Pith Number

pith:D4MVO3OW

pith:2011:D4MVO3OWECPB2IZYOXBPZYDI4G

not attested not anchored not stored refs pending

The distribution of totients

Kevin Ford

arxiv:1104.3264 v2 · 2011-04-16 · 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{D4MVO3OWECPB2IZYOXBPZYDI4G}

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	2026-05-18T03:18:32.124953Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1f19576dd6209e1d233875c2fce068e196b7d8979fc01d96df4a76dab58de96f

Aliases

arxiv: 1104.3264 · arxiv_version: 1104.3264v2 · doi: 10.48550/arxiv.1104.3264 · pith_short_12: D4MVO3OWECPB · pith_short_16: D4MVO3OWECPB2IZY · pith_short_8: D4MVO3OW

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/D4MVO3OWECPB2IZYOXBPZYDI4G \
  | 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: 1f19576dd6209e1d233875c2fce068e196b7d8979fc01d96df4a76dab58de96f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ee49a3c81f5fe53c3f0fd0e69e3a8e64f55af771e8c384a870de0eabc6d3cd9c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2011-04-16T21:43:56Z",
    "title_canon_sha256": "892679123968442533a97a1a81d0f6ba8d94d4ca3966d537f79b772fea226a51"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1104.3264",
    "kind": "arxiv",
    "version": 2
  }
}