Pith Number

pith:JC2QYGCR

pith:2008:JC2QYGCR4K3JC2TTNAEAUVJR3Z

not attested not anchored not stored refs pending

Global wellposedness and scattering for the defocusing energy-critical nonlinear Schrodinger equations of fourth order in dimensions $d\geq9$

Changxing Miao, Guixiang Xu, Lifeng Zhao

arxiv:0807.0692 v2 · 2008-07-04 · 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{JC2QYGCR4K3JC2TTNAEAUVJR3Z}

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	2026-05-18T04:12:19.342197Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

48b50c1851e2b6916a7368080a5531de612e6192f52d7113aa8b29798ff22acd

Aliases

arxiv: 0807.0692 · arxiv_version: 0807.0692v2 · doi: 10.48550/arxiv.0807.0692 · pith_short_12: JC2QYGCR4K3J · pith_short_16: JC2QYGCR4K3JC2TT · pith_short_8: JC2QYGCR

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/JC2QYGCR4K3JC2TTNAEAUVJR3Z \
  | 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: 48b50c1851e2b6916a7368080a5531de612e6192f52d7113aa8b29798ff22acd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "79500619c586014bfe5ad6fb084671d786e79d21e0409339508be0f9b96dce3f",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2008-07-04T08:21:23Z",
    "title_canon_sha256": "c2f19e06c9e7d4f6fbc9d97d7df70cbf266f0a02b29ff6b9b17a7969989383c6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0807.0692",
    "kind": "arxiv",
    "version": 2
  }
}