Pith Number

pith:SHYAGCW6

pith:2015:SHYAGCW65WQNO65GY76GZOPCYH

not attested not anchored not stored refs pending

The Liouville theorem as a problem of common eigenfunctions

G.F. Torres del Castillo

arxiv:1503.06789 v1 · 2015-03-23 · physics.class-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{SHYAGCW65WQNO65GY76GZOPCYH}

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	2026-05-18T02:20:30.018951Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

91f0030adeeda0d77ba6c7fc6cb9e2c1c27475bbdcff499272398e7be8269799

Aliases

arxiv: 1503.06789 · arxiv_version: 1503.06789v1 · doi: 10.48550/arxiv.1503.06789 · pith_short_12: SHYAGCW65WQN · pith_short_16: SHYAGCW65WQNO65G · pith_short_8: SHYAGCW6

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/SHYAGCW65WQNO65GY76GZOPCYH \
  | 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: 91f0030adeeda0d77ba6c7fc6cb9e2c1c27475bbdcff499272398e7be8269799

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e1302f478765773ee2c7553077d863792b5e7c0ea03b317ba64ae7fce81f5fca",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "physics.class-ph",
    "submitted_at": "2015-03-23T18:03:12Z",
    "title_canon_sha256": "1fc41490d313ff3642791b5f50b79f09b1d1a35b650104affad35605259be36e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1503.06789",
    "kind": "arxiv",
    "version": 1
  }
}