Pith Number

pith:GC3FC5KD

pith:2016:GC3FC5KDVXOCZSPFFCG4VND72C

not attested not anchored not stored refs pending

The Pontryagin's maximum principle for stochastic differential systems under state constraints

Shuzhen Yang

arxiv:1610.05843 v2 · 2016-10-19 · 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{GC3FC5KDVXOCZSPFFCG4VND72C}

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	2026-05-18T00:18:00.508556Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

30b6517543addc2cc9e5288dcab47fd0828a8b6484e2522c8f831f3ecda8243a

Aliases

arxiv: 1610.05843 · arxiv_version: 1610.05843v2 · doi: 10.48550/arxiv.1610.05843 · pith_short_12: GC3FC5KDVXOC · pith_short_16: GC3FC5KDVXOCZSPF · pith_short_8: GC3FC5KD

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/GC3FC5KDVXOCZSPFFCG4VND72C \
  | 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: 30b6517543addc2cc9e5288dcab47fd0828a8b6484e2522c8f831f3ecda8243a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4ff438c53f7dd24b17ef692cf831478c54abba2d9bcf2f2abca005123a56267a",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2016-10-19T01:54:59Z",
    "title_canon_sha256": "4a2dc43bcb7a5875137f7c10299ca5fe98004f16bd03bb79f5445ec89851cc35"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1610.05843",
    "kind": "arxiv",
    "version": 2
  }
}