Pith Number

pith:QAGYHB7E

pith:2010:QAGYHB7EQNPSVQC6C6PIISF3ZA

not attested not anchored not stored refs pending

Ascending HNN extensions of polycyclic groups have the same cohomology as their profinite completions

Karl Lorensen

arxiv:1009.2645 v5 · 2010-09-14 · 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{QAGYHB7EQNPSVQC6C6PIISF3ZA}

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	2026-05-18T04:37:10.040254Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

800d8387e4835f2ac05e179e8448bbc83f765c5f04577cb547bfb8d4dad22794

Aliases

arxiv: 1009.2645 · arxiv_version: 1009.2645v5 · doi: 10.48550/arxiv.1009.2645 · pith_short_12: QAGYHB7EQNPS · pith_short_16: QAGYHB7EQNPSVQC6 · pith_short_8: QAGYHB7E

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/QAGYHB7EQNPSVQC6C6PIISF3ZA \
  | 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: 800d8387e4835f2ac05e179e8448bbc83f765c5f04577cb547bfb8d4dad22794

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "70f7f470b57d6b0b2a1e826fae7d8ef04652fb39260f5239560900f07c12c301",
    "cross_cats_sorted": [
      "math.KT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2010-09-14T13:05:24Z",
    "title_canon_sha256": "a3d1b4a4bb4244be28d1799ef2123f7368cd410405e45b1798b8f8572ba9f2ab"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1009.2645",
    "kind": "arxiv",
    "version": 5
  }
}