Pith Number

pith:GWOQGVFK

pith:2017:GWOQGVFKGRLM2MGOPCBAS7O22C

not attested not anchored not stored refs pending

A formula for the Entropy of the Convolution of Gibbs probabilities on the circle

Artur O. Lopes

arxiv:1702.03134 v3 · 2017-02-10 · math.DS · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{GWOQGVFKGRLM2MGOPCBAS7O22C}

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	2026-05-18T00:11:44.027510Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

359d0354aa3456cd30ce7882097ddad086eb6d6a081a91843b7b911803d342a7

Aliases

arxiv: 1702.03134 · arxiv_version: 1702.03134v3 · doi: 10.48550/arxiv.1702.03134 · pith_short_12: GWOQGVFKGRLM · pith_short_16: GWOQGVFKGRLM2MGO · pith_short_8: GWOQGVFK

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/GWOQGVFKGRLM2MGOPCBAS7O22C \
  | 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: 359d0354aa3456cd30ce7882097ddad086eb6d6a081a91843b7b911803d342a7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d61844fb31149c1165dd55cfebd7fe8a95b4879e3859f7a8dfd9074cee0522ba",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2017-02-10T11:20:28Z",
    "title_canon_sha256": "08d23b61e97a1ebe50cae74020f14c8cf890130ec9bd9cbbe040437213ab1466"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1702.03134",
    "kind": "arxiv",
    "version": 3
  }
}