Pith Number

pith:UCDPAQTZ

pith:2015:UCDPAQTZKN6VPRYCNZW2TF6XZJ

not attested not anchored not stored refs pending

Existence of extremal functions for a family of Caffarelli-Kohn-Nirenberg inequalities

Wenming Zou, Xuexiu Zhong

arxiv:1504.00433 v1 · 2015-04-02 · 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{UCDPAQTZKN6VPRYCNZW2TF6XZJ}

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	2026-05-18T02:19:43.324089Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a086f04279537d57c7026e6da997d7ca7fdbb8b3a470e12c426630eeae9c8a22

Aliases

arxiv: 1504.00433 · arxiv_version: 1504.00433v1 · doi: 10.48550/arxiv.1504.00433 · pith_short_12: UCDPAQTZKN6V · pith_short_16: UCDPAQTZKN6VPRYC · pith_short_8: UCDPAQTZ

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/UCDPAQTZKN6VPRYCNZW2TF6XZJ \
  | 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: a086f04279537d57c7026e6da997d7ca7fdbb8b3a470e12c426630eeae9c8a22

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1f5015473dcc395d1455ac8baff181b89143edc6453ce0f93af3194f9a2e9209",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2015-04-02T02:49:35Z",
    "title_canon_sha256": "3ed162aa9256edc09057d927f26dcba15e65d4052d92536c141fd1564bd8ba17"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1504.00433",
    "kind": "arxiv",
    "version": 1
  }
}