Pith Number

pith:CS56OQJS

pith:2010:CS56OQJSNA3VTHJSCNFHXCVSRA

not attested not anchored not stored refs pending

Sharp rate for the dual quantization problem

Benedikt Wilbertz (LPMA), Gilles Pag\`es (LPMA)

arxiv:1012.3441 v3 · 2010-12-15 · 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{CS56OQJSNA3VTHJSCNFHXCVSRA}

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	2026-05-18T02:23:07.134512Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

14bbe741326837599d32134a7b8ab28838e4f4730a45114aa0a387aa9dff5c4c

Aliases

arxiv: 1012.3441 · arxiv_version: 1012.3441v3 · doi: 10.48550/arxiv.1012.3441 · pith_short_12: CS56OQJSNA3V · pith_short_16: CS56OQJSNA3VTHJS · pith_short_8: CS56OQJS

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/CS56OQJSNA3VTHJSCNFHXCVSRA \
  | 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: 14bbe741326837599d32134a7b8ab28838e4f4730a45114aa0a387aa9dff5c4c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0523bc6abfbb2d46088508cf4694a2386fd525117c63f18f738a7b542b427d62",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2010-12-15T19:48:53Z",
    "title_canon_sha256": "22ca2dfc0be72c10bcdb5226521fcce16f4847786b29287253e62c188b2c9b92"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1012.3441",
    "kind": "arxiv",
    "version": 3
  }
}