Pith Number

pith:3NH26ATM

pith:2010:3NH26ATML5ZDC6X5CFIFOB5WVS

not attested not anchored not stored refs pending

On harmonic numbers and Lucas sequences

Zhi-Wei Sun

arxiv:1001.0348 v2 · 2010-01-04 · math.NT · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{3NH26ATML5ZDC6X5CFIFOB5WVS}

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	2026-05-18T04:21:30.070714Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

db4faf026c5f72317afd11505707b6acb9cc9eff7b068fcc10919fb1c84697b8

Aliases

arxiv: 1001.0348 · arxiv_version: 1001.0348v2 · doi: 10.48550/arxiv.1001.0348 · pith_short_12: 3NH26ATML5ZD · pith_short_16: 3NH26ATML5ZDC6X5 · pith_short_8: 3NH26ATM

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/3NH26ATML5ZDC6X5CFIFOB5WVS \
  | 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: db4faf026c5f72317afd11505707b6acb9cc9eff7b068fcc10919fb1c84697b8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0ee58d786935a7282d3229b7610d70ac29f05860b6f55911a3e2fafb28e93fbc",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2010-01-04T17:09:07Z",
    "title_canon_sha256": "bc733255b60d582ebb23724976a42cfc08f4e5b7d493f593aff8fcafef549590"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1001.0348",
    "kind": "arxiv",
    "version": 2
  }
}