Pith Number

pith:K3YUFICD

pith:2026:K3YUFICD7BD7NETIXXQLOS4LJY

not attested not anchored not stored refs pending

A Trainable-by-Parts Operator Learning Framework: Bridging DeepONet and Karhunen-Loeve Expansions for Large-Scale Applications

Alexandre Tartakovsky, Christian Munoz

arxiv:2606.28519 v1 · 2026-06-26 · 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{K3YUFICD7BD7NETIXXQLOS4LJY}

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	2026-06-30T00:15:16.709761Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

56f142a043f847f69268bde0b74b8b4e3e5a93b831df07faf32d27f8bdb29b67

Aliases

arxiv: 2606.28519 · arxiv_version: 2606.28519v1 · doi: 10.48550/arxiv.2606.28519 · pith_short_12: K3YUFICD7BD7 · pith_short_16: K3YUFICD7BD7NETI · pith_short_8: K3YUFICD

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/K3YUFICD7BD7NETIXXQLOS4LJY \
  | 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: 56f142a043f847f69268bde0b74b8b4e3e5a93b831df07faf32d27f8bdb29b67

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d137140115573137f6ccd48a672cdf68c3e99edb4e837c284679f215980a5e73",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-06-26T18:15:24Z",
    "title_canon_sha256": "77faa05860d65fb0580da53786e9b2721e40284a8eb96bc19b7fa62b5197be14"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.28519",
    "kind": "arxiv",
    "version": 1
  }
}