Pith Number

pith:SNTQ5WL4

pith:2025:SNTQ5WL4O2OQAOAHJCLSCHE4GG

not attested not anchored not stored refs pending

Bifurcation and multiplicity results for critical Grushin-Choquard problems

Giovanni Molica Bisci, Pawan Kumar Mishra, Suman Kanungo

arxiv:2510.13299 v2 · 2025-10-15 · 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{SNTQ5WL4O2OQAOAHJCLSCHE4GG}

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	2026-05-20T00:01:36.200473Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

93670ed97c769d0038074897211c9c31be779c565265b9ba33a0037475feb33a

Aliases

arxiv: 2510.13299 · arxiv_version: 2510.13299v2 · doi: 10.48550/arxiv.2510.13299 · pith_short_12: SNTQ5WL4O2OQ · pith_short_16: SNTQ5WL4O2OQAOAH · pith_short_8: SNTQ5WL4

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/SNTQ5WL4O2OQAOAHJCLSCHE4GG \
  | 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: 93670ed97c769d0038074897211c9c31be779c565265b9ba33a0037475feb33a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "54ec8513f0fe620c7768945ae4aaecc9a359a62579db30cd12c7e7495cafe7ec",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2025-10-15T08:39:51Z",
    "title_canon_sha256": "108636d4cffa536dc8f2b88380bdb23b72964eda9310b179717fa76a2e51f71c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2510.13299",
    "kind": "arxiv",
    "version": 2
  }
}