Pith Number

pith:CFE2XBSO

pith:2013:CFE2XBSOR5Q6ASFWAUOYLV3DE4

not attested not anchored not stored refs pending

An Extended Discrete Hardy-Littlewood-Sobolev Inequality

Congming Li, Ze Cheng

arxiv:1306.1649 v1 · 2013-06-07 · 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{CFE2XBSOR5Q6ASFWAUOYLV3DE4}

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	2026-05-18T03:21:32.835264Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1149ab864e8f61e048b6051d85d763273c6f53c57cbb3ac9bf7770a623779969

Aliases

arxiv: 1306.1649 · arxiv_version: 1306.1649v1 · doi: 10.48550/arxiv.1306.1649 · pith_short_12: CFE2XBSOR5Q6 · pith_short_16: CFE2XBSOR5Q6ASFW · pith_short_8: CFE2XBSO

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/CFE2XBSOR5Q6ASFWAUOYLV3DE4 \
  | 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: 1149ab864e8f61e048b6051d85d763273c6f53c57cbb3ac9bf7770a623779969

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "200134e573627f4d006297d7feb2c2b8ce85ae81340119c6b4ded2379d022df0",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2013-06-07T08:15:50Z",
    "title_canon_sha256": "796480c7fef5f5bb8845f564e9dad5e78f2737e2a062eac54f5c694c3322c3bc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1306.1649",
    "kind": "arxiv",
    "version": 1
  }
}