Pith Number

pith:T3WO57WO

pith:2013:T3WO57WODEYPE3GO3YEHSISAXY

not attested not anchored not stored refs pending

Sharp Hardy-Littlewood-Sobolev inequality on the upper half space

Jingbo Dou, Meijun Zhu

arxiv:1309.2341 v1 · 2013-09-09 · 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{T3WO57WODEYPE3GO3YEHSISAXY}

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	2026-05-18T03:13:45.062108Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9eeceefece1930f26ccede08792240be06d5adaf4204871f77f3dbd7f183a7d8

Aliases

arxiv: 1309.2341 · arxiv_version: 1309.2341v1 · doi: 10.48550/arxiv.1309.2341 · pith_short_12: T3WO57WODEYP · pith_short_16: T3WO57WODEYPE3GO · pith_short_8: T3WO57WO

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/T3WO57WODEYPE3GO3YEHSISAXY \
  | 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: 9eeceefece1930f26ccede08792240be06d5adaf4204871f77f3dbd7f183a7d8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f4fd8f6956a0c9567bdb54a24b4eb71aed80df7ccd452c40fbb5c6e84ca682a7",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2013-09-09T23:18:11Z",
    "title_canon_sha256": "6ea81247c0874a7e5e5e6945eb7638c0c21591a42a0e50b44b0b277c0b8eab22"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1309.2341",
    "kind": "arxiv",
    "version": 1
  }
}