Pith Number

pith:4UHWZD2T

pith:2012:4UHWZD2TXFKPVPARNH3WTE2KKZ

not attested not anchored not stored refs pending

A note on the Neuman-S\'andor Mean

Bao-Yu Liu, Tie-Hong Zhao, Yu-Ming Chu

arxiv:1211.0089 v1 · 2012-11-01 · 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{4UHWZD2TXFKPVPARNH3WTE2KKZ}

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	2026-05-18T03:39:16.022300Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e50f6c8f53b954fabc1169f769934a5645f569a588a44a99c791af16d29a93fb

Aliases

arxiv: 1211.0089 · arxiv_version: 1211.0089v1 · doi: 10.48550/arxiv.1211.0089 · pith_short_12: 4UHWZD2TXFKP · pith_short_16: 4UHWZD2TXFKPVPAR · pith_short_8: 4UHWZD2T

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/4UHWZD2TXFKPVPARNH3WTE2KKZ \
  | 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: e50f6c8f53b954fabc1169f769934a5645f569a588a44a99c791af16d29a93fb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4b18d70d1bddd411adec6e75b6b3c6a4b1d84dd308d1df6ce312d14e0912b631",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2012-11-01T04:25:31Z",
    "title_canon_sha256": "6902bbc4f5d3e78255498cafeff896a1f0cc2865d7d12800546ecd80cb63b684"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1211.0089",
    "kind": "arxiv",
    "version": 1
  }
}