Pith Number

pith:PTER5F74

pith:2012:PTER5F74KNTCN2547XQ7TG7M4C

not attested not anchored not stored refs pending

Representation growth and representation zeta functions of groups

Benjamin Klopsch

arxiv:1209.2896 v1 · 2012-09-13 · math.GR · math.NT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PTER5F74KNTCN2547XQ7TG7M4C}

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	2026-05-18T03:45:40.655386Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7cc91e97fc536626ebbcfde1f99bece083f333ab5608da4c229e55595106ed73

Aliases

arxiv: 1209.2896 · arxiv_version: 1209.2896v1 · doi: 10.48550/arxiv.1209.2896 · pith_short_12: PTER5F74KNTC · pith_short_16: PTER5F74KNTCN254 · pith_short_8: PTER5F74

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/PTER5F74KNTCN2547XQ7TG7M4C \
  | 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: 7cc91e97fc536626ebbcfde1f99bece083f333ab5608da4c229e55595106ed73

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4964b5a9efd418ef8286768f9c4b8bd03789ee45b374733ca807af51abf50332",
    "cross_cats_sorted": [
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2012-09-13T14:04:41Z",
    "title_canon_sha256": "9cabd779100137eca3d39c5e3dd99a5e39f3f8661f8f1e2344553efef751a7d5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1209.2896",
    "kind": "arxiv",
    "version": 1
  }
}