Pith Number

pith:3X2PDDO6

pith:2025:3X2PDDO62OCEFP4EQJ4YICDATQ

not attested not anchored not stored refs pending

Optimal Bregman quantization : existence and uniqueness of optimal quantizers revisited

Gilles Pag\`es, Guillaume Boutoille

arxiv:2506.01746 v1 · 2025-06-02 · 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{3X2PDDO62OCEFP4EQJ4YICDATQ}

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.

Cited by

1 paper in Pith

Zador Theorem for optimal quantization with respect to Bregman divergences

Receipt and verification

First computed	2026-07-05T11:14:18.858543Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ddf4f18dded38442bf8482798408609c32027b785fa55383f13ff968d8c9fa97

Aliases

arxiv: 2506.01746 · arxiv_version: 2506.01746v1 · doi: 10.48550/arxiv.2506.01746 · pith_short_12: 3X2PDDO62OCE · pith_short_16: 3X2PDDO62OCEFP4E · pith_short_8: 3X2PDDO6

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/3X2PDDO62OCEFP4EQJ4YICDATQ \
  | 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: ddf4f18dded38442bf8482798408609c32027b785fa55383f13ff968d8c9fa97

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "dd7833ede3bef78a46f92d402cffd6e13b289d5b5cbf86099174175b7f08e8bc",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2025-06-02T14:53:48Z",
    "title_canon_sha256": "31a9eee3f45d78f516654a8452d3235ab818ed45675e7be29a6deadd4e806e94"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2506.01746",
    "kind": "arxiv",
    "version": 1
  }
}