Pith Number

pith:2NLXOOVX

pith:2013:2NLXOOVXN6C4ZZGAAY2KK5NB3L

not attested not anchored not stored refs pending

Representative functions on discrete groupoids and duality with Hopf algebroids

Laiachi El Kaoutit

arxiv:1311.3109 v2 · 2013-11-12 · math.RA · math.AC · math.AG · math.GN

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{2NLXOOVXN6C4ZZGAAY2KK5NB3L}

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	2026-05-18T03:05:57.278230Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d357773ab76f85cce4c00634a575a1dafaa43fa64ec16a0cda43a7053860b574

Aliases

arxiv: 1311.3109 · arxiv_version: 1311.3109v2 · doi: 10.48550/arxiv.1311.3109 · pith_short_12: 2NLXOOVXN6C4 · pith_short_16: 2NLXOOVXN6C4ZZGA · pith_short_8: 2NLXOOVX

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/2NLXOOVXN6C4ZZGAAY2KK5NB3L \
  | 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: d357773ab76f85cce4c00634a575a1dafaa43fa64ec16a0cda43a7053860b574

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1e3675dad347896f5f4038792ec188d4bb90ce39b46df6689a5e4c6f973d11e1",
    "cross_cats_sorted": [
      "math.AC",
      "math.AG",
      "math.GN"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.RA",
    "submitted_at": "2013-11-12T09:37:13Z",
    "title_canon_sha256": "316647d1d1a400b3af3723120515b43363f0663f35548fb7e56d6344274937ef"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1311.3109",
    "kind": "arxiv",
    "version": 2
  }
}