Pith Number

pith:VA5JVYWB

pith:2020:VA5JVYWBJY3KSHKQ4YNPTR3ZQF

not attested not anchored not stored refs pending

Learning Bounded Koopman Observables: Results on Stability, Continuity, and Controllability

Craig Bakker, Thiagarajan Ramachandran, W. Steven Rosenthal

arxiv:2004.14921 v1 · 2020-04-30 · math.DS · math.OC

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VA5JVYWBJY3KSHKQ4YNPTR3ZQF}

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.

Cited by

1 paper in Pith

On the algebra of Koopman eigenfunctions and on some of their infinities

Receipt and verification

First computed	2026-07-05T00:59:31.072014Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a83a9ae2c14e36a91d50e61af9c779817000fb859bb15bdd9702bd5d7402a6af

Aliases

arxiv: 2004.14921 · arxiv_version: 2004.14921v1 · doi: 10.48550/arxiv.2004.14921 · pith_short_12: VA5JVYWBJY3K · pith_short_16: VA5JVYWBJY3KSHKQ · pith_short_8: VA5JVYWB

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/VA5JVYWBJY3KSHKQ4YNPTR3ZQF \
  | 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: a83a9ae2c14e36a91d50e61af9c779817000fb859bb15bdd9702bd5d7402a6af

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c42c77caeaeb3681f45bb1203300b28fe54de6ee1ff7716e18c85a02bb123aba",
    "cross_cats_sorted": [
      "math.OC"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2020-04-30T16:24:13Z",
    "title_canon_sha256": "9090c87de9a07a31cb4521a1300e7d66b391a1ec09dab2c33700831c64bec540"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2004.14921",
    "kind": "arxiv",
    "version": 1
  }
}