Pith Number

pith:MXR673YQ

pith:2012:MXR673YQOOV7I7CUGFW2KWDWCG

not attested not anchored not stored refs pending

Quantization of Gaussian measures with R\'enyi-\alpha-entropy constraints

Wolfgang Kreitmeier

arxiv:1212.6530 v2 · 2012-12-28 · 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{MXR673YQOOV7I7CUGFW2KWDWCG}

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	2026-05-18T03:20:09.380239Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

65e3efef1073abf47c54316da55876118816c0e794c96412ebbc6f298234190d

Aliases

arxiv: 1212.6530 · arxiv_version: 1212.6530v2 · doi: 10.48550/arxiv.1212.6530 · pith_short_12: MXR673YQOOV7 · pith_short_16: MXR673YQOOV7I7CU · pith_short_8: MXR673YQ

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/MXR673YQOOV7I7CUGFW2KWDWCG \
  | 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: 65e3efef1073abf47c54316da55876118816c0e794c96412ebbc6f298234190d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "df7bbae756759e3e48b925f00b7b97e787a0c27d4c6ea211446d4dfac56eb5cf",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2012-12-28T16:02:54Z",
    "title_canon_sha256": "5ad982f8a7a3846159d02e5bd8296dbdf8ec299f375b8b602da9684579fd37f9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1212.6530",
    "kind": "arxiv",
    "version": 2
  }
}