Pith Number

pith:DG4NR3ND

pith:2021:DG4NR3NDTHXZPZURURIUY45W2Y

not attested not anchored not stored refs pending

Almost Everything About the Unitary Almost Mathieu Operator

Christopher Cedzich, Darren C. Ong, Jake Fillman

arxiv:2112.03216 v2 · 2021-12-06 · math.SP · math-ph · math.FA · math.MP · quant-ph

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{DG4NR3NDTHXZPZURURIUY45W2Y}

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

3 papers in Pith

Bottleneck Effects and Harmonic-Type Velocity Bounds for Periodic Quantum Walks

Mobility edges in pseudo-unitary quasiperiodic quantum walks

Absence of Ballistic Transport in Quantum Walks with Asymptotically Reflecting Sites

Receipt and verification

First computed	2026-07-05T09:16:42.844540Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

19b8d8eda399ef97e691a4514c73b6d63b15533e096a0c0bfd91dd75ca1432f1

Aliases

arxiv: 2112.03216 · arxiv_version: 2112.03216v2 · doi: 10.48550/arxiv.2112.03216 · pith_short_12: DG4NR3NDTHXZ · pith_short_16: DG4NR3NDTHXZPZUR · pith_short_8: DG4NR3ND

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/DG4NR3NDTHXZPZURURIUY45W2Y \
  | 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: 19b8d8eda399ef97e691a4514c73b6d63b15533e096a0c0bfd91dd75ca1432f1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "63c13f04ac06aea05b848eae98419d8f61164e7bbdafeddd66603638325e45de",
    "cross_cats_sorted": [
      "math-ph",
      "math.FA",
      "math.MP",
      "quant-ph"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SP",
    "submitted_at": "2021-12-06T18:17:31Z",
    "title_canon_sha256": "d07c39f6f2a2e47fe40f40cc754146d80541d2042999c4d0849c8f8a57df812b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2112.03216",
    "kind": "arxiv",
    "version": 2
  }
}