Pith Number

pith:4ICYVHPJ

pith:2013:4ICYVHPJAXR7WTUI6ZT4MBCIT2

not attested not anchored not stored refs pending

Hermite-Hadamard type inequalities for harmonically ({\alpha},m)-convex functions

Imdat Iscan

arxiv:1307.5402 v3 · 2013-07-20 · 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{4ICYVHPJAXR7WTUI6ZT4MBCIT2}

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	2026-05-18T02:18:33.232795Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e2058a9de905e3fb4e88f667c604489e864f8cc5ee34d5caeeecafbc008044f4

Aliases

arxiv: 1307.5402 · arxiv_version: 1307.5402v3 · doi: 10.48550/arxiv.1307.5402 · pith_short_12: 4ICYVHPJAXR7 · pith_short_16: 4ICYVHPJAXR7WTUI · pith_short_8: 4ICYVHPJ

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/4ICYVHPJAXR7WTUI6ZT4MBCIT2 \
  | 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: e2058a9de905e3fb4e88f667c604489e864f8cc5ee34d5caeeecafbc008044f4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "71c46bac2cfd7ed530be8b1a5de698378485ce65a6206174c575fe5af783ac38",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2013-07-20T10:21:17Z",
    "title_canon_sha256": "6f3f6db4a6925c2438bc44af2a8a4f01503edb2802e4b69851c987a18ffed019"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1307.5402",
    "kind": "arxiv",
    "version": 3
  }
}