Pith Number

pith:5ZR4ECDC

pith:2006:5ZR4ECDC4KHF5J7QQ7VVPVCSJG

not attested not anchored not stored refs pending

Finite solvable groups whose Quillen complex is Cohen-Macaulay

Francesco Matucci

arxiv:math/0606234 v2 · 2006-06-09 · 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{5ZR4ECDC4KHF5J7QQ7VVPVCSJG}

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	2026-05-18T04:21:51.913975Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ee63c20862e28e5ea7f087eb57d452499e01c23dbe88981c1e36a661fe2cfebf

Aliases

arxiv: math/0606234 · arxiv_version: math/0606234v2 · doi: 10.48550/arxiv.math/0606234 · pith_short_12: 5ZR4ECDC4KHF · pith_short_16: 5ZR4ECDC4KHF5J7Q · pith_short_8: 5ZR4ECDC

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/5ZR4ECDC4KHF5J7QQ7VVPVCSJG \
  | 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: ee63c20862e28e5ea7f087eb57d452499e01c23dbe88981c1e36a661fe2cfebf

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2e6eba205054c57ad39d11723ab8d3a9573c939fba2048e18193a2f767051eba",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2006-06-09T21:48:20Z",
    "title_canon_sha256": "e6457a38d94ea6026321843639c2aeba0efde97d34f7951be42257c33e191789"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0606234",
    "kind": "arxiv",
    "version": 2
  }
}