Pith Number

pith:J7TWGOMF

pith:2019:J7TWGOMFIRNIUFIHRUT76VCBG7

not attested not anchored not stored refs pending

Morawetz estimates and spacetime bounds for quasilinear Schr\"{o}dinger equations with critical Sobolev exponent

Xianfa Song

arxiv:1904.09702 v1 · 2019-04-22 · 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{J7TWGOMFIRNIUFIHRUT76VCBG7}

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	2026-05-17T23:48:03.619109Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4fe7633985445a8a15078d27ff544137e32634916a65d8f02e0fd61c3f443511

Aliases

arxiv: 1904.09702 · arxiv_version: 1904.09702v1 · doi: 10.48550/arxiv.1904.09702 · pith_short_12: J7TWGOMFIRNI · pith_short_16: J7TWGOMFIRNIUFIH · pith_short_8: J7TWGOMF

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/J7TWGOMFIRNIUFIHRUT76VCBG7 \
  | 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: 4fe7633985445a8a15078d27ff544137e32634916a65d8f02e0fd61c3f443511

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "43af2b112fad72d5c273e566cc0fdb0cc235ff48d7ab34015f29216b742cbda1",
    "cross_cats_sorted": [
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2019-04-22T02:46:21Z",
    "title_canon_sha256": "a0cc72acd1484718fe649e25acf4262aac62037c2d8c72d2c7e4e2cb2dcb5c7a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1904.09702",
    "kind": "arxiv",
    "version": 1
  }
}