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Pith Number

pith:LNA4FWRW

pith:2011:LNA4FWRWDDYCSUWBL7LSVDSVAJ
not attested not anchored not stored refs pending

Existence of a ground state and blow-up problem for a nonlinear Schrodinger equation with critical growth

Hayato Nawa, Hiroaki Kikuchi, Slim Ibrahim, Takafumi Akahori

arxiv:1112.1102 v1 · 2011-12-05 · 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{LNA4FWRWDDYCSUWBL7LSVDSVAJ}

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 2026-05-18T04:06:56.304560Z
Builder pith-number-builder-2026-05-17-v1
Signature Pith Ed25519 (pith-v1-2026-05) · public key
Schema pith-number/v1.0

Canonical hash

5b41c2da3618f02952c15fd72a8e55026639370b44e2f616757198cc67464bc1

Aliases

arxiv: 1112.1102 · arxiv_version: 1112.1102v1 · doi: 10.48550/arxiv.1112.1102 · pith_short_12: LNA4FWRWDDYC · pith_short_16: LNA4FWRWDDYCSUWB · pith_short_8: LNA4FWRW
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/LNA4FWRWDDYCSUWBL7LSVDSVAJ \
  | 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: 5b41c2da3618f02952c15fd72a8e55026639370b44e2f616757198cc67464bc1
Canonical record JSON 
{
  "metadata": {
    "abstract_canon_sha256": "598f9a3c985d679d3e60cc2e0e18ed93d7995ba73e0e822032cd66d723ce903b",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2011-12-05T21:35:02Z",
    "title_canon_sha256": "a23687d78cdddeee66805a39e3729501bc2a80063c3546f811bad0086e1d0e2b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1112.1102",
    "kind": "arxiv",
    "version": 1
  }
}