Pith Number

pith:U2NEHUIE

pith:2011:U2NEHUIEEIPPH2NB3GLUAWWSRT

not attested not anchored not stored refs pending

Values of the Euler phi-function not divisible by a given odd prime, and the distribution of Euler-Kronecker constants for cyclotomic fields

Florian Luca, Kevin Ford, Pieter Moree

arxiv:1108.3805 v3 · 2011-08-18 · 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{U2NEHUIEEIPPH2NB3GLUAWWSRT}

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	2026-05-18T02:55:57.705205Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a69a43d104221ef3e9a1d997405ad28cff4e5495e74fd3d0dd6a8a9f55ae731a

Aliases

arxiv: 1108.3805 · arxiv_version: 1108.3805v3 · doi: 10.48550/arxiv.1108.3805 · pith_short_12: U2NEHUIEEIPP · pith_short_16: U2NEHUIEEIPPH2NB · pith_short_8: U2NEHUIE

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/U2NEHUIEEIPPH2NB3GLUAWWSRT \
  | 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: a69a43d104221ef3e9a1d997405ad28cff4e5495e74fd3d0dd6a8a9f55ae731a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6e3909fff53244f6a3d42ca0697a695edf00aa123aa4c7d2e21e9ea3b8354789",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2011-08-18T18:23:57Z",
    "title_canon_sha256": "7943ffb271b3902b2959f81207e2469e84051a509a52c11d03c9ed8983ed587b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1108.3805",
    "kind": "arxiv",
    "version": 3
  }
}