Pith Number

pith:WBWKUDAC

pith:2005:WBWKUDACUQZBUQSR7R62ML65TJ

not attested not anchored not stored refs pending

Optimal quantizers for Radon random vectors in a Banach space

Harald Luschgy, Pag\`es Gilles (PMA), Siegried Graf (Universit\"at Passau)

arxiv:math/0504236 v1 · 2005-04-12 · 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{WBWKUDACUQZBUQSR7R62ML65TJ}

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	2026-05-18T01:08:51.204683Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b06caa0c02a4321a4251fc7da62fdd9a4292534f9b882c1ca5510d012a5fb1fc

Aliases

arxiv: math/0504236 · arxiv_version: math/0504236v1 · doi: 10.48550/arxiv.math/0504236 · pith_short_12: WBWKUDACUQZB · pith_short_16: WBWKUDACUQZBUQSR · pith_short_8: WBWKUDAC

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/WBWKUDACUQZBUQSR7R62ML65TJ \
  | 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: b06caa0c02a4321a4251fc7da62fdd9a4292534f9b882c1ca5510d012a5fb1fc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c8d18b88c46929bd0a38365efeab358f756f98c4b04b8d5a34c38592bdd8eaab",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.PR",
    "submitted_at": "2005-04-12T08:43:54Z",
    "title_canon_sha256": "437710f356384f3bcd26be469e6cb214c483f9d09080c2fa0bc8e3e9c64f0c8f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0504236",
    "kind": "arxiv",
    "version": 1
  }
}