Pith Number

pith:USOHR3EM

pith:2012:USOHR3EMV22B4PN43ZRQWCAMCW

not attested not anchored not stored refs pending

Sharp bounds for the difference between the arithmetic and geometric means

J. M. Aldaz

arxiv:1203.4454 v1 · 2012-03-20 · 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{USOHR3EMV22B4PN43ZRQWCAMCW}

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	2026-05-18T03:59:39.042853Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a49c78ec8caeb41e3dbcde630b080c1588ed5fa020590cfb9d0c109eeca5cf60

Aliases

arxiv: 1203.4454 · arxiv_version: 1203.4454v1 · doi: 10.48550/arxiv.1203.4454 · pith_short_12: USOHR3EMV22B · pith_short_16: USOHR3EMV22B4PN4 · pith_short_8: USOHR3EM

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/USOHR3EMV22B4PN43ZRQWCAMCW \
  | 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: a49c78ec8caeb41e3dbcde630b080c1588ed5fa020590cfb9d0c109eeca5cf60

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bbdcd3e3d2cc00c4e0bf5d671daf5cbfccbe8511324ec5c53957bf27aaf38720",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2012-03-20T14:46:33Z",
    "title_canon_sha256": "967c75f8623a291937dd160f3fe1d9e4b35a49da2a4aeb204ce417eb3880417c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1203.4454",
    "kind": "arxiv",
    "version": 1
  }
}