Pith Number

pith:2UJV44A7

pith:2011:2UJV44A7N6I437KBOISDKOETAB

not attested not anchored not stored refs pending

Hardy spaces, commutators of singular integral operators related to Schr\"odinger operators and applications

Luong Dang Ky (MAPMO)

arxiv:1112.4935 v4 · 2011-12-21 · 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{2UJV44A7N6I437KBOISDKOETAB}

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	2026-05-18T03:58:26.149674Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d5135e701f6f91cdfd41722435389300631e7d055c8d28435392c340bfe43337

Aliases

arxiv: 1112.4935 · arxiv_version: 1112.4935v4 · doi: 10.48550/arxiv.1112.4935 · pith_short_12: 2UJV44A7N6I4 · pith_short_16: 2UJV44A7N6I437KB · pith_short_8: 2UJV44A7

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/2UJV44A7N6I437KBOISDKOETAB \
  | 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: d5135e701f6f91cdfd41722435389300631e7d055c8d28435392c340bfe43337

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4bc5d0e99e2c24013bcc6190c71f8fd2f179e2053ab5c434deaf70cd300eadec",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2011-12-21T07:34:40Z",
    "title_canon_sha256": "dec5aa0866a0f450b38ccf347141037fe202c39dc662b7df7fdfe8c3398a370f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1112.4935",
    "kind": "arxiv",
    "version": 4
  }
}