Pith Number

pith:YZWDAPWW

pith:2017:YZWDAPWW6ENLQQ5KWRBWPPPNXH

not attested not anchored not stored refs pending

M\"obius Disjointness for Skew Products on the Heisenberg Nilmanifold

Matthew Litman, Zhiren Wang

arxiv:1707.07748 v1 · 2017-07-24 · math.DS · math.NT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{YZWDAPWW6ENLQQ5KWRBWPPPNXH}

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	2026-05-18T00:39:30.530032Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c66c303ed6f11ab843aab44367bdedb9f2bf07260dfdf1fed96047016be0314b

Aliases

arxiv: 1707.07748 · arxiv_version: 1707.07748v1 · doi: 10.48550/arxiv.1707.07748 · pith_short_12: YZWDAPWW6ENL · pith_short_16: YZWDAPWW6ENLQQ5K · pith_short_8: YZWDAPWW

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/YZWDAPWW6ENLQQ5KWRBWPPPNXH \
  | 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: c66c303ed6f11ab843aab44367bdedb9f2bf07260dfdf1fed96047016be0314b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3f946bae2798e0a6becfb3f25872dc56d2a2776bf9cccb4812273a35ee9aee09",
    "cross_cats_sorted": [
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2017-07-24T20:49:57Z",
    "title_canon_sha256": "22297a9ca444ee8ad897f4eeb88f6e576042fe6f539c6a32ad3f072660fd5174"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1707.07748",
    "kind": "arxiv",
    "version": 1
  }
}