Pith Number

pith:NCPIOGPA

pith:2023:NCPIOGPALFG47YZJ7S4JOQTTLE

not attested not anchored not stored refs pending

Generalizations of the Erd\H{o}s-Kac Theorem and the Prime Number Theorem

Biao Wang, Pan Yan, Shaoyun Yi, Zhining Wei

arxiv:2303.05803 v1 · 2023-03-10 · math.NT · 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{NCPIOGPALFG47YZJ7S4JOQTTLE}

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	2026-06-09T01:05:02.570562Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

689e8719e0594dcfe329fcb897427359361af3ab1ccd727122a065b37aa3d2f8

Aliases

arxiv: 2303.05803 · arxiv_version: 2303.05803v1 · doi: 10.48550/arxiv.2303.05803 · pith_short_12: NCPIOGPALFG4 · pith_short_16: NCPIOGPALFG47YZJ · pith_short_8: NCPIOGPA

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/NCPIOGPALFG47YZJ7S4JOQTTLE \
  | 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: 689e8719e0594dcfe329fcb897427359361af3ab1ccd727122a065b37aa3d2f8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "64401e6799d33732a8a8ce4db1844db6e0df9eb0ef8bf59f7f38bdb15452f37c",
    "cross_cats_sorted": [
      "math.DS"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2023-03-10T09:19:14Z",
    "title_canon_sha256": "d7beb894789b64b894a63db324dee735131471d8fb0a1b8dfa5f738a627e8a7d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2303.05803",
    "kind": "arxiv",
    "version": 1
  }
}