Pith Number

pith:5PIVCTE6

pith:2014:5PIVCTE6LL6I5YZVT3SA454ZOL

not attested not anchored not stored refs pending

Sharp Hardy-Littlewood-Sobolev Inequalities on Octonionic Heisenberg Group

An Zhang, Heping Liu, Michael Christ

arxiv:1407.3419 v1 · 2014-07-12 · math.FA · math.AP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{5PIVCTE6LL6I5YZVT3SA454ZOL}

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	2026-05-18T02:47:42.949074Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ebd1514c9e5afc8ee3359ee40e779972ee75bcc8a88bfc77d0247f1a2eb6ae46

Aliases

arxiv: 1407.3419 · arxiv_version: 1407.3419v1 · doi: 10.48550/arxiv.1407.3419 · pith_short_12: 5PIVCTE6LL6I · pith_short_16: 5PIVCTE6LL6I5YZV · pith_short_8: 5PIVCTE6

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/5PIVCTE6LL6I5YZVT3SA454ZOL \
  | 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: ebd1514c9e5afc8ee3359ee40e779972ee75bcc8a88bfc77d0247f1a2eb6ae46

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "73a9aebcd1ea4f606fe546ce78f8099c8465a2c5dbaee871e692f2b1f7892bc8",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2014-07-12T20:35:38Z",
    "title_canon_sha256": "3d24fcfa9a6ea121db6d117851d5704c45f09ea0d70630787a76d1f06fd4b1bc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1407.3419",
    "kind": "arxiv",
    "version": 1
  }
}