Pith Number

pith:GHMPFVQP

pith:2021:GHMPFVQPR2XBWKN5K55WN7DWNH

not attested not anchored not stored refs pending

The Linear-Time-Invariance Notion of the Koopman Analysis-Part 2: Physical Interpretations of Invariant Koopman Modes and Phenomenological Revelations

Asiri Umenga Weerasuriya, Cruz Y. Li, Tim K.T. Tse, Xisheng Lin, Xuelin Zhang, Yunfei Fu, Zengshun Chen

arxiv:2112.03029 v2 · 2021-12-06 · physics.flu-dyn

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{GHMPFVQPR2XBWKN5K55WN7DWNH}

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	2026-07-05T05:56:37.629349Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

31d8f2d60f8eae1b29bd577b66fc7669c73167cdfdde269e8969d2d7ba7006ff

Aliases

arxiv: 2112.03029 · arxiv_version: 2112.03029v2 · doi: 10.48550/arxiv.2112.03029 · pith_short_12: GHMPFVQPR2XB · pith_short_16: GHMPFVQPR2XBWKN5 · pith_short_8: GHMPFVQP

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/GHMPFVQPR2XBWKN5K55WN7DWNH \
  | 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: 31d8f2d60f8eae1b29bd577b66fc7669c73167cdfdde269e8969d2d7ba7006ff

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "79b6d5a76d539583f668b0b9927b2edebd247ba7c5e45b881b7b276f33241534",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "physics.flu-dyn",
    "submitted_at": "2021-12-06T13:26:38Z",
    "title_canon_sha256": "72dd401d2c967bf8d2319bbe050006e356cb9b52d4987b7daad3a0c7647374df"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2112.03029",
    "kind": "arxiv",
    "version": 2
  }
}