Pith Number

pith:MAF4G2V2

pith:2016:MAF4G2V27YJJM2AAFG4SURBUM2

not attested not anchored not stored refs pending

Crossed modules as maps between connected components of topological groups

Emmanuel D. Farjoun, Yoav Segev

arxiv:1604.06551 v1 · 2016-04-22 · 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{MAF4G2V27YJJM2AAFG4SURBUM2}

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	2026-05-18T01:16:28.789029Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

600bc36abafe1296680029b92a443466b09760030c6c4f760f0eb977e7bf052d

Aliases

arxiv: 1604.06551 · arxiv_version: 1604.06551v1 · doi: 10.48550/arxiv.1604.06551 · pith_short_12: MAF4G2V27YJJ · pith_short_16: MAF4G2V27YJJM2AA · pith_short_8: MAF4G2V2

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/MAF4G2V27YJJM2AAFG4SURBUM2 \
  | 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: 600bc36abafe1296680029b92a443466b09760030c6c4f760f0eb977e7bf052d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "060db83df6990f961641548c33cefe33d96764a7f27c86efadbec8047cfc6507",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AT",
    "submitted_at": "2016-04-22T06:49:02Z",
    "title_canon_sha256": "452c3cf947bb92c99cc970335d6f7fc80a3fb4a46f336914872fa6aab49f024d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1604.06551",
    "kind": "arxiv",
    "version": 1
  }
}