Pith Number

pith:5UFTXBAI

pith:2026:5UFTXBAIQ7N7N7NWV44SLW72MG

not attested not anchored not stored refs pending

Learning the Koopman Operator using Attention Free Transformers

Alexey Yermakov, Evangelos-Marios Nikolados, Filippo Menolascina, Mars Gao, Mohammed Nagdi, Nathan Kutz

arxiv:2606.23957 v1 · 2026-06-22 · cs.LG · cs.SY · eess.SY · q-bio.MN

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{5UFTXBAIQ7N7N7NWV44SLW72MG}

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	2026-06-24T00:14:31.280120Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ed0b3b840887dbf6fdb6af3925dbfa61a2113fe701264d74c01328694fee2c54

Aliases

arxiv: 2606.23957 · arxiv_version: 2606.23957v1 · doi: 10.48550/arxiv.2606.23957 · pith_short_12: 5UFTXBAIQ7N7 · pith_short_16: 5UFTXBAIQ7N7N7NW · pith_short_8: 5UFTXBAI

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/5UFTXBAIQ7N7N7NWV44SLW72MG \
  | 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: ed0b3b840887dbf6fdb6af3925dbfa61a2113fe701264d74c01328694fee2c54

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "21030b70cdf98a62498552a556af97c5db9928c41e27c3583ed872f87eba3eef",
    "cross_cats_sorted": [
      "cs.SY",
      "eess.SY",
      "q-bio.MN"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-06-22T21:36:55Z",
    "title_canon_sha256": "e359a9173bd2e7fa754115548305ee4a2ddd7cc0476314dcbf8eab33dd102877"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.23957",
    "kind": "arxiv",
    "version": 1
  }
}