Pith Number

pith:73K5O2FY

pith:2007:73K5O2FYR5KWSQADH5JUPWDGD6

not attested not anchored not stored refs pending

On the blow up phenomenon for the $L^2$-critical focusing Hartree equation in $\Bbb R^4$

Changxing Miao, Guixiang Xu, Lifeng Zhao

arxiv:0708.2614 v4 · 2007-08-20 · 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{73K5O2FYR5KWSQADH5JUPWDGD6}

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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	2026-07-04T17:23:58.322866Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fed5d768b88f556940033f5347d8661f998630e276f03b1d964cfd2258a83957

Aliases

arxiv: 0708.2614 · arxiv_version: 0708.2614v4 · doi: 10.48550/arxiv.0708.2614 · pith_short_12: 73K5O2FYR5KW · pith_short_16: 73K5O2FYR5KWSQAD · pith_short_8: 73K5O2FY

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/73K5O2FYR5KWSQADH5JUPWDGD6 \
  | 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: fed5d768b88f556940033f5347d8661f998630e276f03b1d964cfd2258a83957

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a0f9435e29e13c8f774b3aed9764871a28f39c52cb3c080700c98b8210ee60c3",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2007-08-20T09:17:57Z",
    "title_canon_sha256": "89481fb98c56c328561ba196ef0ab93d5386d5c2f0959c21843d41a5e5871e9f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0708.2614",
    "kind": "arxiv",
    "version": 4
  }
}