Pith Number

pith:FGRG6ENP

pith:2019:FGRG6ENPUUS6BVVHFDVU7QUTZU

not attested not anchored not stored refs pending

The effect of topology on the number of positive solutions of elliptic equation involving Hardy-Littlewood-Sobolev critical exponent

Divya Goel

arxiv:1902.07437 v1 · 2019-02-20 · 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{FGRG6ENPUUS6BVVHFDVU7QUTZU}

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	2026-05-17T23:53:07.882098Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

29a26f11afa525e0d6a728eb4fc293cd3dc44e51f0f45181299c0158b94d9c6b

Aliases

arxiv: 1902.07437 · arxiv_version: 1902.07437v1 · doi: 10.48550/arxiv.1902.07437 · pith_short_12: FGRG6ENPUUS6 · pith_short_16: FGRG6ENPUUS6BVVH · pith_short_8: FGRG6ENP

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/FGRG6ENPUUS6BVVHFDVU7QUTZU \
  | 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: 29a26f11afa525e0d6a728eb4fc293cd3dc44e51f0f45181299c0158b94d9c6b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7b55f60e66a832694d2b80af6f633e550ff6ffcb3d8854951566534dfd51b4ae",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2019-02-20T07:38:33Z",
    "title_canon_sha256": "97d0f706a68059c435d444c90235b29918275865b84ee58e6b0e69225346977d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1902.07437",
    "kind": "arxiv",
    "version": 1
  }
}