Pith Number

pith:57PU4T66

pith:2012:57PU4T66OZPWA3ZZ3S3WAIQKBY

not attested not anchored not stored refs pending

A family of summation formulas involving generalized harmonic numbers

Chuanan Wei, Dianxuan Gong, Qinglun Yan

arxiv:1203.2863 v1 · 2012-03-13 · math.CO · 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{57PU4T66OZPWA3ZZ3S3WAIQKBY}

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	2026-05-18T04:00:14.349826Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

efdf4e4fde765f606f39dcb760220a0e29846feec1badf6d6cedb8a27d2bf9be

Aliases

arxiv: 1203.2863 · arxiv_version: 1203.2863v1 · doi: 10.48550/arxiv.1203.2863 · pith_short_12: 57PU4T66OZPW · pith_short_16: 57PU4T66OZPWA3ZZ · pith_short_8: 57PU4T66

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/57PU4T66OZPWA3ZZ3S3WAIQKBY \
  | 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: efdf4e4fde765f606f39dcb760220a0e29846feec1badf6d6cedb8a27d2bf9be

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5ffc7a52aa089c84c7a45dbb4133ac6b4602a02046c2c340a218143cfaac0094",
    "cross_cats_sorted": [
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2012-03-13T17:03:42Z",
    "title_canon_sha256": "81d1f9c75b6eccf9febebdd6d4affba5f78d2cd9f73fdc0bf8e5366dee427ab6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1203.2863",
    "kind": "arxiv",
    "version": 1
  }
}