Pith Number

pith:R6WAMTT2

pith:2026:R6WAMTT2UTXCQELSVR642B37FP

not attested not anchored not stored refs pending

PRONE: Petrov-Galerkin Operator Learning Unifies DMD, SINDy & Koopmanism

April Herwig, J. Nathan Kutz, Matthew J. Colbrook

arxiv:2606.27982 v1 · 2026-06-26 · 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{R6WAMTT2UTXCQELSVR642B37FP}

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	2026-06-29T01:14:54.493323Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8fac064e7aa4ee281172ac7dcd077f2bfd04f31212a6a26bd96b30bfcdde5d04

Aliases

arxiv: 2606.27982 · arxiv_version: 2606.27982v1 · doi: 10.48550/arxiv.2606.27982 · pith_short_12: R6WAMTT2UTXC · pith_short_16: R6WAMTT2UTXCQELS · pith_short_8: R6WAMTT2

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/R6WAMTT2UTXCQELSVR642B37FP \
  | 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: 8fac064e7aa4ee281172ac7dcd077f2bfd04f31212a6a26bd96b30bfcdde5d04

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8b16db7b4303dc3d938fd735b006c3b8499cdd4a014866744afe4e4d909ee3e4",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2026-06-26T11:30:55Z",
    "title_canon_sha256": "4a4c9db58b9b91a4ada6d405303b002bc2bdb47a3fdfa9e16a73bdecbba86eb2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.27982",
    "kind": "arxiv",
    "version": 1
  }
}