Pith Number

pith:YG5X4SNA

pith:2015:YG5X4SNA42UTK7LDKLLKR7SDZS

not attested not anchored not stored refs pending

The Gagliardo-Nirenberg inequality on metric measure spaces

Chuanxi Wu, Feng Du, Jing Mao, Qiaoling Wang

arxiv:1511.04696 v1 · 2015-11-15 · math.DG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{YG5X4SNA42UTK7LDKLLKR7SDZS}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more

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	2026-05-18T01:26:51.971677Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c1bb7e49a0e6a9357d6352d6a8fe43cc802ea928fc36d3efb56db16074f0ff77

Aliases

arxiv: 1511.04696 · arxiv_version: 1511.04696v1 · doi: 10.48550/arxiv.1511.04696 · pith_short_12: YG5X4SNA42UT · pith_short_16: YG5X4SNA42UTK7LD · pith_short_8: YG5X4SNA

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/YG5X4SNA42UTK7LDKLLKR7SDZS \
  | 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: c1bb7e49a0e6a9357d6352d6a8fe43cc802ea928fc36d3efb56db16074f0ff77

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f5414657a9d2b374e7da9e40f478b241cb6cea36e78a7d13476e92d507c755b3",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2015-11-15T13:02:58Z",
    "title_canon_sha256": "352e0f85381ee82b2709214534036a04da54099ee8c6cb61a5365388001b3b51"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1511.04696",
    "kind": "arxiv",
    "version": 1
  }
}