Pith Number

pith:ZLNM2QVE

pith:2016:ZLNM2QVEHBWPQGMWDWO3EBJVCA

not attested not anchored not stored refs pending

On localization and the spectrum of multi-frequency quasi-periodic operators

Michael Goldstein, Mircea Voda, Wilhelm Schlag

arxiv:1610.00380 v1 · 2016-10-03 · math.SP · math-ph · math.MP

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Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ZLNM2QVEHBWPQGMWDWO3EBJVCA}

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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.

Cited by

1 paper in Pith

Finite and full scale localization for the multi-frequency quasi-periodic CMV matrices

Receipt and verification

First computed	2026-05-18T01:03:25.611562Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cadacd42a4386cf819961d9db2053510053e5a2505679d04566f9d81f71dd49a

Aliases

arxiv: 1610.00380 · arxiv_version: 1610.00380v1 · doi: 10.48550/arxiv.1610.00380 · pith_short_12: ZLNM2QVEHBWP · pith_short_16: ZLNM2QVEHBWPQGMW · pith_short_8: ZLNM2QVE

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/ZLNM2QVEHBWPQGMWDWO3EBJVCA \
  | 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: cadacd42a4386cf819961d9db2053510053e5a2505679d04566f9d81f71dd49a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0a0a301939ccab2d98104a789c7b8577bf0b46578a503f364d13654ad515a139",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SP",
    "submitted_at": "2016-10-03T00:57:04Z",
    "title_canon_sha256": "aed7f8eda95965ef20d6a18028bbd51207a441bc1a8a05c88362e548bd2409d9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1610.00380",
    "kind": "arxiv",
    "version": 1
  }
}