Pith Number

pith:VMNOQKRR

pith:2025:VMNOQKRRJVHQ5PL3JNK4XARSGV

not attested not anchored not stored refs pending

Control, Optimal Transport and Neural Differential Equations in Supervised Learning

Minh-Binh Tran, Minh-Nhat Phung

arxiv:2503.15105 v4 · 2025-03-19 · math.NA · cs.LG · cs.NA · 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{VMNOQKRRJVHQ5PL3JNK4XARSGV}

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	2026-05-21T01:04:13.364423Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ab1ae82a314d4f0ebd7b4b55cb823235702d1300754e487ca80af8e448750922

Aliases

arxiv: 2503.15105 · arxiv_version: 2503.15105v4 · doi: 10.48550/arxiv.2503.15105 · pith_short_12: VMNOQKRRJVHQ · pith_short_16: VMNOQKRRJVHQ5PL3 · pith_short_8: VMNOQKRR

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/VMNOQKRRJVHQ5PL3JNK4XARSGV \
  | 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: ab1ae82a314d4f0ebd7b4b55cb823235702d1300754e487ca80af8e448750922

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1c7f581a017611ab9fc4230e945a4ac24c14856f5529e16981f38f2901f3840f",
    "cross_cats_sorted": [
      "cs.LG",
      "cs.NA",
      "math.OC"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2025-03-19T11:04:36Z",
    "title_canon_sha256": "2e25553e514d0fa2c3cb8f41278660bd1c40d314daac12cdce4eb1a411fd8b7a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2503.15105",
    "kind": "arxiv",
    "version": 4
  }
}