Pith Number

pith:QOMKV3FK

pith:2011:QOMKV3FK6YGOMTXAGFRVY3JLQJ

not attested not anchored not stored refs pending

Character sums for primitive root densities

H. W. Lenstra Jr, P. Moree, P. Stevenhagen

arxiv:1112.4816 v4 · 2011-12-20 · 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{QOMKV3FK6YGOMTXAGFRVY3JLQJ}

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	2026-05-17T23:53:36.381145Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8398aaecaaf60ce64ee031635c6d2b826ad7463dc6ee783accca427da15c15ba

Aliases

arxiv: 1112.4816 · arxiv_version: 1112.4816v4 · doi: 10.48550/arxiv.1112.4816 · pith_short_12: QOMKV3FK6YGO · pith_short_16: QOMKV3FK6YGOMTXA · pith_short_8: QOMKV3FK

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/QOMKV3FK6YGOMTXAGFRVY3JLQJ \
  | 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: 8398aaecaaf60ce64ee031635c6d2b826ad7463dc6ee783accca427da15c15ba

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "db50ac36ed98c4ea5c7437f7535651219b3eeecc97f237f9c9819d4e2569e2ea",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2011-12-20T20:07:21Z",
    "title_canon_sha256": "d179ff01c64d0b11cbe857844181d1c95ed6f98cdf9fa1c0ca0a7e50f11af8da"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1112.4816",
    "kind": "arxiv",
    "version": 4
  }
}