Pith Number

pith:PK45ZGG2

pith:2013:PK45ZGG2T57BUL2XKXQIJ7BFBA

not attested not anchored not stored refs pending

Hermite-Hadamard type inequalities for harmonically convex functions via fractional integrals

Imdat Iscan

arxiv:1312.7103 v1 · 2013-12-26 · 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{PK45ZGG2T57BUL2XKXQIJ7BFBA}

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	2026-05-18T03:03:45.872369Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7ab9dc98da9f7e1a2f5755e084fc25083786cb037a101edc7ae21031650ee9d4

Aliases

arxiv: 1312.7103 · arxiv_version: 1312.7103v1 · doi: 10.48550/arxiv.1312.7103 · pith_short_12: PK45ZGG2T57B · pith_short_16: PK45ZGG2T57BUL2X · pith_short_8: PK45ZGG2

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/PK45ZGG2T57BUL2XKXQIJ7BFBA \
  | 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: 7ab9dc98da9f7e1a2f5755e084fc25083786cb037a101edc7ae21031650ee9d4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a6f39bd3c3c36726e1b0b6e7b1f28dfd2c292fb0afd44378178754cfa067b6c3",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2013-12-26T13:06:48Z",
    "title_canon_sha256": "2964a09f51e84a30046f09a29a74e2ee9275928c64a7cb24a667eddfc3f38c87"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1312.7103",
    "kind": "arxiv",
    "version": 1
  }
}