Pith Number

pith:BZYZ6QOF

pith:2018:BZYZ6QOFDNB6UDJIJZPM2UBT2R

not attested not anchored not stored refs pending

On property (T) for $\operatorname{Aut}(F_n)$ and $\operatorname{SL}_n(\mathbb{Z})$

Dawid Kielak, Marek Kaluba, Piotr W. Nowak

arxiv:1812.03456 v2 · 2018-12-09 · math.OA · 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{BZYZ6QOFDNB6UDJIJZPM2UBT2R}

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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.

Cited by

1 paper in Pith

Abelianizations of finite-index subgroups of the handlebody group

Receipt and verification

First computed	2026-07-05T02:08:15.930220Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0e719f41c51b43ea0d284e5ecd5033d44ac455eb113b1e9aef0bd52efc2c50be

Aliases

arxiv: 1812.03456 · arxiv_version: 1812.03456v2 · doi: 10.48550/arxiv.1812.03456 · pith_short_12: BZYZ6QOFDNB6 · pith_short_16: BZYZ6QOFDNB6UDJI · pith_short_8: BZYZ6QOF

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/BZYZ6QOFDNB6UDJIJZPM2UBT2R \
  | 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: 0e719f41c51b43ea0d284e5ecd5033d44ac455eb113b1e9aef0bd52efc2c50be

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "23d5457ffd26a9d581141c38731657709c7ab9948387cb56a225b1df051a2b96",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://creativecommons.org/licenses/by-sa/4.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2018-12-09T10:27:55Z",
    "title_canon_sha256": "75f36c77a52cb245e309e0f3ce9aba180eceef09ff11109f26f90b9317f65720"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1812.03456",
    "kind": "arxiv",
    "version": 2
  }
}