Pith Number

pith:O5MMS3UF

pith:2012:O5MMS3UFGUIX6ZQGLCENTTNWB6

not attested not anchored not stored refs pending

On fields of definition of arithmetic Kleinian reflection groups II

Benjamin Linowitz, Mikhail Belolipetsky

arxiv:1211.4443 v2 · 2012-11-19 · math.GT · 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{O5MMS3UFGUIX6ZQGLCENTTNWB6}

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	2026-05-18T03:30:25.369846Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7758c96e8535117f66065888d9cdb60fa354a3b5ad3d53397e385a88a8126e51

Aliases

arxiv: 1211.4443 · arxiv_version: 1211.4443v2 · doi: 10.48550/arxiv.1211.4443 · pith_short_12: O5MMS3UFGUIX · pith_short_16: O5MMS3UFGUIX6ZQG · pith_short_8: O5MMS3UF

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/O5MMS3UFGUIX6ZQGLCENTTNWB6 \
  | 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: 7758c96e8535117f66065888d9cdb60fa354a3b5ad3d53397e385a88a8126e51

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f9776259659af39bfcbfd1054222fae460c5a1b7669c67656de258c814ed2efe",
    "cross_cats_sorted": [
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2012-11-19T14:44:02Z",
    "title_canon_sha256": "f3d863f8913c4b991d95848b530be3f56c66b952587e1d819b7ea75c07fe36b1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1211.4443",
    "kind": "arxiv",
    "version": 2
  }
}