Pith Number

pith:P7MPJVPF

pith:2013:P7MPJVPFTL7PRH3XDFTJEPQV7W

not attested not anchored not stored refs pending

Kronecker's limit formula, holomorphic modular functions and $q$-expansions on certain moonshine groups

Holger Then, Jay Jorgenson, Lejla Smajlovi\'c

arxiv:1309.0648 v2 · 2013-09-03 · math.NT · 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{P7MPJVPFTL7PRH3XDFTJEPQV7W}

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	2026-05-18T01:19:39.099920Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7fd8f4d5e59afef89f771966923e15fdaeba938cde1c883194a4e0a4299d0268

Aliases

arxiv: 1309.0648 · arxiv_version: 1309.0648v2 · doi: 10.48550/arxiv.1309.0648 · pith_short_12: P7MPJVPFTL7P · pith_short_16: P7MPJVPFTL7PRH3X · pith_short_8: P7MPJVPF

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/P7MPJVPFTL7PRH3XDFTJEPQV7W \
  | 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: 7fd8f4d5e59afef89f771966923e15fdaeba938cde1c883194a4e0a4299d0268

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1ae8435229895dc7e8d334cad5e4ffa18819a1f4ce69422345bfd29b4873fe20",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2013-09-03T11:44:52Z",
    "title_canon_sha256": "f70119f70e2f31cc17abb53a9d8d59fc59fc5466ed1dc07b44c5ec7fe0d37c2b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1309.0648",
    "kind": "arxiv",
    "version": 2
  }
}