Pith Number

pith:CETRRGT5

pith:2013:CETRRGT57NXZMUTJG5GPZ6GSOW

not attested not anchored not stored refs pending

Abstract commensurators of right-angled Artin groups and mapping class groups

Christopher J. Leininger, Dan Margalit, Matt Clay

arxiv:1307.8387 v2 · 2013-07-31 · 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{CETRRGT57NXZMUTJG5GPZ6GSOW}

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	2026-05-18T02:56:11.561550Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1127189a7dfb6f965269374cfcf8d275ad977d1d723b0fe3bf9945f85409af6c

Aliases

arxiv: 1307.8387 · arxiv_version: 1307.8387v2 · doi: 10.48550/arxiv.1307.8387 · pith_short_12: CETRRGT57NXZ · pith_short_16: CETRRGT57NXZMUTJ · pith_short_8: CETRRGT5

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/CETRRGT57NXZMUTJG5GPZ6GSOW \
  | 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: 1127189a7dfb6f965269374cfcf8d275ad977d1d723b0fe3bf9945f85409af6c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "41d4e8b9389b90b65cf47c25e59ee1892e1947a193dd93a500e7225d1cc71d40",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2013-07-31T16:58:31Z",
    "title_canon_sha256": "9ef0bbf149ba0c7798c1f44876dba1c705fdcec2a92181865e155fd6e6693bbb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1307.8387",
    "kind": "arxiv",
    "version": 2
  }
}