Pith Number

pith:KMGIFNQZ

pith:2025:KMGIFNQZ35OL4TJ33HGFLOF3UQ

not attested not anchored not stored refs pending

Mixed local-nonlocal equations with critical nonlinearity on $\mathbb{R}^N$: Non-existence, Existence, and Multiplicity of positive solutions

Nirjan Biswas, Paramananda Das, Souptik Chakraborty

arxiv:2510.15507 v3 · 2025-10-17 · 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{KMGIFNQZ35OL4TJ33HGFLOF3UQ}

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	2026-05-26T01:03:16.985671Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

530c82b619df5cbe4d3bd9cc55b8bba41c7da2657c867c77719747996d88ce20

Aliases

arxiv: 2510.15507 · arxiv_version: 2510.15507v3 · doi: 10.48550/arxiv.2510.15507 · pith_short_12: KMGIFNQZ35OL · pith_short_16: KMGIFNQZ35OL4TJ3 · pith_short_8: KMGIFNQZ

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/KMGIFNQZ35OL4TJ33HGFLOF3UQ \
  | 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: 530c82b619df5cbe4d3bd9cc55b8bba41c7da2657c867c77719747996d88ce20

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "18c132f0a44ab93f2360620118cd8190117c8b38f161d9d7d433b9561eb17a04",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2025-10-17T10:21:13Z",
    "title_canon_sha256": "0d053f564178f8635a214ea906a41eee98d15411b3b01ac0c1a50c951d5e2e22"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2510.15507",
    "kind": "arxiv",
    "version": 3
  }
}