Pith Number

pith:56YVGTEQ

pith:2009:56YVGTEQ4W2GTD2MNIQA7ZNKN7

not attested not anchored not stored refs pending

Semisimple actions of mapping class groups on CAT(0) spaces

Martin R Bridson

arxiv:0908.0685 v1 · 2009-08-05 · math.GT · 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{56YVGTEQ4W2GTD2MNIQA7ZNKN7}

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.

Cited by

1 paper in Pith

Abelianizations of finite-index subgroups of the handlebody group

Receipt and verification

First computed	2026-07-04T15:47:28.112648Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

efb1534c90e5b4698f4c6a200fe5aa6fedbac425c492978d0a8a61050e34b6d3

Aliases

arxiv: 0908.0685 · arxiv_version: 0908.0685v1 · doi: 10.48550/arxiv.0908.0685 · pith_short_12: 56YVGTEQ4W2G · pith_short_16: 56YVGTEQ4W2GTD2M · pith_short_8: 56YVGTEQ

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/56YVGTEQ4W2GTD2MNIQA7ZNKN7 \
  | 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: efb1534c90e5b4698f4c6a200fe5aa6fedbac425c492978d0a8a61050e34b6d3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "36dfa79ecd329d3f67bffe4e151978899950eabf7f1e3959e6ac90041eb12bc8",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2009-08-05T15:47:00Z",
    "title_canon_sha256": "14a3a1818c2ba749609e033e07584bef4fe0d2559b70d2d83f1dc01c96146c1a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0908.0685",
    "kind": "arxiv",
    "version": 1
  }
}