Pith Number

pith:QU4U4SXE

pith:2013:QU4U4SXE5AS3TQLK3FK2IG6DFZ

not attested not anchored not stored refs pending

Zero measure Cantor spectra for continuum one-dimensional quasicrystals

Christian Seifert, Daniel Lenz, Peter Stollmann

arxiv:1308.3431 v1 · 2013-08-15 · 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{QU4U4SXE5AS3TQLK3FK2IG6DFZ}

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	2026-05-18T01:11:55.508112Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

85394e4ae4e825b9c16ad955a41bc32e717e73c966963319df1b75360404d078

Aliases

arxiv: 1308.3431 · arxiv_version: 1308.3431v1 · doi: 10.48550/arxiv.1308.3431 · pith_short_12: QU4U4SXE5AS3 · pith_short_16: QU4U4SXE5AS3TQLK · pith_short_8: QU4U4SXE

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/QU4U4SXE5AS3TQLK3FK2IG6DFZ \
  | 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: 85394e4ae4e825b9c16ad955a41bc32e717e73c966963319df1b75360404d078

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5daff1a4e016528f2b3eb2a9736ac06d7b322a916f2b7e6d61c8f0c2df01295e",
    "cross_cats_sorted": [
      "math.MP",
      "math.SP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2013-08-15T15:18:37Z",
    "title_canon_sha256": "26b15e071a6bfc2602f84645f71cf716700ef5788fe335c972575bf46dfa7bfb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1308.3431",
    "kind": "arxiv",
    "version": 1
  }
}