Pith Number

pith:XPU764IJ

pith:2010:XPU764IJ3G6DC2WUIRKMT55VIE

not attested not anchored not stored refs pending

Complex Powers of the Laplacian on Affine Nested Fractals as Calder\'on-Zygmund operators

Luke Rogers, Marius Ionescu

arxiv:1002.2011 v2 · 2010-02-10 · math.FA · math.AP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{XPU764IJ3G6DC2WUIRKMT55VIE}

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	2026-05-18T03:08:16.418836Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bbe9ff7109d9bc316ad44454c9f7b5412de7d0d5d1346410a643daac6a096ec0

Aliases

arxiv: 1002.2011 · arxiv_version: 1002.2011v2 · doi: 10.48550/arxiv.1002.2011 · pith_short_12: XPU764IJ3G6D · pith_short_16: XPU764IJ3G6DC2WU · pith_short_8: XPU764IJ

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/XPU764IJ3G6DC2WUIRKMT55VIE \
  | 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: bbe9ff7109d9bc316ad44454c9f7b5412de7d0d5d1346410a643daac6a096ec0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "00ad796ba2ce8d441fa51753ea7f159d6d656e17b95a88c8446272ee98215e47",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2010-02-10T01:15:18Z",
    "title_canon_sha256": "a85922db1c6931091bc67f228c3fa01085590f2ac0cbf3d7ca1190aa3e483d81"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1002.2011",
    "kind": "arxiv",
    "version": 2
  }
}