not anchored not stored refs pending

Sharp error bounds for Jacobi expansions and Gengenbauer-Gauss quadrature of analytic functions

Li-Lian Wang, Xiaodan Zhao, Ziqing Xie

arxiv:1210.2141 v1 · 2012-10-08 · math.NA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4YQOF435UAOER4KIWAEGXE4PDS}

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	2026-05-18T03:43:50.984171Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e620e2f37da01c48f148b0086b938f1c83d69844e467576c998a0b9c4a1f1ac0

Aliases

arxiv: 1210.2141 · arxiv_version: 1210.2141v1 · doi: 10.48550/arxiv.1210.2141 · pith_short_12: 4YQOF435UAOE · pith_short_16: 4YQOF435UAOER4KI · pith_short_8: 4YQOF435

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/4YQOF435UAOER4KIWAEGXE4PDS \
  | 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: e620e2f37da01c48f148b0086b938f1c83d69844e467576c998a0b9c4a1f1ac0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "706f2d68345ccf1d50df0c316369672a956c53942341d43a9ee472c243b764ec",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/3.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2012-10-08T04:02:52Z",
    "title_canon_sha256": "4b1cfbde40ceb07f494c1574dc48440676d0386c00eaecd773aec3865bd116fd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1210.2141",
    "kind": "arxiv",
    "version": 1
  }
}