Pith Number

pith:WDDF4DTG

pith:2013:WDDF4DTGZMO5BH5KYWRWGXYALE

not attested not anchored not stored refs pending

Singular Density of States Measure for Subshift and Quasi-Periodic Schr\"odinger Operators

Artur Avila (CNRS, David Damanik (Rice University), IMPA), Zhenghe Zhang (Northwestern University)

arxiv:1304.0519 v2 · 2013-04-02 · math.SP · math-ph · math.DS · 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{WDDF4DTGZMO5BH5KYWRWGXYALE}

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	2026-05-18T01:50:50.204381Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b0c65e0e66cb1dd09faac5a3635f005925fe18addbb06e166fa65fd026a53e5d

Aliases

arxiv: 1304.0519 · arxiv_version: 1304.0519v2 · doi: 10.48550/arxiv.1304.0519 · pith_short_12: WDDF4DTGZMO5 · pith_short_16: WDDF4DTGZMO5BH5K · pith_short_8: WDDF4DTG

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/WDDF4DTGZMO5BH5KYWRWGXYALE \
  | 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: b0c65e0e66cb1dd09faac5a3635f005925fe18addbb06e166fa65fd026a53e5d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2f313df31aeabb336c93c84539991f06797f0c47ad5a28cd6d33c0f11473faae",
    "cross_cats_sorted": [
      "math-ph",
      "math.DS",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SP",
    "submitted_at": "2013-04-02T03:06:45Z",
    "title_canon_sha256": "b1ac8b6b12a1c31b9eafb35c29bdfa4641b67fcd7696fcff5c21cba6403f8e1a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1304.0519",
    "kind": "arxiv",
    "version": 2
  }
}