Pith Number

pith:KDAHF6AG

pith:2012:KDAHF6AGU7SYKRPYKDGCRBJMM2

not attested not anchored not stored refs pending

Refinements of the inequalities between Neuman-Sandor, arithmetic, contra-harmonic and quadratic means

Miao-Kun Wang, Yu-Ming Chu

arxiv:1209.2920 v1 · 2012-09-13 · math.CA · math.OC

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{KDAHF6AGU7SYKRPYKDGCRBJMM2}

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	2026-05-18T03:41:42.455312Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

50c072f806a7e58545f850cc28852c66947b92b2bbf945e5bcf14c05de81b73f

Aliases

arxiv: 1209.2920 · arxiv_version: 1209.2920v1 · doi: 10.48550/arxiv.1209.2920 · pith_short_12: KDAHF6AGU7SY · pith_short_16: KDAHF6AGU7SYKRPY · pith_short_8: KDAHF6AG

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/KDAHF6AGU7SYKRPYKDGCRBJMM2 \
  | 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: 50c072f806a7e58545f850cc28852c66947b92b2bbf945e5bcf14c05de81b73f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d68dded72f10ae680ad593e74b082da24c2118d73a102f1f5aca3c587f8127ab",
    "cross_cats_sorted": [
      "math.OC"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2012-09-13T15:05:37Z",
    "title_canon_sha256": "a1813fec63b24b8c53ae60bd2372cc7df5c318aa9a6db022aab2e2a217600ace"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1209.2920",
    "kind": "arxiv",
    "version": 1
  }
}