Pith Number

pith:OZ2IADOJ

pith:2015:OZ2IADOJ7VKUZ2NOK6NMWLNRQT

not attested not anchored not stored refs pending

A sharp Trudinger-Moser inequality on any bounded and convex planar domain

Guozhen Lu, Qiaohua Yang

arxiv:1512.07163 v1 · 2015-12-22 · math.AP · math.CA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{OZ2IADOJ7VKUZ2NOK6NMWLNRQT}

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	2026-05-18T01:23:52.745395Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7674800dc9fd554ce9ae579acb2db184d2db980d598ca525d63b4c3d917bc451

Aliases

arxiv: 1512.07163 · arxiv_version: 1512.07163v1 · doi: 10.48550/arxiv.1512.07163 · pith_short_12: OZ2IADOJ7VKU · pith_short_16: OZ2IADOJ7VKUZ2NO · pith_short_8: OZ2IADOJ

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/OZ2IADOJ7VKUZ2NOK6NMWLNRQT \
  | 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: 7674800dc9fd554ce9ae579acb2db184d2db980d598ca525d63b4c3d917bc451

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2dea6758cf5702ba084141c5e91e2dd1475e959d614bfb27bf399713d962ab7b",
    "cross_cats_sorted": [
      "math.CA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2015-12-22T17:20:47Z",
    "title_canon_sha256": "db01b500ab8a107e6a17f73f30e8f4d5dfcffaaf8b26df9c1fa632a078f61fa8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1512.07163",
    "kind": "arxiv",
    "version": 1
  }
}