Pith Number

pith:X3Z43FUK

pith:2018:X3Z43FUKM5OVHNJAPJR4BF7FNH

not attested not anchored not stored refs pending

Hardy-Sobolev inequality with higher dimensional singularity

El Hadji Abdoulaye Thiam

arxiv:1801.10493 v1 · 2018-01-30 · 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{X3Z43FUKM5OVHNJAPJR4BF7FNH}

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	2026-05-18T00:24:40.697137Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bef3cd968a675d53b5207a63c097e569ce8efa4979f67f403b76bce7901f269d

Aliases

arxiv: 1801.10493 · arxiv_version: 1801.10493v1 · doi: 10.48550/arxiv.1801.10493 · pith_short_12: X3Z43FUKM5OV · pith_short_16: X3Z43FUKM5OVHNJA · pith_short_8: X3Z43FUK

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/X3Z43FUKM5OVHNJAPJR4BF7FNH \
  | 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: bef3cd968a675d53b5207a63c097e569ce8efa4979f67f403b76bce7901f269d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "48dcf724990385179496944c720a513f13f732305524194400ac599e98f2f39c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2018-01-30T10:52:55Z",
    "title_canon_sha256": "227e57a07bc44f99626d16802956042914512f3acd0fcb449f4c382b4232d23f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1801.10493",
    "kind": "arxiv",
    "version": 1
  }
}