Pith Number

pith:5PRYRCS4

pith:2025:5PRYRCS46ZOOKINANT3WZTOJ6P

not attested not anchored not stored refs pending

MD-PNOP: Equation-Recast Neural Operators for Minimal-Data Extrapolation and PDE Solver Acceleration

Huihua Yang, Md Hossain Sahadath, Qiyun Cheng, Shaowu Pan, Wei Ji

arxiv:2509.01416 v2 · 2025-09-01 · 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{5PRYRCS46ZOOKINANT3WZTOJ6P}

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	2026-05-17T23:39:17.637548Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ebe3888a5cf65ce521a06cf76ccdc9f3cfafc709ef2a79e5627b61d2b30063ed

Aliases

arxiv: 2509.01416 · arxiv_version: 2509.01416v2 · doi: 10.48550/arxiv.2509.01416 · pith_short_12: 5PRYRCS46ZOO · pith_short_16: 5PRYRCS46ZOOKINA · pith_short_8: 5PRYRCS4

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/5PRYRCS46ZOOKINANT3WZTOJ6P \
  | 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: ebe3888a5cf65ce521a06cf76ccdc9f3cfafc709ef2a79e5627b61d2b30063ed

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c8870cd5174884a703a3653c28bd19e80dc88cb82267ceef8a3230b940763fd9",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2025-09-01T12:14:58Z",
    "title_canon_sha256": "8a097032924ea05fbeb0b7eead90338d5c4d23d93af39d5f3aefd127317f22b7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2509.01416",
    "kind": "arxiv",
    "version": 2
  }
}