Pith Number

pith:4M63UJ2G

pith:2011:4M63UJ2GQ5ONNPSUNJ2DWVFR23

not attested not anchored not stored refs pending

Mixed means of commutators of central integral means and CMO

Jian Wang, Shunchao Long

arxiv:1103.0107 v1 · 2011-03-01 · 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{4M63UJ2GQ5ONNPSUNJ2DWVFR23}

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	2026-05-18T04:19:55.773126Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e33dba2746875cd6be546a743b54b1d6d146031870662b5e74aef7b45175b303

Aliases

arxiv: 1103.0107 · arxiv_version: 1103.0107v1 · doi: 10.48550/arxiv.1103.0107 · pith_short_12: 4M63UJ2GQ5ON · pith_short_16: 4M63UJ2GQ5ONNPSU · pith_short_8: 4M63UJ2G

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/4M63UJ2GQ5ONNPSUNJ2DWVFR23 \
  | 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: e33dba2746875cd6be546a743b54b1d6d146031870662b5e74aef7b45175b303

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "53a777ca8cbf5b3a6395788938a0f3f142cdf9691c47cecb37ab83f450ad4db2",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2011-03-01T09:00:05Z",
    "title_canon_sha256": "521b3e6f0a4563c341288580d6705852411ec690013ee0364ab8e3ab1b4d35bf"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1103.0107",
    "kind": "arxiv",
    "version": 1
  }
}