Pith Number

pith:TAKRWIEM

pith:2015:TAKRWIEMM2QMC6NZWAFF374CYU

not attested not anchored not stored refs pending

Weak Width of Subgroups

Rita Gitik

arxiv:1512.09185 v1 · 2015-12-31 · 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{TAKRWIEMM2QMC6NZWAFF374CYU}

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	2026-05-18T01:23:33.082743Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

98151b208c66a0c179b9b00a5dff82c53a40a0d49320988db68730052ecad46b

Aliases

arxiv: 1512.09185 · arxiv_version: 1512.09185v1 · doi: 10.48550/arxiv.1512.09185 · pith_short_12: TAKRWIEMM2QM · pith_short_16: TAKRWIEMM2QMC6NZ · pith_short_8: TAKRWIEM

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/TAKRWIEMM2QMC6NZWAFF374CYU \
  | 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: 98151b208c66a0c179b9b00a5dff82c53a40a0d49320988db68730052ecad46b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "92c00f648ac2bfa028e80b9f09e1d09431b7da303daeff7d95a9ba24ce1e858e",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2015-12-31T00:00:46Z",
    "title_canon_sha256": "7ad23f46b9604e016007f3f90f3c5c4b77ca2a283af42990c182b503de22c42f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1512.09185",
    "kind": "arxiv",
    "version": 1
  }
}