Pith Number

pith:6WM4MGD3

pith:2015:6WM4MGD3KCRXI6DCJTCQWFEMIB

not attested not anchored not stored refs pending

Virtually torsion-free covers of minimax groups

Karl Lorensen, Peter Kropholler

arxiv:1510.07583 v3 · 2015-10-26 · 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{6WM4MGD3KCRXI6DCJTCQWFEMIB}

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	2026-05-18T00:03:37.588750Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f599c6187b50a37478624cc50b148c407c3cfde9f5f4916060f5e0f9fe06216d

Aliases

arxiv: 1510.07583 · arxiv_version: 1510.07583v3 · doi: 10.48550/arxiv.1510.07583 · pith_short_12: 6WM4MGD3KCRX · pith_short_16: 6WM4MGD3KCRXI6DC · pith_short_8: 6WM4MGD3

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/6WM4MGD3KCRXI6DCJTCQWFEMIB \
  | 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: f599c6187b50a37478624cc50b148c407c3cfde9f5f4916060f5e0f9fe06216d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "873b4e9e9845b2aa5d6c96d889923a4cf83937a7e0f17b25b987641d6ed562b6",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2015-10-26T18:24:45Z",
    "title_canon_sha256": "254e837f508302806aa8d42817d2132627e3240743bca6e1f71922252155b00b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1510.07583",
    "kind": "arxiv",
    "version": 3
  }
}