Pith Number

pith:GQ5NO6RO

pith:2011:GQ5NO6ROT6WVSEQQ3BQ77H33T2

not attested not anchored not stored refs pending

On generalized trigonometric functions with two parameters

Barkat Ali Bhayo, Matti Vuorinen

arxiv:1112.0483 v2 · 2011-12-02 · 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{GQ5NO6ROT6WVSEQQ3BQ77H33T2}

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	2026-05-18T03:53:54.571211Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

343ad77a2e9fad591210d861ff9f7b9e91a21fec20e5117e7db0ca3cb791b44e

Aliases

arxiv: 1112.0483 · arxiv_version: 1112.0483v2 · doi: 10.48550/arxiv.1112.0483 · pith_short_12: GQ5NO6ROT6WV · pith_short_16: GQ5NO6ROT6WVSEQQ · pith_short_8: GQ5NO6RO

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/GQ5NO6ROT6WVSEQQ3BQ77H33T2 \
  | 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: 343ad77a2e9fad591210d861ff9f7b9e91a21fec20e5117e7db0ca3cb791b44e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5c6ea67c30865c7e6468c258cba210052fcca461b95ccda1b24a4a36bc422256",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2011-12-02T15:33:52Z",
    "title_canon_sha256": "1fbb36703f2f3d09fbf80ddb2bf3f10e45cea468cd8eef53f1a5f58e44ba0efc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1112.0483",
    "kind": "arxiv",
    "version": 2
  }
}