Pith Number

pith:PQZQPFYR

pith:2012:PQZQPFYRNPHWLY2GAVN5EGIUIB

not attested not anchored not stored refs pending

On the Dimension of Cohomology of Bianchi Groups

Mehmet Haluk Sengun, Seyfi Turkelli

arxiv:1204.0470 v4 · 2012-04-02 · math.NT · math.GN · math.GR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PQZQPFYRNPHWLY2GAVN5EGIUIB}

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	2026-05-18T03:09:22.937392Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7c330797116bcf65e346055bd2191440455b95fa64cc75b05c87300e69924a74

Aliases

arxiv: 1204.0470 · arxiv_version: 1204.0470v4 · doi: 10.48550/arxiv.1204.0470 · pith_short_12: PQZQPFYRNPHW · pith_short_16: PQZQPFYRNPHWLY2G · pith_short_8: PQZQPFYR

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/PQZQPFYRNPHWLY2GAVN5EGIUIB \
  | 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: 7c330797116bcf65e346055bd2191440455b95fa64cc75b05c87300e69924a74

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9a1cec1d0a4451cdf17b71015f82b8a0a7f9b3ce6db97e12d2e3d2350e44765e",
    "cross_cats_sorted": [
      "math.GN",
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2012-04-02T17:10:30Z",
    "title_canon_sha256": "2706509df5f973c0b4c591664e9df4c2270ee7a215f678f97bc9f8540fe9a603"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1204.0470",
    "kind": "arxiv",
    "version": 4
  }
}