Pith Number

pith:ZX5PTSNI

pith:2016:ZX5PTSNIWO5SXVWLX3IQ3RKQYZ

not attested not anchored not stored refs pending

Normality and quotient in crossed modules, cat$^1$-groups and internal groupoids within groups with operations

Osman Mucuk, Tun\c{c}ar \c{S}ahan

arxiv:1601.07095 v1 · 2016-01-26 · 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{ZX5PTSNIWO5SXVWLX3IQ3RKQYZ}

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	2026-05-18T01:21:57.472484Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cdfaf9c9a8b3bb2bd6cbbed10dc550c65376b5a925fc7f2a81db0c85fee32f69

Aliases

arxiv: 1601.07095 · arxiv_version: 1601.07095v1 · doi: 10.48550/arxiv.1601.07095 · pith_short_12: ZX5PTSNIWO5S · pith_short_16: ZX5PTSNIWO5SXVWL · pith_short_8: ZX5PTSNI

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/ZX5PTSNIWO5SXVWLX3IQ3RKQYZ \
  | 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: cdfaf9c9a8b3bb2bd6cbbed10dc550c65376b5a925fc7f2a81db0c85fee32f69

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bc3b36ba765d21bbf6cb2e9130a04365c3b9ee1b966ff608658f65d3a045b6ec",
    "cross_cats_sorted": [
      "math.AT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CT",
    "submitted_at": "2016-01-26T17:00:54Z",
    "title_canon_sha256": "d1bc3826beb9bd779e79a16c6a7857fc42fef8a22ce3a9e36d4b3f21a7993d54"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1601.07095",
    "kind": "arxiv",
    "version": 1
  }
}