Pith Number

pith:D3QRYINT

pith:2018:D3QRYINT2WMLJ7U5IPOJ4SOPHR

not attested not anchored not stored refs pending

An integral representation of operator means via the power means and an application to the Ando-Hiai inequality

Takeaki Yamazaki

arxiv:1803.04630 v1 · 2018-03-13 · math.FA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{D3QRYINT2WMLJ7U5IPOJ4SOPHR}

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	2026-05-18T00:21:18.387194Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1ee11c21b3d598b4fe9d43dc9e49cf3c5cfdcb6c2ebd1adfaf69ff4c856aa164

Aliases

arxiv: 1803.04630 · arxiv_version: 1803.04630v1 · doi: 10.48550/arxiv.1803.04630 · pith_short_12: D3QRYINT2WML · pith_short_16: D3QRYINT2WMLJ7U5 · pith_short_8: D3QRYINT

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/D3QRYINT2WMLJ7U5IPOJ4SOPHR \
  | 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: 1ee11c21b3d598b4fe9d43dc9e49cf3c5cfdcb6c2ebd1adfaf69ff4c856aa164

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f36f63f23dbaf42b7df0523be4c6be46f7cba4616c0f9fca200cfb54e432b2b9",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2018-03-13T05:37:32Z",
    "title_canon_sha256": "a6273ed832e7f68e71b6b3457c692b324a5ea030f182a32d2529b5ca608ec078"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1803.04630",
    "kind": "arxiv",
    "version": 1
  }
}