Pith Number

pith:ATZQYNFB

pith:2011:ATZQYNFBLDLDBUCGHFBHKOO5SK

not attested not anchored not stored refs pending

Bilinear decompositions and commutators of singular integral operators

Luong Dang Ky (MAPMO)

arxiv:1105.0486 v5 · 2011-05-03 · math.CA · math.FA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ATZQYNFBLDLDBUCGHFBHKOO5SK}

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	2026-05-18T04:04:42.288949Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

04f30c34a158d630d04639427539dd928b62b3fe7c18212a41a061596ae5ec35

Aliases

arxiv: 1105.0486 · arxiv_version: 1105.0486v5 · doi: 10.48550/arxiv.1105.0486 · pith_short_12: ATZQYNFBLDLD · pith_short_16: ATZQYNFBLDLDBUCG · pith_short_8: ATZQYNFB

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/ATZQYNFBLDLDBUCGHFBHKOO5SK \
  | 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: 04f30c34a158d630d04639427539dd928b62b3fe7c18212a41a061596ae5ec35

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9857a690bce6aedf50309d8ad3eaec73e5098b343988d134ca146561ca2a3d13",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2011-05-03T06:52:11Z",
    "title_canon_sha256": "0dd41493657f7748b62605464bd89fd09b020c41ca1b6c865c4ba0ff55707f47"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1105.0486",
    "kind": "arxiv",
    "version": 5
  }
}