Pith Number

pith:OKFV2BAR

pith:2024:OKFV2BARQ2A43AAQNPGQ2TFBOS

not attested not anchored not stored refs pending

Existence of solutions for a system with general Hardy--Sobolev singular criticalities

Alejandro Ortega, \'Angel Arroyo, Rafael L\'opez-Soriano

arxiv:2405.20845 v1 · 2024-05-31 · 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{OKFV2BARQ2A43AAQNPGQ2TFBOS}

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	2026-07-05T08:25:42.814017Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

728b5d04118681cd80106bcd0d4ca174a403864c7aa816d2d3c69e7216d096cf

Aliases

arxiv: 2405.20845 · arxiv_version: 2405.20845v1 · doi: 10.48550/arxiv.2405.20845 · pith_short_12: OKFV2BARQ2A4 · pith_short_16: OKFV2BARQ2A43AAQ · pith_short_8: OKFV2BAR

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/OKFV2BARQ2A43AAQNPGQ2TFBOS \
  | 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: 728b5d04118681cd80106bcd0d4ca174a403864c7aa816d2d3c69e7216d096cf

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b4c7cb269b50b5a53fc1b9d4b131c9f986c0c06a52ac997fb9d6d2bb5e4f7634",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2024-05-31T14:31:45Z",
    "title_canon_sha256": "8620f3ee7ac220404b51601e01ae60a67813840cc90051880fbadee395bfb19c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2405.20845",
    "kind": "arxiv",
    "version": 1
  }
}