Pith Number

pith:V4MUBKKC

pith:2018:V4MUBKKCQDYIPL2CJPUDTHU7QB

not attested not anchored not stored refs pending

Stochastic nonlinear Schroedinger equations in the defocusing mass and energy critical cases

Deng Zhang

arxiv:1811.00167 v2 · 2018-11-01 · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{V4MUBKKCQDYIPL2CJPUDTHU7QB}

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.

Cited by

1 paper in Pith

The stochastic nonlinear Schr\"odinger equation in unbounded domains and manifolds

Receipt and verification

First computed	2026-05-18T00:01:37.309688Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

af1940a94280f087af424be8399e9f804d438eb6d67e45e17ded8e863c88db15

Aliases

arxiv: 1811.00167 · arxiv_version: 1811.00167v2 · doi: 10.48550/arxiv.1811.00167 · pith_short_12: V4MUBKKCQDYI · pith_short_16: V4MUBKKCQDYIPL2C · pith_short_8: V4MUBKKC

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/V4MUBKKCQDYIPL2CJPUDTHU7QB \
  | 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: af1940a94280f087af424be8399e9f804d438eb6d67e45e17ded8e863c88db15

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8f29c07dbfbac6472451d1794987ff559a7a2a7e37054733fd30f8f8174ee936",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2018-11-01T00:17:03Z",
    "title_canon_sha256": "8f4ba8e9bc298b099d524cdd1988aaad53f7af4aa0d7580fe22cd72d5c56aab0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1811.00167",
    "kind": "arxiv",
    "version": 2
  }
}