Pith Number

pith:CU7HBN3F

pith:2008:CU7HBN3FBQT7JMUE7PIZXC3IC5

not attested not anchored not stored refs pending

Groups with the same cohomology as their pro-$p$ completions

Karl Lorensen

arxiv:0809.3046 v3 · 2008-09-18 · math.GR · math.KT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{CU7HBN3FBQT7JMUE7PIZXC3IC5}

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	2026-05-18T04:40:56.268052Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

153e70b7650c27f4b284fbd19b8b68177dacf485c4c04cdec502deedae880e1c

Aliases

arxiv: 0809.3046 · arxiv_version: 0809.3046v3 · doi: 10.48550/arxiv.0809.3046 · pith_short_12: CU7HBN3FBQT7 · pith_short_16: CU7HBN3FBQT7JMUE · pith_short_8: CU7HBN3F

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/CU7HBN3FBQT7JMUE7PIZXC3IC5 \
  | 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: 153e70b7650c27f4b284fbd19b8b68177dacf485c4c04cdec502deedae880e1c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "33f8de89ad806df875ac303522f56293a857ec3fd9100d231488ecab11fbfd39",
    "cross_cats_sorted": [
      "math.KT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2008-09-18T01:17:17Z",
    "title_canon_sha256": "55c2823b5a330638cef77aea598cc8bc0859ad9f56b981527975032e080c0da5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0809.3046",
    "kind": "arxiv",
    "version": 3
  }
}