Pith Number

pith:3G6HW5B5

pith:2014:3G6HW5B5NOQXIUTKU7ITP7VEBE

not attested not anchored not stored refs pending

Existence of optimizers of the Stein-Weiss inequalities on Carnot groups

Pengcheng Niu, Tingxi Hu

arxiv:1402.7121 v1 · 2014-02-28 · 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{3G6HW5B5NOQXIUTKU7ITP7VEBE}

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	2026-05-18T02:57:34.910898Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d9bc7b743d6ba174526aa7d137fea40911c99b367d555009ed1f8ecd48bdeae4

Aliases

arxiv: 1402.7121 · arxiv_version: 1402.7121v1 · doi: 10.48550/arxiv.1402.7121 · pith_short_12: 3G6HW5B5NOQX · pith_short_16: 3G6HW5B5NOQXIUTK · pith_short_8: 3G6HW5B5

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/3G6HW5B5NOQXIUTKU7ITP7VEBE \
  | 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: d9bc7b743d6ba174526aa7d137fea40911c99b367d555009ed1f8ecd48bdeae4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "05ecdac43d6d1dc951a6f4309c17b7a6d7ee982a31102f8f3c870cb7da943caf",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2014-02-28T02:31:13Z",
    "title_canon_sha256": "26ac04a21f9809f0cde2bfd0bf8712084c89ed2b9ed7c318dc52024f305fc7ec"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1402.7121",
    "kind": "arxiv",
    "version": 1
  }
}