Pith Number

pith:6RNIJVJX

pith:2009:6RNIJVJXFUQRN5NSSBBDNYJILF

not attested not anchored not stored refs pending

On the mapping class groups of $#_r(S^p \times S^p)$ for $p = 3, 7$

Diarmuid Crowley

arxiv:0905.0423 v2 · 2009-05-04 · 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{6RNIJVJXFUQRN5NSSBBDNYJILF}

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	2026-05-18T04:10:09.253239Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f45a84d5372d2116f5b2904236e128594eda0c38ce476e543f7bea21be1da13b

Aliases

arxiv: 0905.0423 · arxiv_version: 0905.0423v2 · doi: 10.48550/arxiv.0905.0423 · pith_short_12: 6RNIJVJXFUQR · pith_short_16: 6RNIJVJXFUQRN5NS · pith_short_8: 6RNIJVJX

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/6RNIJVJXFUQRN5NSSBBDNYJILF \
  | 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: f45a84d5372d2116f5b2904236e128594eda0c38ce476e543f7bea21be1da13b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c82cf15c81d94872f0743c4bc2aa0acca47ddf0b13b33b59e2dbf424adb7a099",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2009-05-04T17:36:33Z",
    "title_canon_sha256": "1e805fd6957a9d0b4f84313e328093c8938393bc99637e31a49197a553800850"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0905.0423",
    "kind": "arxiv",
    "version": 2
  }
}