Pith Number

pith:DYBAVPJ2

pith:2023:DYBAVPJ25T5NXEW5GD5T5PXHGR

not attested not anchored not stored refs pending

Beyond scalar quasi-arithmetic means: Quasi-arithmetic averages and quasi-arithmetic mixtures in information geometry

Frank Nielsen

arxiv:2301.10980 v5 · 2023-01-26 · cs.IT · math.IT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{DYBAVPJ25T5NXEW5GD5T5PXHGR}

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	2026-07-05T11:12:14.910518Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1e020abd3aecfadb92dd30fb3ebee7346c29650527e93cf38f7f84ff476f8d63

Aliases

arxiv: 2301.10980 · arxiv_version: 2301.10980v5 · doi: 10.48550/arxiv.2301.10980 · pith_short_12: DYBAVPJ25T5N · pith_short_16: DYBAVPJ25T5NXEW5 · pith_short_8: DYBAVPJ2

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/DYBAVPJ25T5NXEW5GD5T5PXHGR \
  | 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: 1e020abd3aecfadb92dd30fb3ebee7346c29650527e93cf38f7f84ff476f8d63

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "533da857f12535baf37ec5c8b7f81ac2aa0473205ccf96058d14100f6b58b367",
    "cross_cats_sorted": [
      "math.IT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.IT",
    "submitted_at": "2023-01-26T08:16:34Z",
    "title_canon_sha256": "efce2925ecefec6e61262c1d4fa43ff5e6f6e020c59042be198e8a9d0a26cdb4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2301.10980",
    "kind": "arxiv",
    "version": 5
  }
}