Pith Number

pith:S37HGGA6

pith:2024:S37HGGA6SEVETGQZV4FY3UAPXP

not attested not anchored not stored refs pending

A Natural Primal-Dual Hybrid Gradient Method for Adversarial Neural Network Training on Solving Partial Differential Equations

Shu Liu, Stanley Osher, Wuchen Li

arxiv:2411.06278 v4 · 2024-11-09 · math.NA · cs.LG · cs.NA · math.OC

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Add to your LaTeX paper

\usepackage{pith}
\pithnumber{S37HGGA6SEVETGQZV4FY3UAPXP}

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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

1 paper in Pith

Fixed-Point Neural Optimal Transport without Implicit Differentiation

Receipt and verification

First computed	2026-05-26T01:02:25.523025Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

96fe73181e912a499a19af0b8dd00fbbd91961c2fec87664fef74f4746160d50

Aliases

arxiv: 2411.06278 · arxiv_version: 2411.06278v4 · doi: 10.48550/arxiv.2411.06278 · pith_short_12: S37HGGA6SEVE · pith_short_16: S37HGGA6SEVETGQZ · pith_short_8: S37HGGA6

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/S37HGGA6SEVETGQZV4FY3UAPXP \
  | 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: 96fe73181e912a499a19af0b8dd00fbbd91961c2fec87664fef74f4746160d50

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c8f2d7935514317c5e006e35138b103ec43e01d46630cf18ef17d69c0fe9df3d",
    "cross_cats_sorted": [
      "cs.LG",
      "cs.NA",
      "math.OC"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2024-11-09T20:39:10Z",
    "title_canon_sha256": "a822fc93fa329242576e079977d9dc3575b241e084b6f715e5d22ad78f676ef5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2411.06278",
    "kind": "arxiv",
    "version": 4
  }
}