Pith Number

pith:3QGK6RLP

pith:2015:3QGK6RLPGYAJWRUSALN4ZEA7M7

not attested not anchored not stored refs pending

An improved Hardy-Trudinger-Moser inequality

Xiaobao Zhu, Yunyan Yang

arxiv:1501.03678 v2 · 2015-01-15 · 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{3QGK6RLPGYAJWRUSALN4ZEA7M7}

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	2026-05-18T01:33:16.182686Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

dc0caf456f36009b469202dbcc901f67ce60173c5385412848d111ee1c56e735

Aliases

arxiv: 1501.03678 · arxiv_version: 1501.03678v2 · doi: 10.48550/arxiv.1501.03678 · pith_short_12: 3QGK6RLPGYAJ · pith_short_16: 3QGK6RLPGYAJWRUS · pith_short_8: 3QGK6RLP

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/3QGK6RLPGYAJWRUSALN4ZEA7M7 \
  | 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: dc0caf456f36009b469202dbcc901f67ce60173c5385412848d111ee1c56e735

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8c5c8a4dfa0e4108b2d204a113f75b93a07a4b394dfa36b6a35bcfd871c6e0d8",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2015-01-15T13:43:18Z",
    "title_canon_sha256": "b1d3410be345d8842803385f48b0895f2f573fff14cc9f03ee2a96b749784f6a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1501.03678",
    "kind": "arxiv",
    "version": 2
  }
}