Pith Number

pith:GAU424DE

pith:2004:GAU424DE4TS5KXHOCVWA7P3I7W

not attested not anchored not stored refs pending

New identities involving Bernoulli and Euler polynomials

Hao Pan, Zhi-Wei Sun

arxiv:math/0407363 v2 · 2004-07-21 · 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{GAU424DE4TS5KXHOCVWA7P3I7W}

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	2026-07-04T14:38:56.400547Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3029cd7064e4e5d55cee156c0fbf68fdbaf6a88ab18a0db933402d226d9dbda8

Aliases

arxiv: math/0407363 · arxiv_version: math/0407363v2 · doi: 10.48550/arxiv.math/0407363 · pith_short_12: GAU424DE4TS5 · pith_short_16: GAU424DE4TS5KXHO · pith_short_8: GAU424DE

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/GAU424DE4TS5KXHOCVWA7P3I7W \
  | 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: 3029cd7064e4e5d55cee156c0fbf68fdbaf6a88ab18a0db933402d226d9dbda8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cb0d8af281c9d147f041503ee80b9dc21be3260d987501422442585a66cf8325",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "",
    "primary_cat": "math.NT",
    "submitted_at": "2004-07-21T17:19:33Z",
    "title_canon_sha256": "1e042cc81c146c1282c475dee6e6f65dd710640dc8e96f9b99f85c71be7ad2a9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0407363",
    "kind": "arxiv",
    "version": 2
  }
}