Pith Number

pith:4HAAHR23

pith:2018:4HAAHR23VPT56NONYZKKAO5DOC

not attested not anchored not stored refs pending

Normality and quotient in crossed modules over groupoids and double groupoids

Osman Mucuk, Serap Demir

arxiv:1801.08762 v1 · 2018-01-26 · math.CT · math.AT

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4HAAHR23VPT56NONYZKKAO5DOC}

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	2026-05-18T00:25:03.090019Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e1c003c75babe7df35cdc654a03ba370aeace7c569b6071cc83d1b4e0709e168

Aliases

arxiv: 1801.08762 · arxiv_version: 1801.08762v1 · doi: 10.48550/arxiv.1801.08762 · pith_short_12: 4HAAHR23VPT5 · pith_short_16: 4HAAHR23VPT56NON · pith_short_8: 4HAAHR23

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/4HAAHR23VPT56NONYZKKAO5DOC \
  | 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: e1c003c75babe7df35cdc654a03ba370aeace7c569b6071cc83d1b4e0709e168

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fd7a393cf067e630ce790e33b0a4d700abab48b13d9081662d3b587f26bd155d",
    "cross_cats_sorted": [
      "math.AT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CT",
    "submitted_at": "2018-01-26T11:30:48Z",
    "title_canon_sha256": "d331204169dad4c153b72f295d2262a39ca63c0917b0cd6bce7191b9007e71e7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1801.08762",
    "kind": "arxiv",
    "version": 1
  }
}