Pith Number

pith:5KPM6RJW

pith:2009:5KPM6RJWO3G4LZ65SCB6GHPGLF

not attested not anchored not stored refs pending

Fundamental domains for congruence subgroups of SL2 in positive characteristic

Leigh Cobbs, Lisa Carbone, Scott H. Murray

arxiv:0909.0062 v2 · 2009-09-01 · math.GR · math.RT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{5KPM6RJWO3G4LZ65SCB6GHPGLF}

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	2026-05-18T04:02:12.217341Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ea9ecf453676cdc5e7dd9083e31de6596a0e7c6c8f149bda076e230db016752d

Aliases

arxiv: 0909.0062 · arxiv_version: 0909.0062v2 · doi: 10.48550/arxiv.0909.0062 · pith_short_12: 5KPM6RJWO3G4 · pith_short_16: 5KPM6RJWO3G4LZ65 · pith_short_8: 5KPM6RJW

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/5KPM6RJWO3G4LZ65SCB6GHPGLF \
  | 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: ea9ecf453676cdc5e7dd9083e31de6596a0e7c6c8f149bda076e230db016752d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0dfdcb79c2c442f6699fb5d45641be1f6ba778aa09fa0fc1a5de27641225d82d",
    "cross_cats_sorted": [
      "math.RT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2009-09-01T01:03:25Z",
    "title_canon_sha256": "43b43ec476d7bcd8bfa3ab51ea3dc34057851e6ffdae857bf9f92d18617ab3c8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0909.0062",
    "kind": "arxiv",
    "version": 2
  }
}