Pith Number

pith:HOUJSKIZ

pith:2019:HOUJSKIZM3J5XPGDWY27O6MAHF

not attested not anchored not stored refs pending

A generalization on the average ratio of the smallest and largest prime divisor of $n$

Biao Wang

arxiv:1907.09129 v1 · 2019-07-15 · 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{HOUJSKIZM3J5XPGDWY27O6MAHF}

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	2026-05-17T23:40:00.025771Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3ba899291966d3dbbcc3b635f77980397b007a0300a144c0e4d8216af2aa9714

Aliases

arxiv: 1907.09129 · arxiv_version: 1907.09129v1 · doi: 10.48550/arxiv.1907.09129 · pith_short_12: HOUJSKIZM3J5 · pith_short_16: HOUJSKIZM3J5XPGD · pith_short_8: HOUJSKIZ

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/HOUJSKIZM3J5XPGDWY27O6MAHF \
  | 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: 3ba899291966d3dbbcc3b635f77980397b007a0300a144c0e4d8216af2aa9714

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e8ff7156b5f0520d90dfa33174132523a2697f58e7d7ff268de2166b1a7ea83b",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2019-07-15T21:01:19Z",
    "title_canon_sha256": "da7f20d99a89d0bf76cdb7d37d5adad72430fee67da9bcd9a3388c867a0f05ba"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1907.09129",
    "kind": "arxiv",
    "version": 1
  }
}