Pith Number

pith:VR5LXWVE

pith:2024:VR5LXWVEI23CGOBTMJJ6VQ54FR

not attested not anchored not stored refs pending

Multiplicity of solutions to a class of degenerate elliptic equations in both sub-critical and critical cases

Kaushik Bal, Sanjit Biswas

arxiv:2412.04794 v2 · 2024-12-06 · 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{VR5LXWVEI23CGOBTMJJ6VQ54FR}

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.

Cited by

1 paper in Pith

Existence and multiplicity of solutions for a critical Grushin problem with a singular nonlinearity

Receipt and verification

First computed	2026-06-19T16:12:44.768425Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ac7abbdaa446b62338336253eac3bc2c4d0410d4e09f6338d239fe7e641c42fa

Aliases

arxiv: 2412.04794 · arxiv_version: 2412.04794v2 · doi: 10.48550/arxiv.2412.04794 · pith_short_12: VR5LXWVEI23C · pith_short_16: VR5LXWVEI23CGOBT · pith_short_8: VR5LXWVE

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/VR5LXWVEI23CGOBTMJJ6VQ54FR \
  | 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: ac7abbdaa446b62338336253eac3bc2c4d0410d4e09f6338d239fe7e641c42fa

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1c4917044ecc83a5d44ccddb51aa73c515bfad10dbd52ea04ce841b4e7533344",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2024-12-06T06:00:35Z",
    "title_canon_sha256": "7b9ea1a446bcc9b2a8c7fc90d008891e46dd30382ec4c470ee8307bb79bc3402"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2412.04794",
    "kind": "arxiv",
    "version": 2
  }
}