Pith Number

pith:FNYTTMON

pith:2016:FNYTTMONFGSUILR2CZUNE5UBYR

not attested not anchored not stored refs pending

Quotients of mapping class groups from $\text{Out}(F_n)$

Christopher J. Leininger, Khalid Bou-Rabee

arxiv:1608.03868 v3 · 2016-08-12 · math.GR · math.GN · 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{FNYTTMONFGSUILR2CZUNE5UBYR}

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	2026-05-18T00:19:59.438430Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2b7139b1cd29a5442e3a1668d27681c44fa76455c991d4aa37b663467a5bd95d

Aliases

arxiv: 1608.03868 · arxiv_version: 1608.03868v3 · doi: 10.48550/arxiv.1608.03868 · pith_short_12: FNYTTMONFGSU · pith_short_16: FNYTTMONFGSUILR2 · pith_short_8: FNYTTMON

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/FNYTTMONFGSUILR2CZUNE5UBYR \
  | 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: 2b7139b1cd29a5442e3a1668d27681c44fa76455c991d4aa37b663467a5bd95d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f5915509afc1b25a35d0730220120b1759a725d29087a60e9411b4f31f0c958c",
    "cross_cats_sorted": [
      "math.GN",
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2016-08-12T18:39:00Z",
    "title_canon_sha256": "6c4419b0826a943add76876b00dce56799360bccbf250235c8866b9306fb5bcf"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1608.03868",
    "kind": "arxiv",
    "version": 3
  }
}