Pith Number

pith:D7Z4CWJ7

pith:2013:D7Z4CWJ7RTWLA7ORC4QBMRRH5R

not attested not anchored not stored refs pending

Well-posedness and scattering for nonlinear Schr\"odinger equations with a derivative nonlinearity at the scaling critical regularity

Hiroyuki Hirayama

arxiv:1311.3119 v1 · 2013-11-13 · 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{D7Z4CWJ7RTWLA7ORC4QBMRRH5R}

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	2026-05-18T00:14:01.701682Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1ff3c1593f8cecb07dd11720164627ec62e58e72a4523acce305c8c182498fc8

Aliases

arxiv: 1311.3119 · arxiv_version: 1311.3119v1 · doi: 10.48550/arxiv.1311.3119 · pith_short_12: D7Z4CWJ7RTWL · pith_short_16: D7Z4CWJ7RTWLA7OR · pith_short_8: D7Z4CWJ7

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/D7Z4CWJ7RTWLA7ORC4QBMRRH5R \
  | 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: 1ff3c1593f8cecb07dd11720164627ec62e58e72a4523acce305c8c182498fc8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "23b239b01c97faf375a2ca872ab90f4404d767e36ecc67db97620ebf7446cd35",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2013-11-13T13:16:27Z",
    "title_canon_sha256": "9d96530aeea654c78edbdfc95296aa2f9b5d84dc1b48a08141f4f14694755f7f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1311.3119",
    "kind": "arxiv",
    "version": 1
  }
}