Pith Number

pith:Y5YASGCJ

pith:2014:Y5YASGCJJ4JS2XJLICJID7VZGH

not attested not anchored not stored refs pending

Morita theory for Hopf algebroids, principal bibundles, and weak equivalences

Laiachi El Kaoutit, Niels Kowalzig

arxiv:1407.7461 v3 · 2014-07-28 · math.AT · math.AC · math.RA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{Y5YASGCJJ4JS2XJLICJID7VZGH}

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	2026-05-18T00:50:57.984990Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c7700918494f132d5d2b409281feb931d1c44f9f768f509830108c74421238dc

Aliases

arxiv: 1407.7461 · arxiv_version: 1407.7461v3 · doi: 10.48550/arxiv.1407.7461 · pith_short_12: Y5YASGCJJ4JS · pith_short_16: Y5YASGCJJ4JS2XJL · pith_short_8: Y5YASGCJ

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/Y5YASGCJJ4JS2XJLICJID7VZGH \
  | 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: c7700918494f132d5d2b409281feb931d1c44f9f768f509830108c74421238dc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cdcca60923161db7034c1845b225071eb8d3df7e4d0f50a30cd87b988bd2b3d7",
    "cross_cats_sorted": [
      "math.AC",
      "math.RA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AT",
    "submitted_at": "2014-07-28T16:15:39Z",
    "title_canon_sha256": "65fd3de7c95d9c87ebcf7bb34dd45075f5f599f15ea69510974e12487817be76"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1407.7461",
    "kind": "arxiv",
    "version": 3
  }
}