Pith Number

pith:TRHZJUMO

pith:2010:TRHZJUMOQS2ITLELUIIESAK3NL

not attested not anchored not stored refs pending

Sharp bounds for harmonic numbers

Bai-Ni Guo, Feng Qi

arxiv:1002.3856 v1 · 2010-02-20 · 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{TRHZJUMOQS2ITLELUIIESAK3NL}

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	2026-05-18T03:48:34.573153Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9c4f94d18e84b489ac8ba21049015b6aec15804aeb522d6aef30ea82cedd2288

Aliases

arxiv: 1002.3856 · arxiv_version: 1002.3856v1 · doi: 10.48550/arxiv.1002.3856 · pith_short_12: TRHZJUMOQS2I · pith_short_16: TRHZJUMOQS2ITLEL · pith_short_8: TRHZJUMO

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/TRHZJUMOQS2ITLELUIIESAK3NL \
  | 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: 9c4f94d18e84b489ac8ba21049015b6aec15804aeb522d6aef30ea82cedd2288

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2ead4b00d53512ecc54e96158fc77f76570b858d59381049933ecf887aa2b151",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2010-02-20T07:56:38Z",
    "title_canon_sha256": "470a5a5dca155085054d9fef19a9e67d9f2159560088a6d2706db90ca78adf38"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1002.3856",
    "kind": "arxiv",
    "version": 1
  }
}