Pith Number

pith:7WNDKE23

pith:2013:7WNDKE237NYOPH5LTT7H6DWR2B

not attested not anchored not stored refs pending

Multi-invariant measures and subsets on nilmanifolds

Zhiren Wang

arxiv:1309.6223 v1 · 2013-09-24 · 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{7WNDKE237NYOPH5LTT7H6DWR2B}

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	2026-05-18T03:12:23.453809Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fd9a35135bfb70e79fab9cfe7f0ed1d05c01a5163a0772d0c45963b0f8331b30

Aliases

arxiv: 1309.6223 · arxiv_version: 1309.6223v1 · doi: 10.48550/arxiv.1309.6223 · pith_short_12: 7WNDKE237NYO · pith_short_16: 7WNDKE237NYOPH5L · pith_short_8: 7WNDKE23

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/7WNDKE237NYOPH5LTT7H6DWR2B \
  | 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: fd9a35135bfb70e79fab9cfe7f0ed1d05c01a5163a0772d0c45963b0f8331b30

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9e3974945f1e9dc40f43702f9aa71d176757f6a83b8c677b422a0f4e98fe85ab",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2013-09-24T15:48:03Z",
    "title_canon_sha256": "da1b86f824f3c07a6e09deb50ef5b4f1cba3398c875baf01c9952426ae1366a7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1309.6223",
    "kind": "arxiv",
    "version": 1
  }
}