Pith Number

pith:MPWF3XAM

pith:2011:MPWF3XAMXMZFS7EBW4KUD7ECPQ

not attested not anchored not stored refs pending

Centralizers in $\widetilde A_2$ groups

Guyan Robertson

arxiv:1101.2531 v1 · 2011-01-13 · math.GR · math.MG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{MPWF3XAMXMZFS7EBW4KUD7ECPQ}

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	2026-05-18T03:32:57.452144Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

63ec5ddc0cbb32597c81b71541fc827c17dbb6b9a181a418d16dd33f8aaeac0a

Aliases

arxiv: 1101.2531 · arxiv_version: 1101.2531v1 · doi: 10.48550/arxiv.1101.2531 · pith_short_12: MPWF3XAMXMZF · pith_short_16: MPWF3XAMXMZFS7EB · pith_short_8: MPWF3XAM

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/MPWF3XAMXMZFS7EBW4KUD7ECPQ \
  | 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: 63ec5ddc0cbb32597c81b71541fc827c17dbb6b9a181a418d16dd33f8aaeac0a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c4a1ef6ea67794c1e16e09619f695047c92d4993d73a6e1061df6a25a4f775b4",
    "cross_cats_sorted": [
      "math.MG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2011-01-13T10:40:11Z",
    "title_canon_sha256": "edf1956b17a28d0fab8046007f7b27c15a6a72a0c0f4a6c718aa2389a58b09d6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1101.2531",
    "kind": "arxiv",
    "version": 1
  }
}