Pith Number

pith:5RFFNMYX

pith:2016:5RFFNMYXNWIDSSGNXLSS7PWVB6

not attested not anchored not stored refs pending

The necessary and sufficient conditions for stochastic differential systems with multi-time states cost functional

Shuzhen Yang

arxiv:1609.04188 v1 · 2016-09-14 · 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{5RFFNMYXNWIDSSGNXLSS7PWVB6}

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	2026-05-18T01:04:38.685257Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ec4a56b3176d903948cdbae52fbed50fa054772de3b5b600c3902cead38b7712

Aliases

arxiv: 1609.04188 · arxiv_version: 1609.04188v1 · doi: 10.48550/arxiv.1609.04188 · pith_short_12: 5RFFNMYXNWID · pith_short_16: 5RFFNMYXNWIDSSGN · pith_short_8: 5RFFNMYX

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/5RFFNMYXNWIDSSGNXLSS7PWVB6 \
  | 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: ec4a56b3176d903948cdbae52fbed50fa054772de3b5b600c3902cead38b7712

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9192916090ecb5fc7c39024e5d5a9286629963a22690598f5d4de9866f5d9f83",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2016-09-14T09:33:20Z",
    "title_canon_sha256": "468735c3c8397545cf3cc732835e7a0c1728b88c9fbe6301a7a916d2a828301f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1609.04188",
    "kind": "arxiv",
    "version": 1
  }
}