Pith Number

pith:CI3JX4T4

pith:2012:CI3JX4T4I2Z3SNPYM2PMGR4QCW

not attested not anchored not stored refs pending

Power mean inequality of generalized trigonometric functions

Barkat Ali Bhayo, Matti Vuorinen

arxiv:1209.0873 v1 · 2012-09-05 · 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{CI3JX4T4I2Z3SNPYM2PMGR4QCW}

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	2026-05-18T03:46:15.968762Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

12369bf27c46b3b935f8669ec3479015879986cdfe6c71b82f929284bc8f544e

Aliases

arxiv: 1209.0873 · arxiv_version: 1209.0873v1 · doi: 10.48550/arxiv.1209.0873 · pith_short_12: CI3JX4T4I2Z3 · pith_short_16: CI3JX4T4I2Z3SNPY · pith_short_8: CI3JX4T4

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/CI3JX4T4I2Z3SNPYM2PMGR4QCW \
  | 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: 12369bf27c46b3b935f8669ec3479015879986cdfe6c71b82f929284bc8f544e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1228837459d7bd7acf3778a4c77aaf18a2b3e03c42f1da7f659a05eb5fc018ed",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2012-09-05T07:05:46Z",
    "title_canon_sha256": "9e1674658297617a3a2263f7759b1dffafcc0bf432a8916c8a15de92fc2d323a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1209.0873",
    "kind": "arxiv",
    "version": 1
  }
}