Pith Number

pith:F2VYNY7N

pith:2017:F2VYNY7NCCBFYHM43G4ZMHHVAL

not attested not anchored not stored refs pending

Hardy-Sobolev inequality with singularity a curve

El Hadji Abdoulaye Thiam, Mouhamed Moustapha Fall

arxiv:1702.02202 v1 · 2017-02-07 · math.AP · math.DG

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{F2VYNY7NCCBFYHM43G4ZMHHVAL}

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	2026-05-18T00:51:06.529110Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2eab86e3ed10825c1d9cd9b9961cf502f282a4f65e3e8d8cd11780c1e2eb24bb

Aliases

arxiv: 1702.02202 · arxiv_version: 1702.02202v1 · doi: 10.48550/arxiv.1702.02202 · pith_short_12: F2VYNY7NCCBF · pith_short_16: F2VYNY7NCCBFYHM4 · pith_short_8: F2VYNY7N

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/F2VYNY7NCCBFYHM43G4ZMHHVAL \
  | 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: 2eab86e3ed10825c1d9cd9b9961cf502f282a4f65e3e8d8cd11780c1e2eb24bb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2303cd63970f5dcf2a4c6a27702f1a3f688e6b73ea4081ffc16be36ab16481dc",
    "cross_cats_sorted": [
      "math.DG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2017-02-07T21:17:06Z",
    "title_canon_sha256": "7d4b9a4bcb1f38b2cd346ad50ea48b0b6597e9152101535f86ac16f59165e688"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1702.02202",
    "kind": "arxiv",
    "version": 1
  }
}