Pith Number

pith:OSD5BKE5

pith:2009:OSD5BKE5OSZEOFS7ZZMGWKO5BE

not attested not anchored not stored refs pending

A refinement of the arithmetic-geometric mean inequality

Shigeru Furuichi

arxiv:0912.5227 v2 · 2009-12-28 · 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{OSD5BKE5OSZEOFS7ZZMGWKO5BE}

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	2026-05-18T04:42:02.645126Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7487d0a89d74b247165fce586b29dd090b55510ccc648c32febbef2ba6701f3c

Aliases

arxiv: 0912.5227 · arxiv_version: 0912.5227v2 · doi: 10.48550/arxiv.0912.5227 · pith_short_12: OSD5BKE5OSZE · pith_short_16: OSD5BKE5OSZEOFS7 · pith_short_8: OSD5BKE5

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/OSD5BKE5OSZEOFS7ZZMGWKO5BE \
  | 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: 7487d0a89d74b247165fce586b29dd090b55510ccc648c32febbef2ba6701f3c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d03c2ec5b9187f25592732ea4f0988fb3145c65626e3cad800e5070d5677a6c2",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2009-12-28T23:39:18Z",
    "title_canon_sha256": "522759c9749f2ddd3da0d8a06ab09e9ce21aacf311ea5babaca1a5399f11b644"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0912.5227",
    "kind": "arxiv",
    "version": 2
  }
}