Pith Number

pith:3I4262E2

pith:2007:3I4262E243DCAQVKRBCNUTWHV7

not attested not anchored not stored refs pending

A spectral sequence to compute L2-Betti numbers of groups and groupoids

Andreas Thom, Roman Sauer

arxiv:0707.0906 v3 · 2007-07-06 · math.DS · math.AT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{3I4262E243DCAQVKRBCNUTWHV7}

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	2026-05-18T02:58:12.592726Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

da39af689ae6c62042aa8844da4ec7afe4af2a1fec674bbb71b18df7acb009eb

Aliases

arxiv: 0707.0906 · arxiv_version: 0707.0906v3 · doi: 10.48550/arxiv.0707.0906 · pith_short_12: 3I4262E243DC · pith_short_16: 3I4262E243DCAQVK · pith_short_8: 3I4262E2

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/3I4262E243DCAQVKRBCNUTWHV7 \
  | 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: da39af689ae6c62042aa8844da4ec7afe4af2a1fec674bbb71b18df7acb009eb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9e2c4be77b282170542f7cfe15d5668caa27eb0d18a0ed5de68228340625c9e2",
    "cross_cats_sorted": [
      "math.AT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2007-07-06T19:46:13Z",
    "title_canon_sha256": "cbbca57f2059c3aa1571f7703154b82a9fdbb2aff11e51938e17f8c860bfbc1f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0707.0906",
    "kind": "arxiv",
    "version": 3
  }
}