Pith Number

pith:WNZYBJYH

pith:2013:WNZYBJYHVB7Q3TJC4PD6I4WCGG

not attested not anchored not stored refs pending

Almost sure global well posedness for the radial nonlinear Schr\"odinger equation on the unit ball II: the 3D case

Aynur Bulut, Jean Bourgain

arxiv:1302.5409 v1 · 2013-02-21 · 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{WNZYBJYHVB7Q3TJC4PD6I4WCGG}

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	2026-05-18T01:35:33.194810Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b37380a707a87f0dcd22e3c7e472c2319500f2dc4fe85efd5b089804252fb453

Aliases

arxiv: 1302.5409 · arxiv_version: 1302.5409v1 · doi: 10.48550/arxiv.1302.5409 · pith_short_12: WNZYBJYHVB7Q · pith_short_16: WNZYBJYHVB7Q3TJC · pith_short_8: WNZYBJYH

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/WNZYBJYHVB7Q3TJC4PD6I4WCGG \
  | 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: b37380a707a87f0dcd22e3c7e472c2319500f2dc4fe85efd5b089804252fb453

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0f5c2f67a65058d3d52deb4eab0f8f899ab0c5c6e0040b5303e3a0b1082d23a0",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2013-02-21T20:42:36Z",
    "title_canon_sha256": "0f83863dfdb23c10e2f641d2a1a56e0b18b0497bebf5d45a005a8dfd344dce19"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1302.5409",
    "kind": "arxiv",
    "version": 1
  }
}