Pith Number

pith:TKMFKPAV

pith:2013:TKMFKPAVE5FNONUUWEKJMZVWYD

not attested not anchored not stored refs pending

Densities, submeasures and partitions of groups

Igor Protasov, Sergiy Slobodianiuk, Taras Banakh

arxiv:1303.4612 v4 · 2013-03-19 · math.GR · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{TKMFKPAVE5FNONUUWEKJMZVWYD}

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	2026-05-18T02:32:14.498148Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9a98553c15274ad73694b1149666b6c0f50e24dc4194d384037d83187311dbf9

Aliases

arxiv: 1303.4612 · arxiv_version: 1303.4612v4 · doi: 10.48550/arxiv.1303.4612 · pith_short_12: TKMFKPAVE5FN · pith_short_16: TKMFKPAVE5FNONUU · pith_short_8: TKMFKPAV

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/TKMFKPAVE5FNONUUWEKJMZVWYD \
  | 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: 9a98553c15274ad73694b1149666b6c0f50e24dc4194d384037d83187311dbf9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "de7736ff47684070507a56ca497cfd517d4cc63f5730a13afa24dee9fd0d4845",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2013-03-19T14:20:23Z",
    "title_canon_sha256": "8f114ba7ba583669b73f7ad6b0d18dcd5049bbc73c9fbb874bab4994a955fb82"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1303.4612",
    "kind": "arxiv",
    "version": 4
  }
}