Pith Number

pith:GEECTP7R

pith:2013:GEECTP7RFRP4MWPTSJD62QG3VV

not attested not anchored not stored refs pending

Integral representations of the weighted geometric mean and the logarithmic mean

Feng Qi, Wen-Hui Li, Xiao-Jing Zhang

arxiv:1303.3122 v1 · 2013-03-13 · math.CA · math.CV

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{GEECTP7RFRP4MWPTSJD62QG3VV}

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	2026-05-18T02:52:42.142070Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

310829bff12c5fc659f39247ed40dbad636b235158a05b1a3874c332e0d830af

Aliases

arxiv: 1303.3122 · arxiv_version: 1303.3122v1 · doi: 10.48550/arxiv.1303.3122 · pith_short_12: GEECTP7RFRP4 · pith_short_16: GEECTP7RFRP4MWPT · pith_short_8: GEECTP7R

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/GEECTP7RFRP4MWPTSJD62QG3VV \
  | 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: 310829bff12c5fc659f39247ed40dbad636b235158a05b1a3874c332e0d830af

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c1a0232f58247b7fa7960593b16ece06b993f069a2b4d6ff37e02d9311e385cc",
    "cross_cats_sorted": [
      "math.CV"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2013-03-13T10:17:47Z",
    "title_canon_sha256": "57c705fedd220b6010e8a6708c3db35dd9a5ffcbbd3e00963cc2ff3e4f3368b3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1303.3122",
    "kind": "arxiv",
    "version": 1
  }
}