Pith Number

pith:Q43NNLHL

pith:2012:Q43NNLHLMEMMZTA6H3D5RD4WG3

not attested not anchored not stored refs pending

Sharp two parameter bounds for logarithmic and arithmetic-geometric means

Miao-Kun Wang, Xiao-Yan Ma, Ye-Fang Qiu, Yu-Ming Chu

arxiv:1209.3350 v1 · 2012-09-15 · 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{Q43NNLHLMEMMZTA6H3D5RD4WG3}

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	2026-05-18T03:41:42.444437Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8736d6aceb6118cccc1e3ec7d88f9636f4ab097aa396d329e3a44f011447b6f9

Aliases

arxiv: 1209.3350 · arxiv_version: 1209.3350v1 · doi: 10.48550/arxiv.1209.3350 · pith_short_12: Q43NNLHLMEMM · pith_short_16: Q43NNLHLMEMMZTA6 · pith_short_8: Q43NNLHL

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/Q43NNLHLMEMMZTA6H3D5RD4WG3 \
  | 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: 8736d6aceb6118cccc1e3ec7d88f9636f4ab097aa396d329e3a44f011447b6f9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ad15225b953a7925ad6ed60ed474bf863bdc21b1feabd0df7cefb06851e4fdde",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2012-09-15T03:20:24Z",
    "title_canon_sha256": "cf0f02cff4545bb6bdeff1d50786668581d16b0c207d1244933d0abcbfe1f325"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1209.3350",
    "kind": "arxiv",
    "version": 1
  }
}