Pith Number

pith:2QFNIWEK

pith:2012:2QFNIWEKOQ7ZEWEX2CSK4CHEHO

not attested not anchored not stored refs pending

Upper Beurling Density of Systems formed by Translates of finite Sets of Elements in $L^p(\R^d)$

Bei Liu, Rui Liu

arxiv:1203.6147 v1 · 2012-03-28 · math.FA · math.CA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{2QFNIWEKOQ7ZEWEX2CSK4CHEHO}

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	2026-05-18T03:59:04.047297Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d40ad4588a743f925897d0a4ae08e43b9d482e0ca7e75a6c07edc0ed92361640

Aliases

arxiv: 1203.6147 · arxiv_version: 1203.6147v1 · doi: 10.48550/arxiv.1203.6147 · pith_short_12: 2QFNIWEKOQ7Z · pith_short_16: 2QFNIWEKOQ7ZEWEX · pith_short_8: 2QFNIWEK

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/2QFNIWEKOQ7ZEWEX2CSK4CHEHO \
  | 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: d40ad4588a743f925897d0a4ae08e43b9d482e0ca7e75a6c07edc0ed92361640

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "247a9c87d4c6c694fa523b5fd5cf784f9eb80e36d9718053dac5bb5046d7caf6",
    "cross_cats_sorted": [
      "math.CA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2012-03-28T03:44:23Z",
    "title_canon_sha256": "d4ca86c99ab97d2f9731e0790727173283b23917a00cfe206050ee24d3e7de38"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1203.6147",
    "kind": "arxiv",
    "version": 1
  }
}