Pith Number

pith:SPSVQQTD

pith:2009:SPSVQQTDO7HAJTCAU527NARQIX

not attested not anchored not stored refs pending

The transfer operator for the Hecke triangle groups

Dieter Mayer, Fredrik Str\"omberg, Tobias M\"uhlenbruch

arxiv:0912.2236 v2 · 2009-12-11 · math.NT · 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{SPSVQQTDO7HAJTCAU527NARQIX}

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	2026-05-18T03:44:03.000035Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

93e558426377ce04cc40a775f6823045e42034e0f741169abe2f4420e8560b15

Aliases

arxiv: 0912.2236 · arxiv_version: 0912.2236v2 · doi: 10.48550/arxiv.0912.2236 · pith_short_12: SPSVQQTDO7HA · pith_short_16: SPSVQQTDO7HAJTCA · pith_short_8: SPSVQQTD

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/SPSVQQTDO7HAJTCAU527NARQIX \
  | 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: 93e558426377ce04cc40a775f6823045e42034e0f741169abe2f4420e8560b15

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9afcd8bd5b3bb708b8212e02e70d946702687facc3a07f2fe15d2dce03f62236",
    "cross_cats_sorted": [
      "math.DS"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2009-12-11T14:16:46Z",
    "title_canon_sha256": "d39300d30b3e22a2a2fa1bca12ac95f6e359a3779499946ec068a36b70bf3083"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0912.2236",
    "kind": "arxiv",
    "version": 2
  }
}