Pith Number

pith:ZBPHRCCI

pith:2025:ZBPHRCCIVPODA5UNINW75AXQDD

not attested not anchored not stored refs pending

Control and optimization for Neural Partial Differential Equations in Supervised Learning

Alain Bensoussan, Bangjie Wang, Minh-Binh Tran

arxiv:2506.20764 v2 · 2025-06-25 · 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{ZBPHRCCIVPODA5UNINW75AXQDD}

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	2026-05-21T01:04:14.887378Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c85e788848abdc30768d436dfe82f018ef541f6057d2ae1e8e2c7d1e07eb5641

Aliases

arxiv: 2506.20764 · arxiv_version: 2506.20764v2 · doi: 10.48550/arxiv.2506.20764 · pith_short_12: ZBPHRCCIVPOD · pith_short_16: ZBPHRCCIVPODA5UN · pith_short_8: ZBPHRCCI

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/ZBPHRCCIVPODA5UNINW75AXQDD \
  | 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: c85e788848abdc30768d436dfe82f018ef541f6057d2ae1e8e2c7d1e07eb5641

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6c0d23e20b5d1caab1cc14fb4e0f580c190df6d8632b12b51fcf948d50b963e6",
    "cross_cats_sorted": [
      "cs.LG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2025-06-25T18:54:48Z",
    "title_canon_sha256": "2f269c979213747ad745c5d4660fef6e6335d863074845f65f291ad87aa516a1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2506.20764",
    "kind": "arxiv",
    "version": 2
  }
}