Pith Number

pith:VLQD7ZO2

pith:2007:VLQD7ZO2CSSKE5SILOR4CGIN5R

not attested not anchored not stored refs pending

Global well-posedness, scattering and blow-up for the energy-critical, focusing Hartree equation in the radial case

Changxing Miao, Guixiang Xu, Lifeng Zhao

arxiv:0801.0019 v2 · 2007-12-29 · 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{VLQD7ZO2CSSKE5SILOR4CGIN5R}

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	2026-07-04T15:35:55.547450Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

aae03fe5da14a4a276485ba3c1190dec5eb2a2bc662a1a242448b601248b847f

Aliases

arxiv: 0801.0019 · arxiv_version: 0801.0019v2 · doi: 10.48550/arxiv.0801.0019 · pith_short_12: VLQD7ZO2CSSK · pith_short_16: VLQD7ZO2CSSKE5SI · pith_short_8: VLQD7ZO2

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/VLQD7ZO2CSSKE5SILOR4CGIN5R \
  | 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: aae03fe5da14a4a276485ba3c1190dec5eb2a2bc662a1a242448b601248b847f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7319ebf2144f13db3898bcfd194819748f704145ba25af04fdc7c96b1d2920ad",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "",
    "primary_cat": "math.AP",
    "submitted_at": "2007-12-29T01:26:12Z",
    "title_canon_sha256": "a6e99b946ec917135b1b33d70a356eea85203423de0b2efb3729907d7c7cbf51"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0801.0019",
    "kind": "arxiv",
    "version": 2
  }
}