Pith Number

pith:P7XGAJ2B

pith:2008:P7XGAJ2BM3OB2MUHPUCW2SVHZT

not attested not anchored not stored refs pending

Equidistribution of sparse sequences on nilmanifolds

Nikos Frantzikinakis

arxiv:0810.4661 v5 · 2008-10-27 · 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{P7XGAJ2BM3OB2MUHPUCW2SVHZT}

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	2026-05-18T04:01:39.860175Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7fee60274166dc1d32877d056d4aa7cce0a9bb24bd6fc9c5bfb38417680829c3

Aliases

arxiv: 0810.4661 · arxiv_version: 0810.4661v5 · doi: 10.48550/arxiv.0810.4661 · pith_short_12: P7XGAJ2BM3OB · pith_short_16: P7XGAJ2BM3OB2MUH · pith_short_8: P7XGAJ2B

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/P7XGAJ2BM3OB2MUHPUCW2SVHZT \
  | 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: 7fee60274166dc1d32877d056d4aa7cce0a9bb24bd6fc9c5bfb38417680829c3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fb47b283e5fb6833b1358b694eefbd6b640fb2089cd715ee8f560b9ea85e369a",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2008-10-27T02:31:31Z",
    "title_canon_sha256": "101bfad59b308229ee97ea280cca9b7df20aea52bfe519347c26f97b6af1e5cd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0810.4661",
    "kind": "arxiv",
    "version": 5
  }
}