Pith Number

pith:U2GZED6T

pith:2025:U2GZED6T7U6Q4YQJO3GOIGPW3M

not attested not anchored not stored refs pending

Transforming the Erd\H{o}s-Kac theorem

Kimihiro Noguchi

arxiv:2506.08503 v1 · 2025-06-10 · math.NT · math.PR · math.ST · stat.TH

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{U2GZED6T7U6Q4YQJO3GOIGPW3M}

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	2026-07-05T11:18:50.697742Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a68d920fd3fd3d0e620976cce419f6db396df15fe563bbb21a7fc906e5caf818

Aliases

arxiv: 2506.08503 · arxiv_version: 2506.08503v1 · doi: 10.48550/arxiv.2506.08503 · pith_short_12: U2GZED6T7U6Q · pith_short_16: U2GZED6T7U6Q4YQJ · pith_short_8: U2GZED6T

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/U2GZED6T7U6Q4YQJO3GOIGPW3M \
  | 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: a68d920fd3fd3d0e620976cce419f6db396df15fe563bbb21a7fc906e5caf818

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d55368c4dc555c14f6538b5cf24618a4686062f826f0c84d3695d87abaa492ef",
    "cross_cats_sorted": [
      "math.PR",
      "math.ST",
      "stat.TH"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2025-06-10T06:58:38Z",
    "title_canon_sha256": "94537a4292e123a8cdba9a4496977865c5aac6e72f1c1bee02476b9177265467"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2506.08503",
    "kind": "arxiv",
    "version": 1
  }
}