Pith Number

pith:BU5LLMP3

pith:2013:BU5LLMP3DW2VCDG7GWZXCTAEOO

not attested not anchored not stored refs pending

Absolutely Continuous Spectrum for the Quasi-periodic Schr\"{o}dinger Operator in Exponential Regime

Wencai Liu, Xiaoping Yuan

arxiv:1311.0863 v1 · 2013-11-04 · math.SP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{BU5LLMP3DW2VCDG7GWZXCTAEOO}

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	2026-05-18T03:07:56.208114Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0d3ab5b1fb1db5510cdf35b3714c0473b4bc6e514355d55de07436ec1f6d3f01

Aliases

arxiv: 1311.0863 · arxiv_version: 1311.0863v1 · doi: 10.48550/arxiv.1311.0863 · pith_short_12: BU5LLMP3DW2V · pith_short_16: BU5LLMP3DW2VCDG7 · pith_short_8: BU5LLMP3

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/BU5LLMP3DW2VCDG7GWZXCTAEOO \
  | 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: 0d3ab5b1fb1db5510cdf35b3714c0473b4bc6e514355d55de07436ec1f6d3f01

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fbb45ca8faa25b25e0182bb469003be50449205439cfb7a04228bce0c0afc223",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SP",
    "submitted_at": "2013-11-04T13:01:44Z",
    "title_canon_sha256": "7c6e3e9f42e1a979a31f688082388e911eaf9caa5c37b32da43bbdf265245944"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1311.0863",
    "kind": "arxiv",
    "version": 1
  }
}