Pith Number

pith:F2FPP4TP

pith:2018:F2FPP4TP5LJAMJLKTY2KP2WNIA

not attested not anchored not stored refs pending

Invariance in a class of operations related to weighted quasi-geometric means

Janusz Matkowski, Jimmy Devillet

arxiv:1809.10675 v1 · 2018-09-26 · 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{F2FPP4TP5LJAMJLKTY2KP2WNIA}

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	2026-05-18T00:04:35.302108Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2e8af7f26fead206256a9e34a7eacd400f9d7c73da2dcbcf825697c5e2fefcab

Aliases

arxiv: 1809.10675 · arxiv_version: 1809.10675v1 · doi: 10.48550/arxiv.1809.10675 · pith_short_12: F2FPP4TP5LJA · pith_short_16: F2FPP4TP5LJAMJLK · pith_short_8: F2FPP4TP

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/F2FPP4TP5LJAMJLKTY2KP2WNIA \
  | 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: 2e8af7f26fead206256a9e34a7eacd400f9d7c73da2dcbcf825697c5e2fefcab

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "59c961a90ab6d74c1de72ad5034d0404cdc530fc05642ed768c41023c022a385",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2018-09-26T20:52:41Z",
    "title_canon_sha256": "1c6c2973786e971c090176e0159cb52de0981b0c7ca4afcf470c11516f40c99c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1809.10675",
    "kind": "arxiv",
    "version": 1
  }
}