Pith Number

pith:NSL4NOWE

pith:2016:NSL4NOWEGGN43CGD3Y74W3AQPK

not attested not anchored not stored refs pending

First and second order necessary conditions for stochastic optimal controls

Haisen Zhang, H\'el\`ene Frankowska, Xu Zhang

arxiv:1603.08274 v3 · 2016-03-28 · math.OC

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{NSL4NOWEGGN43CGD3Y74W3AQPK}

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	2026-05-18T00:59:58.616637Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6c97c6bac4319bcd88c3de3fcb6c107aac3846aff8ec37c58bfc49e63604e30a

Aliases

arxiv: 1603.08274 · arxiv_version: 1603.08274v3 · doi: 10.48550/arxiv.1603.08274 · pith_short_12: NSL4NOWEGGN4 · pith_short_16: NSL4NOWEGGN43CGD · pith_short_8: NSL4NOWE

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/NSL4NOWEGGN43CGD3Y74W3AQPK \
  | 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: 6c97c6bac4319bcd88c3de3fcb6c107aac3846aff8ec37c58bfc49e63604e30a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fb4e7700e5aa32bcd401b77c3a26b21c3d098ab05de1b6f2b6bcd6f0a9c6a8af",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2016-03-28T00:47:46Z",
    "title_canon_sha256": "0de91ed225d61034ab52aa836a8c90b444fc1fc6dbb75d4f70ee0370fc7c9108"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1603.08274",
    "kind": "arxiv",
    "version": 3
  }
}