Pith Number

pith:SNF5XMYF

pith:2026:SNF5XMYFWNOIVBLV4U53I543RQ

not attested not anchored not stored refs pending

Two-scale neural networks for optimal control of linear convection-dominated equations

Marcus Sarkis, Sijing Liu, Yi Zhang, Zhongqiang Zhang

arxiv:2605.17740 v1 · 2026-05-18 · math.NA · 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{SNF5XMYFWNOIVBLV4U53I543RQ}

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	2026-05-20T00:04:55.756260Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

934bdbb305b35c8a8575e53bb4779b8c30eb6aaf93be1affea94ca47eda2c0ce

Aliases

arxiv: 2605.17740 · arxiv_version: 2605.17740v1 · doi: 10.48550/arxiv.2605.17740 · pith_short_12: SNF5XMYFWNOI · pith_short_16: SNF5XMYFWNOIVBLV · pith_short_8: SNF5XMYF

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/SNF5XMYFWNOIVBLV4U53I543RQ \
  | 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: 934bdbb305b35c8a8575e53bb4779b8c30eb6aaf93be1affea94ca47eda2c0ce

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "952f5bd67ef4ea46244c7124823206e139a33e4512b44d06be205ee7f1277631",
    "cross_cats_sorted": [
      "cs.NA",
      "math.OC"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2026-05-18T01:43:43Z",
    "title_canon_sha256": "7183c455c8464a383ce3b1e495ef364d589f59ccea6cb8b67dd9c8c96c5c2ccc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.17740",
    "kind": "arxiv",
    "version": 1
  }
}