Pith Number

pith:3WBRNPA5

pith:2012:3WBRNPA5L3LD7KVSFZFW4CBTRS

not attested not anchored not stored refs pending

Sharp inequalities for the Neuman-Sandor mean in terms of arithmetic and contra-harmonic means

Bao-Yu Liu, Miao-Kun Wang, Yu-Ming Chu

arxiv:1209.5825 v1 · 2012-09-26 · 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{3WBRNPA5L3LD7KVSFZFW4CBTRS}

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	2026-05-18T03:41:42.425903Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

dd8316bc1d5ed63faab22e4b6e08338cb928ebe62e07d72ae662b40238226797

Aliases

arxiv: 1209.5825 · arxiv_version: 1209.5825v1 · doi: 10.48550/arxiv.1209.5825 · pith_short_12: 3WBRNPA5L3LD · pith_short_16: 3WBRNPA5L3LD7KVS · pith_short_8: 3WBRNPA5

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/3WBRNPA5L3LD7KVSFZFW4CBTRS \
  | 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: dd8316bc1d5ed63faab22e4b6e08338cb928ebe62e07d72ae662b40238226797

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f0a0da544eaeaecc6675d0d16f41f289822ae2a7d4bd26db997c3005bd0fc5af",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2012-09-26T03:47:57Z",
    "title_canon_sha256": "1e4cdcb8c1fa3c30cc5fba35992c9c7c3b53fde4b0609d7388365c26f97a23cd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1209.5825",
    "kind": "arxiv",
    "version": 1
  }
}