Pith Number

pith:T4VEBAMA

pith:2009:T4VEBAMAAT3LUJHAJ46EO7QQMY

not attested not anchored not stored refs pending

Groups possessing extensive hierarchical decompositions

I. J. Leary, P. H. Kropholler, T. Januszkiewicz

arxiv:0908.3669 v1 · 2009-08-25 · math.GR · math.GT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{T4VEBAMAAT3LUJHAJ46EO7QQMY}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more

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	2026-05-18T02:58:02.850973Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9f2a40818004f6ba24e04f3c477e10663dbe1626c06342142dc82cd0fe243840

Aliases

arxiv: 0908.3669 · arxiv_version: 0908.3669v1 · doi: 10.48550/arxiv.0908.3669 · pith_short_12: T4VEBAMAAT3L · pith_short_16: T4VEBAMAAT3LUJHA · pith_short_8: T4VEBAMA

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/T4VEBAMAAT3LUJHAJ46EO7QQMY \
  | 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: 9f2a40818004f6ba24e04f3c477e10663dbe1626c06342142dc82cd0fe243840

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0db2eb4a0e1cef263729f1beb95ac7e0cc170d1838994500516e1e2466cb53eb",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2009-08-25T19:44:09Z",
    "title_canon_sha256": "32b1a8c570ee0ff377c4854608b147e289ae40fd0ce20e32aff14270c8ba7a3d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0908.3669",
    "kind": "arxiv",
    "version": 1
  }
}