Pith Number

pith:SHKA257L

pith:2010:SHKA257LIAKX5AF5EKIWBPYFK2

not attested not anchored not stored refs pending

New series in the Johnson cokernels of the mapping class groups of surfaces

Naoya Enomoto, Takao Satoh

arxiv:1012.2175 v3 · 2010-12-10 · math.RT · math.AT · 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{SHKA257LIAKX5AF5EKIWBPYFK2}

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.

Cited by

1 paper in Pith

One-dimensionality of certain cocycles for the detection of the Johnson cokernel

Receipt and verification

First computed	2026-05-18T04:28:36.944835Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

91d40d77eb40157e80bd229160bf05568e55229c64360e05504c31526ce4b44f

Aliases

arxiv: 1012.2175 · arxiv_version: 1012.2175v3 · doi: 10.48550/arxiv.1012.2175 · pith_short_12: SHKA257LIAKX · pith_short_16: SHKA257LIAKX5AF5 · pith_short_8: SHKA257L

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/SHKA257LIAKX5AF5EKIWBPYFK2 \
  | 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: 91d40d77eb40157e80bd229160bf05568e55229c64360e05504c31526ce4b44f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bfef9685adece09fa08457dcb7e9d5f07ad11a012791f832c4207cdbb32bc20b",
    "cross_cats_sorted": [
      "math.AT",
      "math.GR",
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.RT",
    "submitted_at": "2010-12-10T03:58:54Z",
    "title_canon_sha256": "cc171eedb7ee7f6bb104569266b3da99a95019921b0d644965aaf0f657dd6f11"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1012.2175",
    "kind": "arxiv",
    "version": 3
  }
}