Pith Number

pith:JZ24TL56

pith:2014:JZ24TL56HZMR2HUQPAOWZM2BFP

not attested not anchored not stored refs pending

Sharp Hardy-Littlewood-Sobolev Inequalities on Quaternionic Heisenberg Groups

An Zhang, Heping Liu, Michael Christ

arxiv:1407.3417 v1 · 2014-07-12 · math.CA · math.AP · 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{JZ24TL56HZMR2HUQPAOWZM2BFP}

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	2026-05-18T02:47:42.960891Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4e75c9afbe3e591d1e90781d6cb3412bf2bb6bf7257d09a28eb3de9269a8eb01

Aliases

arxiv: 1407.3417 · arxiv_version: 1407.3417v1 · doi: 10.48550/arxiv.1407.3417 · pith_short_12: JZ24TL56HZMR · pith_short_16: JZ24TL56HZMR2HUQ · pith_short_8: JZ24TL56

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/JZ24TL56HZMR2HUQPAOWZM2BFP \
  | 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: 4e75c9afbe3e591d1e90781d6cb3412bf2bb6bf7257d09a28eb3de9269a8eb01

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "01537c60a891e921a0e1d0c35689a3bb385e346da896ee58d7943ce0e39524d6",
    "cross_cats_sorted": [
      "math.AP",
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2014-07-12T20:12:49Z",
    "title_canon_sha256": "e2a3da05c5a017755189a72822b676f6f85d3c2e93cc12ed53ba248e9e70ad4f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1407.3417",
    "kind": "arxiv",
    "version": 1
  }
}