Pith Number

pith:CX3FHEOD

pith:2003:CX3FHEODSUFZ4JQRD66UAKCVPS

not attested not anchored not stored refs pending

Schr\"{o}dinger operators with matrix potentials. Transition from the absolutely continuous to the singular spectrum

Boris R. Vainberg, Stanislav A. Molchanov

arxiv:math-ph/0308012 v1 · 2003-08-09 · 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{CX3FHEODSUFZ4JQRD66UAKCVPS}

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	2026-05-18T01:17:53.750412Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

15f65391c3950b9e26111fbd4028557c92bd5f538da7c81fbc066a768fa8c009

Aliases

arxiv: math-ph/0308012 · arxiv_version: math-ph/0308012v1 · doi: 10.48550/arxiv.math-ph/0308012 · pith_short_12: CX3FHEODSUFZ · pith_short_16: CX3FHEODSUFZ4JQR · pith_short_8: CX3FHEOD

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/CX3FHEODSUFZ4JQRD66UAKCVPS \
  | 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: 15f65391c3950b9e26111fbd4028557c92bd5f538da7c81fbc066a768fa8c009

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "959ab853cbaac0f298090f994d6b94711f6d00dba501f2e4f752ccf64b0acd9c",
    "cross_cats_sorted": [
      "math.MP"
    ],
    "license": "",
    "primary_cat": "math-ph",
    "submitted_at": "2003-08-09T19:50:53Z",
    "title_canon_sha256": "822ea46709fd69d2a779cd5d55f8dabdf3aec3f4ad28c0563c7ead58fd0459b8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math-ph/0308012",
    "kind": "arxiv",
    "version": 1
  }
}