Pith Number

pith:FG4VTSMA

pith:2009:FG4VTSMALK7KBGUQWTNOS2BASY

not attested not anchored not stored refs pending

Multiple recurrence and convergence for Hardy sequences of polynomial growth

Nikos Frantzikinakis

arxiv:0903.0042 v6 · 2009-02-28 · math.DS · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{FG4VTSMALK7KBGUQWTNOS2BASY}

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	2026-05-18T03:38:03.063827Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

29b959c9805abea09a90b4dae968209624b0ee4513097c2585df1346a7aebedc

Aliases

arxiv: 0903.0042 · arxiv_version: 0903.0042v6 · doi: 10.48550/arxiv.0903.0042 · pith_short_12: FG4VTSMALK7K · pith_short_16: FG4VTSMALK7KBGUQ · pith_short_8: FG4VTSMA

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/FG4VTSMALK7KBGUQWTNOS2BASY \
  | 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: 29b959c9805abea09a90b4dae968209624b0ee4513097c2585df1346a7aebedc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0e34383f3bdd8c6f92ca4df098defa3f2cc44e88b6beffe6c034af055846649d",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2009-02-28T13:48:16Z",
    "title_canon_sha256": "0b8d1d76a97ebe980717741f1dceb0c9575ef70b132d52a313a4592075095f38"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0903.0042",
    "kind": "arxiv",
    "version": 6
  }
}