Pith Number

pith:AL7OOZ4X

pith:2014:AL7OOZ4XKAXBJN74AM7J7GF54Y

not attested not anchored not stored refs pending

Sharp existence criteria for positive solutions of Hardy-Sobolev type systems

John Villavert

arxiv:1401.5454 v3 · 2014-01-21 · 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{AL7OOZ4XKAXBJN74AM7J7GF54Y}

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	2026-05-18T02:30:15.738763Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

02fee76797502e14b7fc033e9f98bde63149129a26ee7e452698dc12c74ff595

Aliases

arxiv: 1401.5454 · arxiv_version: 1401.5454v3 · doi: 10.48550/arxiv.1401.5454 · pith_short_12: AL7OOZ4XKAXB · pith_short_16: AL7OOZ4XKAXBJN74 · pith_short_8: AL7OOZ4X

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/AL7OOZ4XKAXBJN74AM7J7GF54Y \
  | 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: 02fee76797502e14b7fc033e9f98bde63149129a26ee7e452698dc12c74ff595

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9939eb01023807dd949549112955203c83d9b8987cad6cf08ade1f69a9ba24bf",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2014-01-21T20:33:33Z",
    "title_canon_sha256": "1e9688324b39ded264260abcd2844f2f7303c99ade14ba3f25596c700e476cee"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1401.5454",
    "kind": "arxiv",
    "version": 3
  }
}