Pith Number

pith:2EO43TNK

pith:2025:2EO43TNKOPK3VZ5MGX3BDPEAXX

not attested not anchored not stored refs pending

Reinforcement-Learning-Guided Data-Driven Estimation of Spectral Properties of Stochastic Koopman Semigroups

Isao Ishikawa, Jing Liu, Weiping Ding, Yuanchao Xu, Zhongwei Shen

arxiv:2509.04265 v3 · 2025-09-04 · math.DS

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{2EO43TNKOPK3VZ5MGX3BDPEAXX}

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	2026-06-08T01:05:02.738708Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d11dcdcdaa73d5bae7ac35f611bc80bdc139f60c3cd06280afee3f4a1f809f77

Aliases

arxiv: 2509.04265 · arxiv_version: 2509.04265v3 · doi: 10.48550/arxiv.2509.04265 · pith_short_12: 2EO43TNKOPK3 · pith_short_16: 2EO43TNKOPK3VZ5M · pith_short_8: 2EO43TNK

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/2EO43TNKOPK3VZ5MGX3BDPEAXX \
  | 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: d11dcdcdaa73d5bae7ac35f611bc80bdc139f60c3cd06280afee3f4a1f809f77

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "eb9029ea2e9fa3d34295a853fb8cad0af8c71a0768175b6b7db6b50bfc976fba",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2025-09-04T14:42:22Z",
    "title_canon_sha256": "77fb40b8534ae4dd904094632eda2af2d4b24b5aa1c8a45d2b6d11e3f38f326d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2509.04265",
    "kind": "arxiv",
    "version": 3
  }
}