Pith Number

pith:HLQRPHIP

pith:2019:HLQRPHIPHW7DA7RQYUUSZFA75B

not attested not anchored not stored refs pending

Anderson localization for multi-frequency quasi-periodic operators on $\mathbb{Z}^d$

Svetlana Jitomirskaya, Wencai Liu, Yunfeng Shi

arxiv:1908.03805 v1 · 2019-08-10 · 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{HLQRPHIPHW7DA7RQYUUSZFA75B}

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

Infinite energy quasi-periodic solutions to nonlinear Schr\"odinger equations on $\mathbb R$

Receipt and verification

First computed	2026-07-05T03:28:08.873235Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3ae1179d0f3dbe307e30c5292c941fe87b6311c0c2531094d59745a7f499a053

Aliases

arxiv: 1908.03805 · arxiv_version: 1908.03805v1 · doi: 10.48550/arxiv.1908.03805 · pith_short_12: HLQRPHIPHW7D · pith_short_16: HLQRPHIPHW7DA7RQ · pith_short_8: HLQRPHIP

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/HLQRPHIPHW7DA7RQYUUSZFA75B \
  | 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: 3ae1179d0f3dbe307e30c5292c941fe87b6311c0c2531094d59745a7f499a053

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0504f24e7e929c79316d27442e919d7ef93b684f0599663e3f1897c203c9b351",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SP",
    "submitted_at": "2019-08-10T21:01:04Z",
    "title_canon_sha256": "bbe15b2e4292bbf005d71203f72876c99e661d964478fd861ce63d13104f60b7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1908.03805",
    "kind": "arxiv",
    "version": 1
  }
}