Pith Number

pith:LBOKA7IX

pith:2019:LBOKA7IXUFHLDTUKJ4NRUCZ6R2

not attested not anchored not stored refs pending

Extended Congruences for Harmonic Numbers

Ren\'e Gy

arxiv:1902.05258 v1 · 2019-02-14 · 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{LBOKA7IXUFHLDTUKJ4NRUCZ6R2}

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	2026-05-17T23:54:01.440052Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

585ca07d17a14eb1ce8a4f1b1a0b3e8ea4f3a3d0c33d132e16e17993d48f4188

Aliases

arxiv: 1902.05258 · arxiv_version: 1902.05258v1 · doi: 10.48550/arxiv.1902.05258 · pith_short_12: LBOKA7IXUFHL · pith_short_16: LBOKA7IXUFHLDTUK · pith_short_8: LBOKA7IX

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/LBOKA7IXUFHLDTUKJ4NRUCZ6R2 \
  | 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: 585ca07d17a14eb1ce8a4f1b1a0b3e8ea4f3a3d0c33d132e16e17993d48f4188

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e4353663b302168fc6d9f4055fd159e7e7f736565ea7d5fce6691a3fe9c87791",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2019-02-14T08:31:33Z",
    "title_canon_sha256": "f67a3559f5932b55bcca9fa2e82f1daf81e7e7e293271fab3cc9c7a3d7e7eaa7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1902.05258",
    "kind": "arxiv",
    "version": 1
  }
}