Pith Number

pith:XTFRCVIL

pith:2017:XTFRCVILPDGZAOMA3TRGHPMBTA

not attested not anchored not stored refs pending

Hardy-Sobolev type inequalities and their applications

Bo-Yong Chen

arxiv:1712.02044 v2 · 2017-12-06 · math.CV · 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{XTFRCVILPDGZAOMA3TRGHPMBTA}

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	2026-05-18T00:24:41.881761Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bccb11550b78cd903980dce263bd81980bdcf959366a4e84d3af1924a6997f7c

Aliases

arxiv: 1712.02044 · arxiv_version: 1712.02044v2 · doi: 10.48550/arxiv.1712.02044 · pith_short_12: XTFRCVILPDGZ · pith_short_16: XTFRCVILPDGZAOMA · pith_short_8: XTFRCVIL

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/XTFRCVILPDGZAOMA3TRGHPMBTA \
  | 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: bccb11550b78cd903980dce263bd81980bdcf959366a4e84d3af1924a6997f7c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "932b75be52498f1bc80f50e6b814677cd0ab5d33d333278ee0e7dfed41b38d2b",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CV",
    "submitted_at": "2017-12-06T05:32:00Z",
    "title_canon_sha256": "e4428ade25852d57d9d94308558b72f03295865c8f613a57aa156fe4f2f07678"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1712.02044",
    "kind": "arxiv",
    "version": 2
  }
}