Pith Number

pith:TR72OEHU

pith:2004:TR72OEHUERKNPJJS6QXDS6OVNW

not attested not anchored not stored refs pending

New identities involving Bernoulli and Euler polynomials. II

Hao Pan, Zhi-Wei Sun

arxiv:math/0408223 v3 · 2004-08-17 · math.NT · 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{TR72OEHUERKNPJJS6QXDS6OVNW}

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	2026-07-04T14:39:00.041685Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9c7fa710f42454d7a532f42e3979d56d91558d460960b5dfae1deb2c014f177a

Aliases

arxiv: math/0408223 · arxiv_version: math/0408223v3 · doi: 10.48550/arxiv.math/0408223 · pith_short_12: TR72OEHUERKN · pith_short_16: TR72OEHUERKNPJJS · pith_short_8: TR72OEHU

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/TR72OEHUERKNPJJS6QXDS6OVNW \
  | 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: 9c7fa710f42454d7a532f42e3979d56d91558d460960b5dfae1deb2c014f177a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "272a940af701a247d0a298486ffa60da143c15058da0095ee544c4a83ead1b59",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "",
    "primary_cat": "math.NT",
    "submitted_at": "2004-08-17T16:44:36Z",
    "title_canon_sha256": "b531aa1c59e5d94a6703abaf2e465f5b360a489460193b9bb4647a1d861dce15"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0408223",
    "kind": "arxiv",
    "version": 3
  }
}