Pith Number

pith:T4AXBA2L

pith:2009:T4AXBA2LP4P3LNE7TGTW5QDMNS

not attested not anchored not stored refs pending

Lifts of projective congruence groups

Helena Verrill, Ian Kiming, Matthias Schuett

arxiv:0905.4798 v4 · 2009-05-29 · math.NT · math.AG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{T4AXBA2LP4P3LNE7TGTW5QDMNS}

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	2026-05-18T02:58:03.142062Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9f0170834b7f1fb5b49f99a76ec06c6ca67f1f171a6246930876fc9a9a1d3cae

Aliases

arxiv: 0905.4798 · arxiv_version: 0905.4798v4 · doi: 10.48550/arxiv.0905.4798 · pith_short_12: T4AXBA2LP4P3 · pith_short_16: T4AXBA2LP4P3LNE7 · pith_short_8: T4AXBA2L

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/T4AXBA2LP4P3LNE7TGTW5QDMNS \
  | 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: 9f0170834b7f1fb5b49f99a76ec06c6ca67f1f171a6246930876fc9a9a1d3cae

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d5f9de463cc68df67980cf2b94a7a1434525e46e9236f306d8988d83ca788197",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2009-05-29T07:33:53Z",
    "title_canon_sha256": "8e039bbef8df585e5d963a4a6eab0f2cd6a586cc4042c84801df3193450b9e4e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0905.4798",
    "kind": "arxiv",
    "version": 4
  }
}