Pith Number

pith:ZZONMGEK

pith:2011:ZZONMGEKANQOGQZPLEAO4HKM3M

not attested not anchored not stored refs pending

S-adic version of Minkowski's geometry of numbers and Mahler's compactness criterion

Dmitry Kleinbock, George Tomanov, Ronggang Shi

arxiv:1111.0163 v5 · 2011-11-01 · math.DS

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ZZONMGEKANQOGQZPLEAO4HKM3M}

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	2026-05-18T00:57:32.256951Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ce5cd6188a0360e3432f5900ee1d4cdb3444387132b126f305e77b197ced61ce

Aliases

arxiv: 1111.0163 · arxiv_version: 1111.0163v5 · doi: 10.48550/arxiv.1111.0163 · pith_short_12: ZZONMGEKANQO · pith_short_16: ZZONMGEKANQOGQZP · pith_short_8: ZZONMGEK

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/ZZONMGEKANQOGQZPLEAO4HKM3M \
  | 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: ce5cd6188a0360e3432f5900ee1d4cdb3444387132b126f305e77b197ced61ce

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bc59c95324c9044d1eacb39dbee26b6b5b07bc1a05e13674339b851d2e27ed05",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2011-11-01T10:34:27Z",
    "title_canon_sha256": "9a72cfab80aabf25ce2848bb2dd12be8347a4012173375e6eee03983270c181a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1111.0163",
    "kind": "arxiv",
    "version": 5
  }
}