Pith Number

pith:LZNGHYHS

pith:2010:LZNGHYHSBUFNPAODLW44L7UX4W

not attested not anchored not stored refs pending

Stochastic Verification Theorem of Forward-Backward Controlled Systems for Viscosity Solutions

Liangquan Zhang

arxiv:1010.5742 v6 · 2010-10-27 · math.OC · cs.SY

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{LZNGHYHSBUFNPAODLW44L7UX4W}

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	2026-05-18T03:55:00.582538Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5e5a63e0f20d0ad781c35db9c5fe97e5b9893709899542ba6e4d26d505545a67

Aliases

arxiv: 1010.5742 · arxiv_version: 1010.5742v6 · doi: 10.48550/arxiv.1010.5742 · pith_short_12: LZNGHYHSBUFN · pith_short_16: LZNGHYHSBUFNPAOD · pith_short_8: LZNGHYHS

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/LZNGHYHSBUFNPAODLW44L7UX4W \
  | 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: 5e5a63e0f20d0ad781c35db9c5fe97e5b9893709899542ba6e4d26d505545a67

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d8082b6a49bcdab7c26f6808aec5eaad439f6336bcf8bfe1c7affc62bf9e2fde",
    "cross_cats_sorted": [
      "cs.SY"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2010-10-27T16:54:15Z",
    "title_canon_sha256": "1862d8cded85a81719e70ef4da1fddc39e9760b5c256c4c3d8a9e5d4cb3d5d7f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1010.5742",
    "kind": "arxiv",
    "version": 6
  }
}