Pith Number

pith:UFPGOZQ6

pith:2015:UFPGOZQ6RO6D5WK7LU56QMTDHZ

not attested not anchored not stored refs pending

Cardinal invariants distinguishing permutation groups

Heike Mildenberger, Taras Banakh

arxiv:1506.08969 v1 · 2015-06-30 · math.GR · math.GN · math.LO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{UFPGOZQ6RO6D5WK7LU56QMTDHZ}

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	2026-05-18T01:12:01.805391Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a15e67661e8bbc3ed95f5d3be832633e4e90092dce12977e2cf726620e1a76ad

Aliases

arxiv: 1506.08969 · arxiv_version: 1506.08969v1 · doi: 10.48550/arxiv.1506.08969 · pith_short_12: UFPGOZQ6RO6D · pith_short_16: UFPGOZQ6RO6D5WK7 · pith_short_8: UFPGOZQ6

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/UFPGOZQ6RO6D5WK7LU56QMTDHZ \
  | 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: a15e67661e8bbc3ed95f5d3be832633e4e90092dce12977e2cf726620e1a76ad

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d4b5650b27f7ed5c58f6e8dbd7065482fa20d3ad97d47a9ea731f5bf820668af",
    "cross_cats_sorted": [
      "math.GN",
      "math.LO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2015-06-30T07:35:49Z",
    "title_canon_sha256": "e81d1905f93f875b2ab10978cb60ecd7e04b844a3e37fc1c6b15484bb237d272"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1506.08969",
    "kind": "arxiv",
    "version": 1
  }
}