Pith Number

pith:JYTS5YWT

pith:2009:JYTS5YWT75C7VRGN76TWVTX4UL

not attested not anchored not stored refs pending

A note on quasi-similarity of Koopman operators

Krzysztof Fraczek, Mariusz Lemanczyk

arxiv:0903.3109 v2 · 2009-03-18 · math.DS · math.FA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{JYTS5YWT75C7VRGN76TWVTX4UL}

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	2026-05-18T02:51:48.862286Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4e272ee2d3ff45fac4cdffa76acefca2d6301b4c35333717d6fb55834e789093

Aliases

arxiv: 0903.3109 · arxiv_version: 0903.3109v2 · doi: 10.48550/arxiv.0903.3109 · pith_short_12: JYTS5YWT75C7 · pith_short_16: JYTS5YWT75C7VRGN · pith_short_8: JYTS5YWT

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/JYTS5YWT75C7VRGN76TWVTX4UL \
  | 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: 4e272ee2d3ff45fac4cdffa76acefca2d6301b4c35333717d6fb55834e789093

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8a8ddab699d07c9c7bd3d443d6aad9dd1b3ba9393501c3633a33fc0a56396c94",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2009-03-18T09:02:38Z",
    "title_canon_sha256": "9c76e4b914ac6a78f2d179c17f37ef6e7b69953e970183b79db3626c70a006d8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0903.3109",
    "kind": "arxiv",
    "version": 2
  }
}