Pith Number

pith:AHWGEMQ6

pith:2014:AHWGEMQ6QNGF3X6HIQHHPAKY5C

not attested not anchored not stored refs pending

Operator inequalities among arithmetic mean, geometric mean and harmonic mean

Shigeru Furuichi

arxiv:1410.4905 v1 · 2014-10-18 · 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{AHWGEMQ6QNGF3X6HIQHHPAKY5C}

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	2026-05-18T02:39:47.513585Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

01ec62321e834c5ddfc7440e778158e8a6b551b10cf79111e1e099c112d151a9

Aliases

arxiv: 1410.4905 · arxiv_version: 1410.4905v1 · doi: 10.48550/arxiv.1410.4905 · pith_short_12: AHWGEMQ6QNGF · pith_short_16: AHWGEMQ6QNGF3X6H · pith_short_8: AHWGEMQ6

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/AHWGEMQ6QNGF3X6HIQHHPAKY5C \
  | 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: 01ec62321e834c5ddfc7440e778158e8a6b551b10cf79111e1e099c112d151a9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3083ddc0135bc0d5d45d4fafbf78a1cbb95ccbcbf4408caede9af8408dc9c346",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2014-10-18T03:42:49Z",
    "title_canon_sha256": "10832bde2e6be5872f48454f33d867f28c2a915923fb87b401f39a812f4eec96"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1410.4905",
    "kind": "arxiv",
    "version": 1
  }
}