Pith Number

pith:4P7BWKAV

pith:2018:4P7BWKAVWRG6TJYQNMMPMQ3H3O

not attested not anchored not stored refs pending

Second Order Optimality Conditions for Optimal Control Problems of Stochastic Evolution Equations

Haisen Zhang, Qi Lu, Xu Zhang

arxiv:1811.07337 v1 · 2018-11-18 · 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{4P7BWKAVWRG6TJYQNMMPMQ3H3O}

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	2026-05-18T00:00:28.235012Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e3fe1b2815b44de9a7106b18f64367db9a91cc85cae75958efa50116d6b1eb62

Aliases

arxiv: 1811.07337 · arxiv_version: 1811.07337v1 · doi: 10.48550/arxiv.1811.07337 · pith_short_12: 4P7BWKAVWRG6 · pith_short_16: 4P7BWKAVWRG6TJYQ · pith_short_8: 4P7BWKAV

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/4P7BWKAVWRG6TJYQNMMPMQ3H3O \
  | 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: e3fe1b2815b44de9a7106b18f64367db9a91cc85cae75958efa50116d6b1eb62

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "86f83b97c9087d2c4b1063e90d56afa5d170b85407dc3c0252f570a1876d4d68",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2018-11-18T15:08:35Z",
    "title_canon_sha256": "a24aaa5f9768fd414d69db2b276b576a9abe9dbe48fe53930749f43541f38809"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1811.07337",
    "kind": "arxiv",
    "version": 1
  }
}