Pith Number

pith:XN7CMN3L

pith:2018:XN7CMN3L43NKS7XCDW7YPEEHSC

not attested not anchored not stored refs pending

A Mean-Field Optimal Control Formulation of Deep Learning

Jiequn Han, Qianxiao Li, Weinan E

arxiv:1807.01083 v1 · 2018-07-03 · math.OC · cs.LG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{XN7CMN3L43NKS7XCDW7YPEEHSC}

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.

Cited by

2 papers in Pith

Theory of learning of high-dimensional controlled non-linear dynamical systems (I): models and methods

Deep network as memory space: complexity, generalization, disentangled representation and interpretability

Receipt and verification

First computed	2026-07-05T01:20:09.091555Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bb7e26376be6daa97ee21dbf87908790882d8bfd85add7e29628c279c945cd0a

Aliases

arxiv: 1807.01083 · arxiv_version: 1807.01083v1 · doi: 10.48550/arxiv.1807.01083 · pith_short_12: XN7CMN3L43NK · pith_short_16: XN7CMN3L43NKS7XC · pith_short_8: XN7CMN3L

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/XN7CMN3L43NKS7XCDW7YPEEHSC \
  | 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: bb7e26376be6daa97ee21dbf87908790882d8bfd85add7e29628c279c945cd0a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c6f0ba594b05d9bc812ad4725632d799e15392a30f1cca0cea53740a5404c625",
    "cross_cats_sorted": [
      "cs.LG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2018-07-03T11:05:13Z",
    "title_canon_sha256": "0e3a7cda8bd79d8bd73ae975f9da0fc8469ce356b4faed79d7e737c47ace3116"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1807.01083",
    "kind": "arxiv",
    "version": 1
  }
}