Pith Number

pith:VGES46CP

pith:2020:VGES46CPJG6I6GJXSARXUPJKJO

not attested not anchored not stored refs pending

On the set $\{\pi(kn):\ k=1,2,3,\ldots\}$

Lilu Zhao, Zhi-Wei Sun

arxiv:2004.01080 v1 · 2020-04-01 · math.NT · 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{VGES46CPJG6I6GJXSARXUPJKJO}

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	2026-07-05T00:52:24.091257Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a9892e784f49bc8f193790237a3d2a4b83698cf667d0eebd4c2f8f8eb0597707

Aliases

arxiv: 2004.01080 · arxiv_version: 2004.01080v1 · doi: 10.48550/arxiv.2004.01080 · pith_short_12: VGES46CPJG6I · pith_short_16: VGES46CPJG6I6GJX · pith_short_8: VGES46CP

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/VGES46CPJG6I6GJXSARXUPJKJO \
  | 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: a9892e784f49bc8f193790237a3d2a4b83698cf667d0eebd4c2f8f8eb0597707

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5526a0ed6b6c2c5c74bcd0779e7f228c18fad2e8ab419f3a82aa42e03b8a4f5a",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2020-04-01T16:21:30Z",
    "title_canon_sha256": "60e3376542446b2d2a26ff8db644a08ecd04c733bc37641100096cc564670f98"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2004.01080",
    "kind": "arxiv",
    "version": 1
  }
}