Pith Number

pith:6TVI6ULK

pith:2012:6TVI6ULKEHZYN55CHM4ZRMLYY7

not attested not anchored not stored refs pending

Some free-by-cyclic groups

Daniel T. Wise, Graham A. Niblo, Ian J. Leary

arxiv:1210.6591 v1 · 2012-10-24 · 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{6TVI6ULKEHZYN55CHM4ZRMLYY7}

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	2026-05-18T03:42:24.440208Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f4ea8f516a21f386f7a23b3998b178c7ee283394ff5048483bb9200589616729

Aliases

arxiv: 1210.6591 · arxiv_version: 1210.6591v1 · doi: 10.48550/arxiv.1210.6591 · pith_short_12: 6TVI6ULKEHZY · pith_short_16: 6TVI6ULKEHZYN55C · pith_short_8: 6TVI6ULK

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/6TVI6ULKEHZYN55CHM4ZRMLYY7 \
  | 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: f4ea8f516a21f386f7a23b3998b178c7ee283394ff5048483bb9200589616729

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "dc915fc095d5432ac35f854f3bb886b1ae5815660f075d90aa730c9cd909736b",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2012-10-24T16:18:28Z",
    "title_canon_sha256": "054030f3dc384e7df36a381d7760e49569fe315a2ec685023634e249d8b16f40"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1210.6591",
    "kind": "arxiv",
    "version": 1
  }
}