Pith Number

pith:XPIEYJBT

pith:2013:XPIEYJBTDN5KBZ62YSB4SUFYQL

not attested not anchored not stored refs pending

Asymptotic expansions of exponentials of digamma function and identity for Bernoulli polynomials

Neven Elezovi\'c

arxiv:1312.1604 v1 · 2013-12-05 · math.CA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{XPIEYJBTDN5KBZ62YSB4SUFYQL}

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	2026-05-18T03:05:26.759578Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bbd04c24331b7aa0e7dac483c950b882c7defa1a12df50cfc6868f7a51b13f4d

Aliases

arxiv: 1312.1604 · arxiv_version: 1312.1604v1 · doi: 10.48550/arxiv.1312.1604 · pith_short_12: XPIEYJBTDN5K · pith_short_16: XPIEYJBTDN5KBZ62 · pith_short_8: XPIEYJBT

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/XPIEYJBTDN5KBZ62YSB4SUFYQL \
  | 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: bbd04c24331b7aa0e7dac483c950b882c7defa1a12df50cfc6868f7a51b13f4d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "393b8ff18c61324d31b40da78241b672ea2669d5653286636fe96a4d6d75c388",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2013-12-05T16:23:54Z",
    "title_canon_sha256": "ebd0b7e1dd66f4361c54e24c90c2e04f64785a73ebd069bfc41bed4cbd39b55d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1312.1604",
    "kind": "arxiv",
    "version": 1
  }
}