Pith Number

pith:5VQTB5WC

pith:2013:5VQTB5WCUFS6V2ZBVIDMNGYL4W

not attested not anchored not stored refs pending

Existence of maximizers for Hardy-Littlewood-Sobolev inequalities on the Heisenberg group

Xiaolong Han

arxiv:1311.0094 v1 · 2013-11-01 · math.CA · math.OC

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{5VQTB5WCUFS6V2ZBVIDMNGYL4W}

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	2026-05-18T03:07:56.259075Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ed6130f6c2a165eaeb21aa06c69b0be58015e43a0f032e7093ac1627457f4609

Aliases

arxiv: 1311.0094 · arxiv_version: 1311.0094v1 · doi: 10.48550/arxiv.1311.0094 · pith_short_12: 5VQTB5WCUFS6 · pith_short_16: 5VQTB5WCUFS6V2ZB · pith_short_8: 5VQTB5WC

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/5VQTB5WCUFS6V2ZBVIDMNGYL4W \
  | 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: ed6130f6c2a165eaeb21aa06c69b0be58015e43a0f032e7093ac1627457f4609

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "601e3b53f75168bfeb1322c289f4375d9adda6cc09053b868b3bd3fa865b3eb4",
    "cross_cats_sorted": [
      "math.OC"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2013-11-01T06:06:20Z",
    "title_canon_sha256": "e26d6424f55749ac8966d19b277a7be3786abe79a801c8b72fb89e6a3699bae1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1311.0094",
    "kind": "arxiv",
    "version": 1
  }
}