Pith Number

pith:NKKARLLJ

pith:2012:NKKARLLJNC2NKZRWTGI2FL5ZE6

not attested not anchored not stored refs pending

Heights on Groups and Small Multiplicative Dependencies

Jeffrey D. Vaaler

arxiv:1211.5066 v1 · 2012-11-21 · math.NT · math.FA

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{NKKARLLJNC2NKZRWTGI2FL5ZE6}

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	2026-05-18T03:40:15.128555Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6a9408ad6968b4d566369991a2afb92792c91727b588e6287ecb9ec1c145ee28

Aliases

arxiv: 1211.5066 · arxiv_version: 1211.5066v1 · doi: 10.48550/arxiv.1211.5066 · pith_short_12: NKKARLLJNC2N · pith_short_16: NKKARLLJNC2NKZRW · pith_short_8: NKKARLLJ

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/NKKARLLJNC2NKZRWTGI2FL5ZE6 \
  | 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: 6a9408ad6968b4d566369991a2afb92792c91727b588e6287ecb9ec1c145ee28

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7a6cd073778b086b95de7685e8e52e6202f78837416cf879587d51fe93fb04f0",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2012-11-21T15:49:13Z",
    "title_canon_sha256": "e2f809904e5306808585ee2a721a7382c9acc1ab5a3ef4cd090d0dd3a5bac74a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1211.5066",
    "kind": "arxiv",
    "version": 1
  }
}