Pith Number

pith:TQKJX5MT

pith:2015:TQKJX5MTR2AGWVJYRA4SIJC7HC

not attested not anchored not stored refs pending

On irreducibility and disjointness of Koopman and quasi-regular representations of weakly branch groups

Artem Dudko, Rostislav Grigorchuk

arxiv:1508.05452 v3 · 2015-08-22 · 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{TQKJX5MTR2AGWVJYRA4SIJC7HC}

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	2026-05-18T00:27:57.797947Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9c149bf5938e806b5538883924245f388ee7ef62871f26051ce9347f66c10284

Aliases

arxiv: 1508.05452 · arxiv_version: 1508.05452v3 · doi: 10.48550/arxiv.1508.05452 · pith_short_12: TQKJX5MTR2AG · pith_short_16: TQKJX5MTR2AGWVJY · pith_short_8: TQKJX5MT

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/TQKJX5MTR2AGWVJYRA4SIJC7HC \
  | 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: 9c149bf5938e806b5538883924245f388ee7ef62871f26051ce9347f66c10284

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f522a238438c9ebfe04f283d0fbbb5a296c9692f2143c8eed739af4a86edefc0",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.RT",
    "submitted_at": "2015-08-22T01:49:41Z",
    "title_canon_sha256": "57b33b1d1c02b85512b12ca03b1bbd712b191cf01a30f2cdb235538397177588"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1508.05452",
    "kind": "arxiv",
    "version": 3
  }
}