Pith Number

pith:ENWC4XZZ

pith:2009:ENWC4XZZ7DPJNYZBFAUZQXDBE6

not attested not anchored not stored refs pending

Singular integrals on Ahlfors-David regular subsets of the Heisenberg group

Pertti Mattila, Vasilis Chousionis

arxiv:0909.0165 v3 · 2009-09-01 · math.AP · math.MG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ENWC4XZZ7DPJNYZBFAUZQXDBE6}

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	2026-05-18T03:46:45.848448Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

236c2e5f39f8de96e3212829985c6127a78e997c17217b0ae8676f1643589259

Aliases

arxiv: 0909.0165 · arxiv_version: 0909.0165v3 · doi: 10.48550/arxiv.0909.0165 · pith_short_12: ENWC4XZZ7DPJ · pith_short_16: ENWC4XZZ7DPJNYZB · pith_short_8: ENWC4XZZ

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/ENWC4XZZ7DPJNYZBFAUZQXDBE6 \
  | 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: 236c2e5f39f8de96e3212829985c6127a78e997c17217b0ae8676f1643589259

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8a3410fb7bf5f0dc28c13fb16194e0f6f41c63f941469ca25c3669d683c5bcf8",
    "cross_cats_sorted": [
      "math.MG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2009-09-01T12:36:53Z",
    "title_canon_sha256": "28dfacbcdcc5e05d4f6c692d64e4872c8dd38141319333c896fba17f9cbed6df"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0909.0165",
    "kind": "arxiv",
    "version": 3
  }
}