Pith Number

pith:BUOK7QVG

pith:2007:BUOK7QVGI3PRKORUJXQS3VPTBQ

not attested not anchored not stored refs pending

The Schroedinger operator as a generalized Laplacian

Janusz Grabowski, Katarzyna Grabowska, Pawel Urbanski

arxiv:0711.2777 v2 · 2007-11-18 · math-ph · math.DG · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{BUOK7QVGI3PRKORUJXQS3VPTBQ}

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	2026-05-18T04:08:04.311539Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0d1cafc2a646df153a344de12dd5f30c14bc8ec7e195591fed0a109ec701b3cd

Aliases

arxiv: 0711.2777 · arxiv_version: 0711.2777v2 · doi: 10.48550/arxiv.0711.2777 · pith_short_12: BUOK7QVGI3PR · pith_short_16: BUOK7QVGI3PRKORU · pith_short_8: BUOK7QVG

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/BUOK7QVGI3PRKORUJXQS3VPTBQ \
  | 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: 0d1cafc2a646df153a344de12dd5f30c14bc8ec7e195591fed0a109ec701b3cd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9a6c1172b969c677328599ab88e2cebfc72108e5c2680279f0032cc883212712",
    "cross_cats_sorted": [
      "math.DG",
      "math.MP"
    ],
    "license": "",
    "primary_cat": "math-ph",
    "submitted_at": "2007-11-18T08:28:08Z",
    "title_canon_sha256": "cc6c3559575f0159f2470fa1aa983e7e93ae915776df283c3e2003c54a3787d0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0711.2777",
    "kind": "arxiv",
    "version": 2
  }
}