Pith Number

pith:DU5GAYR2

pith:2012:DU5GAYR2D25RVGHBYNJ6MNZQED

not attested not anchored not stored refs pending

Some Best Possible Inequalities Concerning Certain Bivariate Means

Bao-Yu Liu, Tie-Hong Zhao, Yu-Ming Chu

arxiv:1210.4219 v1 · 2012-10-15 · 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{DU5GAYR2D25RVGHBYNJ6MNZQED}

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	2026-05-18T03:41:42.416491Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1d3a60623a1ebb1a98e1c353e6373020f19936e3f17cf1359375f29ce2145f49

Aliases

arxiv: 1210.4219 · arxiv_version: 1210.4219v1 · doi: 10.48550/arxiv.1210.4219 · pith_short_12: DU5GAYR2D25R · pith_short_16: DU5GAYR2D25RVGHB · pith_short_8: DU5GAYR2

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/DU5GAYR2D25RVGHBYNJ6MNZQED \
  | 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: 1d3a60623a1ebb1a98e1c353e6373020f19936e3f17cf1359375f29ce2145f49

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9e7099d11851d6aa60c18d0bc589aa296d164ff307419bd05fd9e158437231ef",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2012-10-15T23:53:54Z",
    "title_canon_sha256": "b3967b094d1a3df48b087d7afb0165c62c54780dec41208284ddd1e90b8a737c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1210.4219",
    "kind": "arxiv",
    "version": 1
  }
}