Pith Number

pith:IRGUPD7Q

pith:2012:IRGUPD7QZZG27SE2COOJSZBPWS

not attested not anchored not stored refs pending

Actions of arithmetic groups on homology spheres and acyclic homology manifolds

F. Grunewald, K. Vogtmann, M. R. Bridson

arxiv:1207.3069 v2 · 2012-07-12 · math.GR · math.GT

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{IRGUPD7QZZG27SE2COOJSZBPWS}

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	2026-05-18T03:21:08.556540Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

444d478ff0ce4dafc89a139c99642fb4aa5e956d64f526214c971cbece1985b8

Aliases

arxiv: 1207.3069 · arxiv_version: 1207.3069v2 · doi: 10.48550/arxiv.1207.3069 · pith_short_12: IRGUPD7QZZG2 · pith_short_16: IRGUPD7QZZG27SE2 · pith_short_8: IRGUPD7Q

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/IRGUPD7QZZG27SE2COOJSZBPWS \
  | 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: 444d478ff0ce4dafc89a139c99642fb4aa5e956d64f526214c971cbece1985b8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d3ce5dac68c329bd255834d59c94024bdcc015535aa93567cada493950ba0619",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2012-07-12T19:29:39Z",
    "title_canon_sha256": "2f070941634fa3862b8f5f029f6f78e88c3a8db7aef1c0a8b00932aa0965358e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1207.3069",
    "kind": "arxiv",
    "version": 2
  }
}