Pith Number

pith:Z4O7SJ76

pith:2010:Z4O7SJ76SVCHDXNLXC5ZF2MBWE

not attested not anchored not stored refs pending

Topological properties of spaces admitting free group actions

Craig R. Guilbault, Ross Geoghegan

arxiv:1005.2766 v2 · 2010-05-16 · math.GT · 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{Z4O7SJ76SVCHDXNLXC5ZF2MBWE}

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	2026-05-18T02:24:06.523985Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cf1df927fe954471ddabb8bb92e981b10523197659c921bab4c87d02a7be0b4e

Aliases

arxiv: 1005.2766 · arxiv_version: 1005.2766v2 · doi: 10.48550/arxiv.1005.2766 · pith_short_12: Z4O7SJ76SVCH · pith_short_16: Z4O7SJ76SVCHDXNL · pith_short_8: Z4O7SJ76

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/Z4O7SJ76SVCHDXNLXC5ZF2MBWE \
  | 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: cf1df927fe954471ddabb8bb92e981b10523197659c921bab4c87d02a7be0b4e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "463ce7c38c9746a5a69d4b2f39fad9d516c40f23a97aa93233f5c1d51278c371",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2010-05-16T18:38:53Z",
    "title_canon_sha256": "979100a0ed7d5ec1fb7156944cfe92e8cdb870f0333ee1aa248f7bf0c72dcd57"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1005.2766",
    "kind": "arxiv",
    "version": 2
  }
}