Pith Number

pith:WOCW26GC

pith:2009:WOCW26GCWIO2N423ZHZSAPBGQO

not attested not anchored not stored refs pending

A concise proof of Oppenheim's double inequality relating to the cosine and sine functions

Bai-Ni Guo, Feng Qi

arxiv:0902.2511 v1 · 2009-02-15 · 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{WOCW26GCWIO2N423ZHZSAPBGQO}

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	2026-05-18T03:46:32.211934Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b3856d78c2b21da6f35bc9f3203c2683bae690643187a3bc4c008c493cc15105

Aliases

arxiv: 0902.2511 · arxiv_version: 0902.2511v1 · doi: 10.48550/arxiv.0902.2511 · pith_short_12: WOCW26GCWIO2 · pith_short_16: WOCW26GCWIO2N423 · pith_short_8: WOCW26GC

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/WOCW26GCWIO2N423ZHZSAPBGQO \
  | 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: b3856d78c2b21da6f35bc9f3203c2683bae690643187a3bc4c008c493cc15105

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5855c40be7b25ff9e127f36896a48f3f8f15d6c66428fe03a074313f85381b6d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2009-02-15T01:39:11Z",
    "title_canon_sha256": "ad7d434df1e5bdd2d0524a6c496d9ce8efd314ca203a93f2b48ea09cb867789c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0902.2511",
    "kind": "arxiv",
    "version": 1
  }
}