Pith Number

pith:QPFVYXRO

pith:2014:QPFVYXROJNTFIR7MHGH5T4OF5O

not attested not anchored not stored refs pending

Discrete Hardy-type Inequalities

Zhong-Wei Liao

arxiv:1406.1984 v2 · 2014-06-08 · 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{QPFVYXROJNTFIR7MHGH5T4OF5O}

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	2026-05-18T02:49:11.492197Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

83cb5c5e2e4b665447ec398fd9f1c5eba20a6774ef1b210874df41a5331ac25f

Aliases

arxiv: 1406.1984 · arxiv_version: 1406.1984v2 · doi: 10.48550/arxiv.1406.1984 · pith_short_12: QPFVYXROJNTF · pith_short_16: QPFVYXROJNTFIR7M · pith_short_8: QPFVYXRO

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/QPFVYXROJNTFIR7MHGH5T4OF5O \
  | 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: 83cb5c5e2e4b665447ec398fd9f1c5eba20a6774ef1b210874df41a5331ac25f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "46163878c8eaf6277430dd1896a1be7d4d80b9f9a0a54814f11b1288e423501c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2014-06-08T13:35:39Z",
    "title_canon_sha256": "77d31de4bedcc444228b9c8739b935c303f05ee7a7da0603acf8309be4c1de45"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1406.1984",
    "kind": "arxiv",
    "version": 2
  }
}