Pith Number

pith:L72XCNVK

pith:2013:L72XCNVK4B42WAATD7NQ2WH4BZ

not attested not anchored not stored refs pending

Totally disconnected groups from Baumslag-Solitar groups

George Willis, Murray Elder

arxiv:1301.4775 v3 · 2013-01-21 · 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{L72XCNVK4B42WAATD7NQ2WH4BZ}

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	2026-05-18T03:24:53.844511Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5ff57136aae079ab00131fdb0d58fc0e5f1006cd50920e8128931f5ae5fe221a

Aliases

arxiv: 1301.4775 · arxiv_version: 1301.4775v3 · doi: 10.48550/arxiv.1301.4775 · pith_short_12: L72XCNVK4B42 · pith_short_16: L72XCNVK4B42WAAT · pith_short_8: L72XCNVK

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/L72XCNVK4B42WAATD7NQ2WH4BZ \
  | 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: 5ff57136aae079ab00131fdb0d58fc0e5f1006cd50920e8128931f5ae5fe221a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "66b048c318dd2b6a0ad7a5d225cd030fd3531d741a0fd86059b97e7378d8d67d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2013-01-21T07:56:33Z",
    "title_canon_sha256": "84519e46a958a1d4f3a044c013f1466cac5e385fd39f6b339aa085848509cec4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1301.4775",
    "kind": "arxiv",
    "version": 3
  }
}