Pith Number

pith:6N5XFV2K

pith:2019:6N5XFV2K2OTFAAMP4IBALFHKIZ

not attested not anchored not stored refs pending

Critical almost Mathieu operator: hidden singularity, gap continuity, and the Hausdorff dimension of the spectrum

Igor Krasovsky, Svetlana Jitomirskaya

arxiv:1909.04429 v1 · 2019-09-10 · 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{6N5XFV2K2OTFAAMP4IBALFHKIZ}

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.

Cited by

1 paper in Pith

Cantor spectrum for multidimensional quasi-periodic Schr\"odinger operators

Receipt and verification

First computed	2026-07-05T00:03:22.158033Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f37b72d74ad3a650018fe2020594ea46408ca84da22e3f7234fb6fb2c1bab6e8

Aliases

arxiv: 1909.04429 · arxiv_version: 1909.04429v1 · doi: 10.48550/arxiv.1909.04429 · pith_short_12: 6N5XFV2K2OTF · pith_short_16: 6N5XFV2K2OTFAAMP · pith_short_8: 6N5XFV2K

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/6N5XFV2K2OTFAAMP4IBALFHKIZ \
  | 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: f37b72d74ad3a650018fe2020594ea46408ca84da22e3f7234fb6fb2c1bab6e8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5a2cae1d7d4fb0d16ce68090e2963b549e55bd5c5aec5921f4d87261dd5ea8a4",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SP",
    "submitted_at": "2019-09-10T12:12:05Z",
    "title_canon_sha256": "4df186cadff7e2bbbcbc1c27396ba2085899b1dd9e50d104afe2efd0aa7dd612"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1909.04429",
    "kind": "arxiv",
    "version": 1
  }
}