Pith Number

pith:KSA4Y4HT

pith:2019:KSA4Y4HTKGZQCP6S5TRQRURV6K

not attested not anchored not stored refs pending

Optimal bilinear control of stochastic nonlinear Schr\"odinger equations: mass-(sub)critical case

Deng Zhang

arxiv:1902.03559 v1 · 2019-02-10 · math.AP · math.PR

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Add to your LaTeX paper

\usepackage{pith}
\pithnumber{KSA4Y4HTKGZQCP6S5TRQRURV6K}

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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	2026-05-17T23:54:20.448005Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5481cc70f351b3013fd2ece308d235f2abaed587a022a42ff613aa7b4653b3aa

Aliases

arxiv: 1902.03559 · arxiv_version: 1902.03559v1 · doi: 10.48550/arxiv.1902.03559 · pith_short_12: KSA4Y4HTKGZQ · pith_short_16: KSA4Y4HTKGZQCP6S · pith_short_8: KSA4Y4HT

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/KSA4Y4HTKGZQCP6S5TRQRURV6K \
  | 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: 5481cc70f351b3013fd2ece308d235f2abaed587a022a42ff613aa7b4653b3aa

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e016ce4c35cb7e2f760504d030d39a4c68fff5408947bf4c7b74b78271476f90",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2019-02-10T08:47:09Z",
    "title_canon_sha256": "e5026390d89909a34389b91728db28aa3d206badd8b26c353edbac452fdcd40c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1902.03559",
    "kind": "arxiv",
    "version": 1
  }
}