Pith Number

pith:6XOGI7DP

pith:2010:6XOGI7DPGYZWTEFPTOPHAMDRYG

not attested not anchored not stored refs pending

The distribution functions of $\sigma(n)/n$ and $n/\phi(n)$, II

Andreas Weingartner

arxiv:1011.4262 v1 · 2010-11-18 · 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{6XOGI7DPGYZWTEFPTOPHAMDRYG}

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	2026-05-18T04:35:36.159422Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f5dc647c6f36336990af9b9e703071c19481a6c8b5e7a63001f49acb5d1ab54a

Aliases

arxiv: 1011.4262 · arxiv_version: 1011.4262v1 · doi: 10.48550/arxiv.1011.4262 · pith_short_12: 6XOGI7DPGYZW · pith_short_16: 6XOGI7DPGYZWTEFP · pith_short_8: 6XOGI7DP

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/6XOGI7DPGYZWTEFPTOPHAMDRYG \
  | 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: f5dc647c6f36336990af9b9e703071c19481a6c8b5e7a63001f49acb5d1ab54a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "09d3c295a46cb76060dfc83fd13d929099b4001537364371449c419c9f64b78f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2010-11-18T19:35:34Z",
    "title_canon_sha256": "b554e2e39d4e13ff1c1258c141f832cc15679acd926c99ff27d6f277dce1647e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1011.4262",
    "kind": "arxiv",
    "version": 1
  }
}