Pith Number

pith:3VU3AHCP

pith:2020:3VU3AHCPIC42SXYJRSW2YXDSKC

not attested not anchored not stored refs pending

Optimal quantization of the mean measure and applications to statistical learning

Cl\'ement Levrard (DATASHAPE, Fr\'ed\'eric Chazal (DATASHAPE), LPSM (UMR\_8001)), Martin Royer (DATASHAPE)

arxiv:2002.01216 v4 · 2020-02-04 · math.ST · stat.TH

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{3VU3AHCPIC42SXYJRSW2YXDSKC}

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	2026-07-05T02:24:09.020236Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

dd69b01c4f40b9a95f098cadac5c72509debe9621b9522e3f901cffc7bf1ef34

Aliases

arxiv: 2002.01216 · arxiv_version: 2002.01216v4 · doi: 10.48550/arxiv.2002.01216 · pith_short_12: 3VU3AHCPIC42 · pith_short_16: 3VU3AHCPIC42SXYJ · pith_short_8: 3VU3AHCP

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/3VU3AHCPIC42SXYJRSW2YXDSKC \
  | 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: dd69b01c4f40b9a95f098cadac5c72509debe9621b9522e3f901cffc7bf1ef34

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "439436074f940b6f1443e11af6d09c326d61f12c81f5fa6c861708668032470b",
    "cross_cats_sorted": [
      "stat.TH"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.ST",
    "submitted_at": "2020-02-04T10:45:51Z",
    "title_canon_sha256": "d2773125c0c40bfac5ceeb2780342b5718852efe59d45e815b61ba76fc20761b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2002.01216",
    "kind": "arxiv",
    "version": 4
  }
}