Pith Number

pith:RRVDV67Z

pith:2026:RRVDV67ZWUIOKUQNLM33GETROA

not attested not anchored not stored refs pending

Koopman operator theory: fundamentals, control, and applications

Armin Lederer, Igor Mezi\'c, Jorge Cort\'es, Karl Worthmann, Mircea Lazar

arxiv:2607.01819 v1 · 2026-07-02 · eess.SY · cs.LG · cs.SY

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{RRVDV67ZWUIOKUQNLM33GETROA}

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	2026-07-03T01:17:30.787852Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8c6a3afbf9b510e5520d5b37b31271700fb58ed6eccf7385c3bb84a3af69f7e3

Aliases

arxiv: 2607.01819 · arxiv_version: 2607.01819v1 · doi: 10.48550/arxiv.2607.01819 · pith_short_12: RRVDV67ZWUIO · pith_short_16: RRVDV67ZWUIOKUQN · pith_short_8: RRVDV67Z

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/RRVDV67ZWUIOKUQNLM33GETROA \
  | 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: 8c6a3afbf9b510e5520d5b37b31271700fb58ed6eccf7385c3bb84a3af69f7e3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "574d64a20140dcb88d3de5ac9271fee02be15a3c767798baca969edba1da1134",
    "cross_cats_sorted": [
      "cs.LG",
      "cs.SY"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "eess.SY",
    "submitted_at": "2026-07-02T07:31:47Z",
    "title_canon_sha256": "0491833a521f0091a14984898fd01925aa2df744264ccc62e379d55610051892"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.01819",
    "kind": "arxiv",
    "version": 1
  }
}