Pith Number

pith:LGB5UPBW

pith:2020:LGB5UPBWF3TYDC7YZCHLDUIXCW

not attested not anchored not stored refs pending

The mapping class group of connect sums of $S^2 \times S^1$

Andrew Putman, Nathan Broaddus, Tara Brendle

arxiv:2012.01529 v4 · 2020-12-02 · 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{LGB5UPBWF3TYDC7YZCHLDUIXCW}

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	2026-07-05T05:57:08.689124Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5983da3c362ee7818bf8c88eb1d11715bdd20a49f522a955268f97f5e4d00e78

Aliases

arxiv: 2012.01529 · arxiv_version: 2012.01529v4 · doi: 10.48550/arxiv.2012.01529 · pith_short_12: LGB5UPBWF3TY · pith_short_16: LGB5UPBWF3TYDC7Y · pith_short_8: LGB5UPBW

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/LGB5UPBWF3TYDC7YZCHLDUIXCW \
  | 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: 5983da3c362ee7818bf8c88eb1d11715bdd20a49f522a955268f97f5e4d00e78

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7f1991034ed987394d2d2f0bb7c9993e32d7cc199e05da65382a9807f91b36f7",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2020-12-02T21:10:40Z",
    "title_canon_sha256": "7167387ba9f7e50e0be62fb63bd0c6b6dbdfb1ba3a73cafc5670a9ef0a9a7540"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2012.01529",
    "kind": "arxiv",
    "version": 4
  }
}