Pith Number

pith:QYV742P5

pith:2013:QYV742P5HEYXQDUM3U7BGCAN5E

not attested not anchored not stored refs pending

$W^{1,1}_0(\Omega)$ in some borderline cases of elliptic equations with degenerate coercivity

Gisella Croce (LMAH), Lucio Boccardo

arxiv:1305.2326 v1 · 2013-05-10 · 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{QYV742P5HEYXQDUM3U7BGCAN5E}

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	2026-05-18T03:26:00.523657Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

862bfe69fd3931780e8cdd3e13080de91074a9acd2e056f0d58cdddf57ab128b

Aliases

arxiv: 1305.2326 · arxiv_version: 1305.2326v1 · doi: 10.48550/arxiv.1305.2326 · pith_short_12: QYV742P5HEYX · pith_short_16: QYV742P5HEYXQDUM · pith_short_8: QYV742P5

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/QYV742P5HEYXQDUM3U7BGCAN5E \
  | 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: 862bfe69fd3931780e8cdd3e13080de91074a9acd2e056f0d58cdddf57ab128b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c823c7142677897370a603172456ca179f9382fd34511f18050caa562bd2707f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2013-05-10T12:19:04Z",
    "title_canon_sha256": "6657bc546c3c230752d8f549f8307103925e7ecc281fe80a90a5becc0e681cd2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1305.2326",
    "kind": "arxiv",
    "version": 1
  }
}