Pith Number

pith:BK5LD3XF

pith:2013:BK5LD3XFR2TNGLBIKMXRSSUZ2H

not attested not anchored not stored refs pending

On Spectral Theory for Schr\"odinger Operators with Operator-Valued Potentials

Fritz Gesztesy, Maxim Zinchenko, Rudi Weikard

arxiv:1301.0682 v2 · 2013-01-04 · math.SP · math-ph · 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{BK5LD3XFR2TNGLBIKMXRSSUZ2H}

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	2026-05-18T03:30:41.157680Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0abab1eee58ea6d32c28532f194a99d1fd4dafd04ef2aa921196090582d4035f

Aliases

arxiv: 1301.0682 · arxiv_version: 1301.0682v2 · doi: 10.48550/arxiv.1301.0682 · pith_short_12: BK5LD3XFR2TN · pith_short_16: BK5LD3XFR2TNGLBI · pith_short_8: BK5LD3XF

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/BK5LD3XFR2TNGLBIKMXRSSUZ2H \
  | 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: 0abab1eee58ea6d32c28532f194a99d1fd4dafd04ef2aa921196090582d4035f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "56d08305c46ff6420af85b736f0f43e0b40a0b93be7c4b3a11cdfa208b5121f7",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SP",
    "submitted_at": "2013-01-04T07:26:26Z",
    "title_canon_sha256": "79c74c8b780c84c0ca53cc3fca75e7561d63e490a598d9c89aa35aa226cf6d67"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1301.0682",
    "kind": "arxiv",
    "version": 2
  }
}