Pith Number

pith:FFCTEFQG

pith:2012:FFCTEFQGI46UQ5CDHLMGXZUNQ3

not attested not anchored not stored refs pending

The Relaxed Stochastic Maximum Principle in the Mean-field Singular Controls

Liangquan Zhang

arxiv:1202.4129 v5 · 2012-02-19 · 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{FFCTEFQGI46UQ5CDHLMGXZUNQ3}

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	2026-05-18T03:41:44.123256Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2945321606473d4874433ad86be68d86cf732ef133b79d8a5e99fbfd837c0052

Aliases

arxiv: 1202.4129 · arxiv_version: 1202.4129v5 · doi: 10.48550/arxiv.1202.4129 · pith_short_12: FFCTEFQGI46U · pith_short_16: FFCTEFQGI46UQ5CD · pith_short_8: FFCTEFQG

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/FFCTEFQGI46UQ5CDHLMGXZUNQ3 \
  | 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: 2945321606473d4874433ad86be68d86cf732ef133b79d8a5e99fbfd837c0052

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f57457e9efa7f0bef8fb11d4e6075a110c41009039389eb890bc7af900a680ac",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2012-02-19T07:02:15Z",
    "title_canon_sha256": "86c2636cd6d6a54c397bb8ac3c314d60a21256b407cc2d98a9e4dc6ec804e392"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1202.4129",
    "kind": "arxiv",
    "version": 5
  }
}