Pith Number

pith:UUN4YSNR

pith:2019:UUN4YSNRMB5VDV2QAIUQLVVLDZ

not attested not anchored not stored refs pending

M\"{o}bius disjointness for skew products on a circle and a nilmanifold

Jianya Liu, Ke Wang, Wen Huang

arxiv:1907.01735 v1 · 2019-07-03 · math.NT · math.DS

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{UUN4YSNRMB5VDV2QAIUQLVVLDZ}

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	2026-05-17T23:41:35.270685Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a51bcc49b1607b51d750022905d6ab1e77f37d28f50f02fd5f2d3aeae51bc851

Aliases

arxiv: 1907.01735 · arxiv_version: 1907.01735v1 · doi: 10.48550/arxiv.1907.01735 · pith_short_12: UUN4YSNRMB5V · pith_short_16: UUN4YSNRMB5VDV2Q · pith_short_8: UUN4YSNR

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/UUN4YSNRMB5VDV2QAIUQLVVLDZ \
  | 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: a51bcc49b1607b51d750022905d6ab1e77f37d28f50f02fd5f2d3aeae51bc851

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "20eb2dced6e5034d1ca42a666e7f1f8415fe973b38233cec0654c4efa846d43f",
    "cross_cats_sorted": [
      "math.DS"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2019-07-03T04:43:27Z",
    "title_canon_sha256": "53f0f86ec5b4684cbc0a4e6ba663ddd650583faadc4249552d49d7281a36d947"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1907.01735",
    "kind": "arxiv",
    "version": 1
  }
}