Pith Number

pith:2BFIAUIB

pith:2026:2BFIAUIBAP22KHV5MDUH4Q7QEI

not attested not anchored not stored refs pending

Generalization Guarantees for Multi-Input Neural Operator Learning in Sobolev Spaces

Hao Liu, Wei Zhu, Wenjing Liao, Yahong Yang, Zecheng Zhang

arxiv:2606.17419 v1 · 2026-06-16 · cs.LG · cs.NA · math.NA

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{2BFIAUIBAP22KHV5MDUH4Q7QEI}

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	2026-06-19T16:10:12.349035Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d04a80510103f5a51ebd60e87e43f02216c64a2597d1c07ea182997e55ff00b2

Aliases

arxiv: 2606.17419 · arxiv_version: 2606.17419v1 · doi: 10.48550/arxiv.2606.17419 · pith_short_12: 2BFIAUIBAP22 · pith_short_16: 2BFIAUIBAP22KHV5 · pith_short_8: 2BFIAUIB

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/2BFIAUIBAP22KHV5MDUH4Q7QEI \
  | 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: d04a80510103f5a51ebd60e87e43f02216c64a2597d1c07ea182997e55ff00b2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7c9f1ad6b374c4c09ea8b26bacdefba066c3ebf0e7a5228e90936771a255c588",
    "cross_cats_sorted": [
      "cs.NA",
      "math.NA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-06-16T02:00:59Z",
    "title_canon_sha256": "c3a7d1abe96782e054119531cb3fb901055ac65e8171ad699fe118eece865de0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.17419",
    "kind": "arxiv",
    "version": 1
  }
}