Pith Number

pith:GKLYVHRS

pith:2011:GKLYVHRSAEJS32SD3BBZUJO32V

not attested not anchored not stored refs pending

Trudinger-Moser inequality on the whole plane with the exact growth condition

Kenji Nakanishi, Nader Masmoudi, Slim Ibrahim

arxiv:1110.1712 v1 · 2011-10-08 · 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{GKLYVHRSAEJS32SD3BBZUJO32V}

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	2026-05-18T04:11:19.792750Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

32978a9e3201132dea43d8439a25dbd557de79c492a3396e749a47e12de83100

Aliases

arxiv: 1110.1712 · arxiv_version: 1110.1712v1 · doi: 10.48550/arxiv.1110.1712 · pith_short_12: GKLYVHRSAEJS · pith_short_16: GKLYVHRSAEJS32SD · pith_short_8: GKLYVHRS

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/GKLYVHRSAEJS32SD3BBZUJO32V \
  | 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: 32978a9e3201132dea43d8439a25dbd557de79c492a3396e749a47e12de83100

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c7701ba341aad6d212b2a100f267c0028701acfcbfcfee081068c17a8411dda7",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2011-10-08T09:24:02Z",
    "title_canon_sha256": "5dd60d2bf5b6919002f683fe43850284927716d9dda38c56199fa55cbbecdf18"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1110.1712",
    "kind": "arxiv",
    "version": 1
  }
}