Pith Number

pith:57TKDIWL

pith:2011:57TKDIWLZNW6D5PWTONYUAVFPG

not attested not anchored not stored refs pending

The Magnus representation and homology cobordism groups of homology cylinders

Takuya Sakasai

arxiv:1108.6111 v2 · 2011-08-31 · math.GT · math.AT · 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{57TKDIWLZNW6D5PWTONYUAVFPG}

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	2026-05-18T01:36:48.613353Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

efe6a1a2cbcb6de1f5f69b9b8a02a57987abe54d7485c6c180230b7b2bc86c83

Aliases

arxiv: 1108.6111 · arxiv_version: 1108.6111v2 · doi: 10.48550/arxiv.1108.6111 · pith_short_12: 57TKDIWLZNW6 · pith_short_16: 57TKDIWLZNW6D5PW · pith_short_8: 57TKDIWL

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/57TKDIWLZNW6D5PWTONYUAVFPG \
  | 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: efe6a1a2cbcb6de1f5f69b9b8a02a57987abe54d7485c6c180230b7b2bc86c83

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e11e5f0724fff1f0b37c439a70ab839d972e633b58848aab704688ddf17b0546",
    "cross_cats_sorted": [
      "math.AT",
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2011-08-31T02:11:17Z",
    "title_canon_sha256": "f830de810237de355ab8d3debcfe5a1f58dc51188839f05f19cb982f014a82d1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1108.6111",
    "kind": "arxiv",
    "version": 2
  }
}