Pith Number

pith:ALK6O7GM

pith:2011:ALK6O7GMFEL5TMDMH5NX4CHDL2

not attested not anchored not stored refs pending

Orthogonal polynomials on the unit circle with Verblunsky coefficients defined by the skew-shift

Helge Krueger

arxiv:1111.4019 v1 · 2011-11-17 · 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{ALK6O7GMFEL5TMDMH5NX4CHDL2}

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	2026-05-18T04:08:12.112252Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

02d5e77ccc2917d9b06c3f5b7e08e35ea799d0a2938b8011d1d212927ec4b44f

Aliases

arxiv: 1111.4019 · arxiv_version: 1111.4019v1 · doi: 10.48550/arxiv.1111.4019 · pith_short_12: ALK6O7GMFEL5 · pith_short_16: ALK6O7GMFEL5TMDM · pith_short_8: ALK6O7GM

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/ALK6O7GMFEL5TMDMH5NX4CHDL2 \
  | 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: 02d5e77ccc2917d9b06c3f5b7e08e35ea799d0a2938b8011d1d212927ec4b44f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "539d8b530637557b138124a463ef210357cdf239be0f12882da03b66e782eb26",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SP",
    "submitted_at": "2011-11-17T04:17:25Z",
    "title_canon_sha256": "c2bbb5c74f41833341ba7319586018bba3b2f3096c14e3f871861227f744512c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1111.4019",
    "kind": "arxiv",
    "version": 1
  }
}