Pith Number

pith:XBHS3AD7

pith:2015:XBHS3AD76VRWUX3GGBJSIDI5CT

not attested not anchored not stored refs pending

All couplings localization for quasiperiodic operators with Lipschitz monotone potentials

Ilya Kachkovskiy, Svetlana Jitomirskaya

arxiv:1509.02226 v1 · 2015-09-07 · 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{XBHS3AD76VRWUX3GGBJSIDI5CT}

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	2026-05-18T01:33:41.439069Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b84f2d807ff5636a5f663053240d1d14d056834cfa9ccb2583151113e34ada89

Aliases

arxiv: 1509.02226 · arxiv_version: 1509.02226v1 · doi: 10.48550/arxiv.1509.02226 · pith_short_12: XBHS3AD76VRW · pith_short_16: XBHS3AD76VRWUX3G · pith_short_8: XBHS3AD7

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/XBHS3AD76VRWUX3GGBJSIDI5CT \
  | 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: b84f2d807ff5636a5f663053240d1d14d056834cfa9ccb2583151113e34ada89

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7ef953f67d5941d042b3d6340b11b2c152ac2db85fadd6e0cdbc7fc58b78ef93",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SP",
    "submitted_at": "2015-09-07T23:41:20Z",
    "title_canon_sha256": "d6a6e24ba9d859a5b434b04173916a6da4830de9ff88970309de240a93bd7584"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1509.02226",
    "kind": "arxiv",
    "version": 1
  }
}