Pith Number

pith:77OKPAEI

pith:2013:77OKPAEI626ZTWCBEC74NAER3M

not attested not anchored not stored refs pending

On harmonic representation of means

Alfred Witkowski

arxiv:1310.3063 v1 · 2013-10-11 · 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{77OKPAEI626ZTWCBEC74NAER3M}

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	2026-05-18T03:10:45.181179Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ffdca78088f6bd99d84120bfc68091db06dfe950c8360350a87f06af0a300c38

Aliases

arxiv: 1310.3063 · arxiv_version: 1310.3063v1 · doi: 10.48550/arxiv.1310.3063 · pith_short_12: 77OKPAEI626Z · pith_short_16: 77OKPAEI626ZTWCB · pith_short_8: 77OKPAEI

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/77OKPAEI626ZTWCBEC74NAER3M \
  | 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: ffdca78088f6bd99d84120bfc68091db06dfe950c8360350a87f06af0a300c38

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d5d3c2c7c089c6a41934000be6a570f75e04395265b4891023c0bb04f0b39d2c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2013-10-11T09:23:13Z",
    "title_canon_sha256": "f5d8fd07544def696c0e2204c80fd2e3d1175441f5a5b9f284e8799136e363ad"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1310.3063",
    "kind": "arxiv",
    "version": 1
  }
}