Pith Number

pith:C7J6XPI7

pith:2013:C7J6XPI74OSJ4IRUFPLZADQRFB

not attested not anchored not stored refs pending

The best bounds for Toader mean in terms of the centroidal and arithmetic means

Feng Qi, Yun Hua

arxiv:1303.2451 v1 · 2013-03-11 · 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{C7J6XPI74OSJ4IRUFPLZADQRFB}

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	2026-05-18T02:43:00.845053Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

17d3ebbd1fe3a49e22342bd7900e112849961d82018601025be336bb57b6cd65

Aliases

arxiv: 1303.2451 · arxiv_version: 1303.2451v1 · doi: 10.48550/arxiv.1303.2451 · pith_short_12: C7J6XPI74OSJ · pith_short_16: C7J6XPI74OSJ4IRU · pith_short_8: C7J6XPI7

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/C7J6XPI74OSJ4IRUFPLZADQRFB \
  | 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: 17d3ebbd1fe3a49e22342bd7900e112849961d82018601025be336bb57b6cd65

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fd6caf048ff1c6d7fc67ee184595c317dab0354161a046fd026fd2689b2a5200",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2013-03-11T08:34:23Z",
    "title_canon_sha256": "be19f56a4f5dcdd1d705464e2f413ebb46b106636c2957b944fa0831ac590f50"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1303.2451",
    "kind": "arxiv",
    "version": 1
  }
}