Pith Number

pith:DG7O7CMC

pith:2008:DG7O7CMCVKANFEY4RF35CMATIC

not attested not anchored not stored refs pending

Global wellposedness and scattering for the focusing energy-critical nonlinear Schrodinger equations of fourth order in the radial case

Changxing Miao, Guixiang Xu, Lifeng Zhao

arxiv:0807.0690 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{DG7O7CMCVKANFEY4RF35CMATIC}

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	2026-07-04T15:40:39.321185Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

19beef8982aa80d2931c8977d1301340853298350be09b33463547a510a82376

Aliases

arxiv: 0807.0690 · arxiv_version: 0807.0690v2 · doi: 10.48550/arxiv.0807.0690 · pith_short_12: DG7O7CMCVKAN · pith_short_16: DG7O7CMCVKANFEY4 · pith_short_8: DG7O7CMC

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/DG7O7CMCVKANFEY4RF35CMATIC \
  | 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: 19beef8982aa80d2931c8977d1301340853298350be09b33463547a510a82376

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6b6a1947e8470a9f65b5df319c599fca9541b5b74609332f04fcf0ecb8d69f57",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2008-07-04T08:15:30Z",
    "title_canon_sha256": "4ac7952b221b5e0e8a4d58570147ae5140d900f7b86191fcf25137fa54cda7d2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0807.0690",
    "kind": "arxiv",
    "version": 2
  }
}