Pith Number

pith:CNNYF5KY

pith:2015:CNNYF5KYQLOIW25NNSN5KPVG2G

not attested not anchored not stored refs pending

Decomposability of Finitely Generated Torsion-free Nilpotent Groups

Charles F. Miller III, Gilbert Baumslag, Gretchen Ostheimer

arxiv:1510.05632 v2 · 2015-10-19 · 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{CNNYF5KYQLOIW25NNSN5KPVG2G}

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	2026-05-18T01:24:10.456639Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

135b82f55882dc8b6bad6c9bd53ea6d18cffdda0f865c7af3c19f270abab5886

Aliases

arxiv: 1510.05632 · arxiv_version: 1510.05632v2 · doi: 10.48550/arxiv.1510.05632 · pith_short_12: CNNYF5KYQLOI · pith_short_16: CNNYF5KYQLOIW25N · pith_short_8: CNNYF5KY

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/CNNYF5KYQLOIW25NNSN5KPVG2G \
  | 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: 135b82f55882dc8b6bad6c9bd53ea6d18cffdda0f865c7af3c19f270abab5886

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ed51cbd7940c686daf98c80c22d6a7cbe1b1bb214a5776b6c622dcf10c612c5b",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2015-10-19T19:39:09Z",
    "title_canon_sha256": "a402218b0d9dd3e75fde2d4b630bf28413b27d473bfe45c02cdf894ba4fbda50"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1510.05632",
    "kind": "arxiv",
    "version": 2
  }
}