Pith Number

pith:GRZK4AXN

pith:2008:GRZK4AXNAKCW35JWCMREV35SBL

not attested not anchored not stored refs pending

A spline interpretation of Eulerian numbers

Renhong Wang, Yan Xu, Zhiqiang Xu

arxiv:0808.2349 v2 · 2008-08-18 · math.NA · cs.NA · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{GRZK4AXNAKCW35JWCMREV35SBL}

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	2026-06-03T22:06:09.098571Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3472ae02ed02856df53613224aefb20ac7ca64857d3b0f818418e7a321a1e506

Aliases

arxiv: 0808.2349 · arxiv_version: 0808.2349v2 · doi: 10.48550/arxiv.0808.2349 · pith_short_12: GRZK4AXNAKCW · pith_short_16: GRZK4AXNAKCW35JW · pith_short_8: GRZK4AXN

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/GRZK4AXNAKCW35JWCMREV35SBL \
  | 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: 3472ae02ed02856df53613224aefb20ac7ca64857d3b0f818418e7a321a1e506

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5663da57ecd0b716b9a0385c7d35481feb75938e38e1d8402df5d06e8804c27f",
    "cross_cats_sorted": [
      "cs.NA",
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2008-08-18T08:14:18Z",
    "title_canon_sha256": "675c33a89034397ea40d632d6b341d29f81003327d126bf76cf461c899825a6b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0808.2349",
    "kind": "arxiv",
    "version": 2
  }
}