Pith Number

pith:H4ZNPVAH

pith:2018:H4ZNPVAHTV3VFP4C67PA6QC4MJ

not attested not anchored not stored refs pending

Summation formulas involving harmonic numbers with even or odd indexes

Chuanan Wei, Dianxuan Gong, Lily Li Liu

arxiv:1806.09985 v1 · 2018-06-24 · 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{H4ZNPVAHTV3VFP4C67PA6QC4MJ}

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	2026-05-18T00:12:22.514176Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3f32d7d4079d7752bf82f7de0f405c625dc37a6a5f8c22d8c59b0ce741e20502

Aliases

arxiv: 1806.09985 · arxiv_version: 1806.09985v1 · doi: 10.48550/arxiv.1806.09985 · pith_short_12: H4ZNPVAHTV3V · pith_short_16: H4ZNPVAHTV3VFP4C · pith_short_8: H4ZNPVAH

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/H4ZNPVAHTV3VFP4C67PA6QC4MJ \
  | 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: 3f32d7d4079d7752bf82f7de0f405c625dc37a6a5f8c22d8c59b0ce741e20502

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7af9db17dfd1da7c3b11f25bc28abe0a747166d0a95c8dd949f269decd7cd7ab",
    "cross_cats_sorted": [
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2018-06-24T00:16:24Z",
    "title_canon_sha256": "fc964bb51f951cf471d1ce43cf680c0c69e71327a21ee6104d47e0b6f4c1c70d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1806.09985",
    "kind": "arxiv",
    "version": 1
  }
}