Pith Number

pith:XQ43SV6D

pith:2011:XQ43SV6DPUBV4LRH5N3FMP3WL2

not attested not anchored not stored refs pending

Zariski density and finite quotients of mapping class groups

Louis Funar

arxiv:1106.4165 v3 · 2011-06-21 · math.GR · math.GT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{XQ43SV6DPUBV4LRH5N3FMP3WL2}

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	2026-05-18T01:17:35.491711Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bc39b957c37d035e2e27eb76563f765e8d8bf24ef0fba5f16501a601e88f0fa3

Aliases

arxiv: 1106.4165 · arxiv_version: 1106.4165v3 · doi: 10.48550/arxiv.1106.4165 · pith_short_12: XQ43SV6DPUBV · pith_short_16: XQ43SV6DPUBV4LRH · pith_short_8: XQ43SV6D

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/XQ43SV6DPUBV4LRH5N3FMP3WL2 \
  | 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: bc39b957c37d035e2e27eb76563f765e8d8bf24ef0fba5f16501a601e88f0fa3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1bf1793fa2324b1e92cfed5b4d7a1e84c01dbc068914c1c674f102dee330bbdd",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2011-06-21T10:45:32Z",
    "title_canon_sha256": "13928b3e9342a49da36fccf8cbc322976ad65cd177dd645b17fbc35398416ee0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1106.4165",
    "kind": "arxiv",
    "version": 3
  }
}