Pith Number

pith:6KBPD35G

pith:2007:6KBPD35GSPJRTLFEOETCU6FCGT

not attested not anchored not stored refs pending

Global well-posedness and scattering for the energy-critical, defocusing Hartree equation in $\mathbb{R}^{1+n}$

Changxing Miao, Guixiang Xu, Lifeng Zhao

arxiv:0707.3254 v2 · 2007-07-22 · 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{6KBPD35GSPJRTLFEOETCU6FCGT}

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	2026-05-18T04:31:00.006531Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f282f1efa693d319aca471262a78a234cff944630bbd5e5c1cc02df6a43086b9

Aliases

arxiv: 0707.3254 · arxiv_version: 0707.3254v2 · doi: 10.48550/arxiv.0707.3254 · pith_short_12: 6KBPD35GSPJR · pith_short_16: 6KBPD35GSPJRTLFE · pith_short_8: 6KBPD35G

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/6KBPD35GSPJRTLFEOETCU6FCGT \
  | 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: f282f1efa693d319aca471262a78a234cff944630bbd5e5c1cc02df6a43086b9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "50f118b70fca931b4ef22f4da3b37436b3feb4b4dcb602c05888dc918b1d54e4",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2007-07-22T11:40:05Z",
    "title_canon_sha256": "c3c2a59ba21c9126c29e21f4912b30374ad8a0a2edfea6d1341e1136497e1017"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0707.3254",
    "kind": "arxiv",
    "version": 2
  }
}