Pith Number

pith:5VWKLHRY

pith:2009:5VWKLHRYXZ5MPNQAXIUBQGD6ZH

not attested not anchored not stored refs pending

Refinements of lower bounds for polygamma functions

Bai-Ni Guo, Feng Qi

arxiv:0903.1996 v1 · 2009-03-11 · 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{5VWKLHRYXZ5MPNQAXIUBQGD6ZH}

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	2026-05-18T03:35:26.766409Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ed6ca59e38be7ac7b600ba2818187ec9d722a36e6df2721a5ef42aa7fd3ea0fd

Aliases

arxiv: 0903.1996 · arxiv_version: 0903.1996v1 · doi: 10.48550/arxiv.0903.1996 · pith_short_12: 5VWKLHRYXZ5M · pith_short_16: 5VWKLHRYXZ5MPNQA · pith_short_8: 5VWKLHRY

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/5VWKLHRYXZ5MPNQAXIUBQGD6ZH \
  | 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: ed6ca59e38be7ac7b600ba2818187ec9d722a36e6df2721a5ef42aa7fd3ea0fd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f04e990f90f012dff126a35fa9eba129566db07b223b3dc606a662bf5319b8ec",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2009-03-11T15:30:59Z",
    "title_canon_sha256": "3b9ae060bd58fef46e4693006514ba94ab52b2ce4823886ac5802af40ab5d43c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0903.1996",
    "kind": "arxiv",
    "version": 1
  }
}