Pith Number

pith:B4K7QDBJ

pith:2012:B4K7QDBJ3BUE3BU2SGD6DSG6OV

not attested not anchored not stored refs pending

Arithmetic Aspects of Bianchi Groups

Mehmet Haluk Sengun

arxiv:1204.6697 v4 · 2012-04-30 · math.NT · math.GR · math.HO · math.KT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{B4K7QDBJ3BUE3BU2SGD6DSG6OV}

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	2026-05-18T03:21:54.148414Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0f15f80c29d8684d869a9187e1c8de756bf4c678a643a1a54dd462a954648123

Aliases

arxiv: 1204.6697 · arxiv_version: 1204.6697v4 · doi: 10.48550/arxiv.1204.6697 · pith_short_12: B4K7QDBJ3BUE · pith_short_16: B4K7QDBJ3BUE3BU2 · pith_short_8: B4K7QDBJ

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/B4K7QDBJ3BUE3BU2SGD6DSG6OV \
  | 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: 0f15f80c29d8684d869a9187e1c8de756bf4c678a643a1a54dd462a954648123

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4de54a12864d9e85ec06e803e22e8304e75b6d7fc1b90013a8e807228aedaee7",
    "cross_cats_sorted": [
      "math.GR",
      "math.HO",
      "math.KT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2012-04-30T16:43:14Z",
    "title_canon_sha256": "c0f0f184b93a2d872379f89c22512618bb395fe57cc8aa8424b7099bbcdefff8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1204.6697",
    "kind": "arxiv",
    "version": 4
  }
}