Pith Number

pith:ZVUIR7ON

pith:2000:ZVUIR7ONEF5Q4YW5FZ4PMFXP4A

not attested not anchored not stored refs pending

A generalization of Gordon's theorem and applications to quasiperiodic Schr\"odinger operators

David Damanik (Caltech), G\"unter Stolz (UAB)

arxiv:math-ph/0005015 v1 · 2000-05-12 · math-ph · math.MP · math.SP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ZVUIR7ONEF5Q4YW5FZ4PMFXP4A}

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	2026-05-18T02:30:16.597909Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cd6888fdcd217b0e62dd2e78f616efe00151ae93716959172fe63dbd5f4244af

Aliases

arxiv: math-ph/0005015 · arxiv_version: math-ph/0005015v1 · doi: 10.48550/arxiv.math-ph/0005015 · pith_short_12: ZVUIR7ONEF5Q · pith_short_16: ZVUIR7ONEF5Q4YW5 · pith_short_8: ZVUIR7ON

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/ZVUIR7ONEF5Q4YW5FZ4PMFXP4A \
  | 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: cd6888fdcd217b0e62dd2e78f616efe00151ae93716959172fe63dbd5f4244af

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cb5d1d259114ad37872b42e13142c6c16612fe789f9fc4dc87d06f7323cf7f00",
    "cross_cats_sorted": [
      "math.MP",
      "math.SP"
    ],
    "license": "",
    "primary_cat": "math-ph",
    "submitted_at": "2000-05-12T21:42:41Z",
    "title_canon_sha256": "e1dc88636269604b391c3e3f2b85190301ee6b9b1d97fd5e9ee4421166789bcf"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math-ph/0005015",
    "kind": "arxiv",
    "version": 1
  }
}