Pith Number

pith:7BTVIP73

pith:2012:7BTVIP73GMO7UKZFYNNM2XXB53

not attested not anchored not stored refs pending

On the integral of the product of four and more Bernoulli polynomials

Daeyeoul Kim, Min-Soo Kim, Su Hu

arxiv:1206.3826 v2 · 2012-06-18 · math.NT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{7BTVIP73GMO7UKZFYNNM2XXB53}

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	2026-05-18T03:14:28.148585Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f867543ffb331dfa2b25c35acd5ee1eec19a176a25775f9caf3941516339bb83

Aliases

arxiv: 1206.3826 · arxiv_version: 1206.3826v2 · doi: 10.48550/arxiv.1206.3826 · pith_short_12: 7BTVIP73GMO7 · pith_short_16: 7BTVIP73GMO7UKZF · pith_short_8: 7BTVIP73

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/7BTVIP73GMO7UKZFYNNM2XXB53 \
  | 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: f867543ffb331dfa2b25c35acd5ee1eec19a176a25775f9caf3941516339bb83

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "09fb695f918fbd0bf2da39fe1dfb0668eac4a60e81b83a33de07cd67f750bcde",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2012-06-18T05:05:34Z",
    "title_canon_sha256": "2b2a87ec7d1a19ecd3cc1a6d70866e4a7b616e7eb72a649d55aa5e7fd5cea642"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1206.3826",
    "kind": "arxiv",
    "version": 2
  }
}