Pith Number

pith:FXGW24VH

pith:2013:FXGW24VHBS5MZ2ZMPMOQCQ7BVB

not attested not anchored not stored refs pending

Ergodic Properties of $k$-Free Integers in Number Fields

Francesco Cellarosi, Ilya Vinogradov

arxiv:1304.0214 v4 · 2013-03-31 · 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{FXGW24VHBS5MZ2ZMPMOQCQ7BVB}

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	2026-05-18T03:11:23.937322Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2dcd6d72a70cbacceb2c7b1d0143e1a8521fae738970040a7b62534931b5151c

Aliases

arxiv: 1304.0214 · arxiv_version: 1304.0214v4 · doi: 10.48550/arxiv.1304.0214 · pith_short_12: FXGW24VHBS5M · pith_short_16: FXGW24VHBS5MZ2ZM · pith_short_8: FXGW24VH

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/FXGW24VHBS5MZ2ZMPMOQCQ7BVB \
  | 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: 2dcd6d72a70cbacceb2c7b1d0143e1a8521fae738970040a7b62534931b5151c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "994aa4f2183b1a87b7081603cc5000f08608663efdc14bc4f8907c078a1bd540",
    "cross_cats_sorted": [
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2013-03-31T15:02:24Z",
    "title_canon_sha256": "8b428d41495d18c0881c32aa91562f57998bed4d0d0d2cf1260043288a44d832"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1304.0214",
    "kind": "arxiv",
    "version": 4
  }
}