Pith Number

pith:KJZIAPCB

pith:2013:KJZIAPCBEC6BIZDY3X4FTGFBEI

not attested not anchored not stored refs pending

Smooth Sums over Smooth $k$-Free Numbers and Statistical Mechanics

Francesco Cellarosi

arxiv:1304.6610 v2 · 2013-04-24 · math.NT · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{KJZIAPCBEC6BIZDY3X4FTGFBEI}

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	2026-05-18T03:11:23.878892Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5272803c4120bc146478ddf85998a122217a368a7229ee73116ec9dabda3ec1a

Aliases

arxiv: 1304.6610 · arxiv_version: 1304.6610v2 · doi: 10.48550/arxiv.1304.6610 · pith_short_12: KJZIAPCBEC6B · pith_short_16: KJZIAPCBEC6BIZDY · pith_short_8: KJZIAPCB

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/KJZIAPCBEC6BIZDY3X4FTGFBEI \
  | 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: 5272803c4120bc146478ddf85998a122217a368a7229ee73116ec9dabda3ec1a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3d48b5199e2ec68ec6d92cb36bdb56f139483e0e5e3fc0160e5a81ec4bde51dd",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2013-04-24T14:50:25Z",
    "title_canon_sha256": "8e1cf3a1dfc00e38a8de7533c86670beebd8ab4b6bc72c995f6e2c1a61bc515b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1304.6610",
    "kind": "arxiv",
    "version": 2
  }
}