Pith Number

pith:WWUIIBLK

pith:2019:WWUIIBLK3VL7DMY4AAJGEGTV7D

not attested not anchored not stored refs pending

Centers of subgroups of big mapping class groups and the Tits alternative

Justin Lanier, Marissa Loving

arxiv:1904.10060 v1 · 2019-04-22 · 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{WWUIIBLK3VL7DMY4AAJGEGTV7D}

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	2026-05-17T23:47:55.183174Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b5a884056add57f1b31c0012621a75f8d0493f34667a35c2a4c68ca336e0bc86

Aliases

arxiv: 1904.10060 · arxiv_version: 1904.10060v1 · doi: 10.48550/arxiv.1904.10060 · pith_short_12: WWUIIBLK3VL7 · pith_short_16: WWUIIBLK3VL7DMY4 · pith_short_8: WWUIIBLK

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/WWUIIBLK3VL7DMY4AAJGEGTV7D \
  | 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: b5a884056add57f1b31c0012621a75f8d0493f34667a35c2a4c68ca336e0bc86

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4d2773186bfcec94677908adeb262e01aab87b8ea7ed6e584f406391b68ef908",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2019-04-22T20:43:03Z",
    "title_canon_sha256": "888518b463b2e3365a98d3068d2f6c5203002c61f0718d243d8a9f14a170de42"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1904.10060",
    "kind": "arxiv",
    "version": 1
  }
}