Pith Number

pith:YF4IMCVN

pith:2020:YF4IMCVNGKDGI64Z2YMAHBHGWP

not attested not anchored not stored refs pending

Approximate Analytical Solution to the Zonal Harmonics Problem Using Koopman Operator Theory

David Arnas, Richard Linares

arxiv:2012.09620 v3 · 2020-12-17 · astro-ph.EP · math.FA · physics.space-ph

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{YF4IMCVNGKDGI64Z2YMAHBHGWP}

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	2026-07-05T03:24:07.915104Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c178860aad3286647b99d6180384e6b3e8160d9acaaedf1c1fd7dab2d3abfe7d

Aliases

arxiv: 2012.09620 · arxiv_version: 2012.09620v3 · doi: 10.48550/arxiv.2012.09620 · pith_short_12: YF4IMCVNGKDG · pith_short_16: YF4IMCVNGKDGI64Z · pith_short_8: YF4IMCVN

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/YF4IMCVNGKDGI64Z2YMAHBHGWP \
  | 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: c178860aad3286647b99d6180384e6b3e8160d9acaaedf1c1fd7dab2d3abfe7d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "77fdcf2cfa23015b04e402dad925381632967a9b2742c88e19a596b093d55d85",
    "cross_cats_sorted": [
      "math.FA",
      "physics.space-ph"
    ],
    "license": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
    "primary_cat": "astro-ph.EP",
    "submitted_at": "2020-12-17T14:45:15Z",
    "title_canon_sha256": "eaa2960de629a6f991e52806d16bd9d564c154174dd2f93af5ef3dd5ed619278"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2012.09620",
    "kind": "arxiv",
    "version": 3
  }
}