Pith Number

pith:KNR3P7L3

pith:2009:KNR3P7L3CWKWYSRUAZHIMPDJJO

not attested not anchored not stored refs pending

Operator log-convex functions and operator means

Fumio Hiai, Tsuyoshi Ando

arxiv:0911.5267 v5 · 2009-11-27 · 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{KNR3P7L3CWKWYSRUAZHIMPDJJO}

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	2026-05-18T02:30:48.134840Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5363b7fd7b15956c4a34064e863c694ba06fff8b30aa1bb7269cae91476b9e6a

Aliases

arxiv: 0911.5267 · arxiv_version: 0911.5267v5 · doi: 10.48550/arxiv.0911.5267 · pith_short_12: KNR3P7L3CWKW · pith_short_16: KNR3P7L3CWKWYSRU · pith_short_8: KNR3P7L3

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/KNR3P7L3CWKWYSRUAZHIMPDJJO \
  | 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: 5363b7fd7b15956c4a34064e863c694ba06fff8b30aa1bb7269cae91476b9e6a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "eeeb04bff88da365fbd02cdf7abdfc0b300c02d50822f11f8dd4b1448a5dd965",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2009-11-27T14:03:15Z",
    "title_canon_sha256": "846a0570075e14bdcd6ae237247e82b092bddce5f41f0e071e7d33ff699cd755"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0911.5267",
    "kind": "arxiv",
    "version": 5
  }
}