Pith Number

pith:M7TMMAGG

pith:2012:M7TMMAGGX6SRHOEBJWHW44ENSF

not attested not anchored not stored refs pending

Profile decompositions and Blowup phenomena of mass critical fractional Schr\"odinger equations

Gyeongha Hwang, Sanghyuk Lee, Soonsik Kwon, Yonggeun Cho

arxiv:1208.2303 v1 · 2012-08-11 · math.AP

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{M7TMMAGGX6SRHOEBJWHW44ENSF}

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	2026-05-18T03:48:58.255124Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

67e6c600c6bfa513b8814d8f6e708d9177499431be4ae5f7f75a98fd1e74cb8b

Aliases

arxiv: 1208.2303 · arxiv_version: 1208.2303v1 · doi: 10.48550/arxiv.1208.2303 · pith_short_12: M7TMMAGGX6SR · pith_short_16: M7TMMAGGX6SRHOEB · pith_short_8: M7TMMAGG

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/M7TMMAGGX6SRHOEBJWHW44ENSF \
  | 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: 67e6c600c6bfa513b8814d8f6e708d9177499431be4ae5f7f75a98fd1e74cb8b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3a2d768f64376d3003ea3b8238954a020c0e5c3bc0dbd1c73a1c4472690f55f7",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2012-08-11T02:15:29Z",
    "title_canon_sha256": "f6342c725013418f9ef30d1483e2f1da88947c4ddf6bfc93133668d9175bbdf8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1208.2303",
    "kind": "arxiv",
    "version": 1
  }
}