Pith Number

pith:4QNG4AYP

pith:2023:4QNG4AYPPXMMKRUTYIPCC2TSVC

not attested not anchored not stored refs pending

A Detailed Study of Kirchhoff-type Critical Elliptic Equations and $p$-Sub-Laplacian Operators within the Heisenberg Group $\mathcal{H}_{n}$ Framework

Subham De

arxiv:2311.16205 v3 · 2023-11-27 · math.GM

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4QNG4AYPPXMMKRUTYIPCC2TSVC}

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	2026-07-05T07:20:42.233249Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e41a6e030f7dd8c54693c21e216a72a8ace5ea916f0cfa12a0331276c355bb8f

Aliases

arxiv: 2311.16205 · arxiv_version: 2311.16205v3 · doi: 10.48550/arxiv.2311.16205 · pith_short_12: 4QNG4AYPPXMM · pith_short_16: 4QNG4AYPPXMMKRUT · pith_short_8: 4QNG4AYP

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/4QNG4AYPPXMMKRUTYIPCC2TSVC \
  | 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: e41a6e030f7dd8c54693c21e216a72a8ace5ea916f0cfa12a0331276c355bb8f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b7da1ca9ddef3ed5295ee70ddeaa287dada37abaee90f8222762b79d3aaa3d4b",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.GM",
    "submitted_at": "2023-11-27T14:29:43Z",
    "title_canon_sha256": "fc07359b8593e617a71d24dd185032b2d6aa36392005dd816cbdb7d7f0493bfb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2311.16205",
    "kind": "arxiv",
    "version": 3
  }
}