Pith Number

pith:GWLUFOCZ

pith:2010:GWLUFOCZI36LSQT667DGMBPLWJ

not attested not anchored not stored refs pending

Uniqueness and Nondegeneracy of Ground States for $(-\Delta)^s Q + Q - Q^{\alpha+1} = 0$ in $\mathbb{R}$

Enno Lenzmann, Rupert L. Frank

arxiv:1009.4042 v2 · 2010-09-21 · math.AP · math-ph · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{GWLUFOCZI36LSQT667DGMBPLWJ}

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	2026-05-18T02:20:48.177536Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

359742b85946fcb9427ef7c66605ebb268594b954b3280a7a1af1170d673f345

Aliases

arxiv: 1009.4042 · arxiv_version: 1009.4042v2 · doi: 10.48550/arxiv.1009.4042 · pith_short_12: GWLUFOCZI36L · pith_short_16: GWLUFOCZI36LSQT6 · pith_short_8: GWLUFOCZ

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/GWLUFOCZI36LSQT667DGMBPLWJ \
  | 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: 359742b85946fcb9427ef7c66605ebb268594b954b3280a7a1af1170d673f345

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1db35dea7e7bbadfa1876998639c1f160f7edaa406b99a5852864bc4c1e2e8f8",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2010-09-21T10:15:31Z",
    "title_canon_sha256": "359ea437771e5b905ffc11556c7f35170ba16425991b09f06897e4a33f5b1f95"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1009.4042",
    "kind": "arxiv",
    "version": 2
  }
}