Pith Number

pith:PM42LYRR

pith:2014:PM42LYRRWOGVLW6BK7KXUDYKTQ

not attested not anchored not stored refs pending

Hopf-Galois extensions for monoidal Hom-Hopf algebras

Liangyun Zhang, Yuanyuan Chen

arxiv:1409.5184 v1 · 2014-09-18 · 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{PM42LYRRWOGVLW6BK7KXUDYKTQ}

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	2026-05-18T02:42:30.667501Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7b39a5e231b38d55dbc157d57a0f0a9c170e47824b317e1a5083e2ce9765b2e0

Aliases

arxiv: 1409.5184 · arxiv_version: 1409.5184v1 · doi: 10.48550/arxiv.1409.5184 · pith_short_12: PM42LYRRWOGV · pith_short_16: PM42LYRRWOGVLW6B · pith_short_8: PM42LYRR

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/PM42LYRRWOGVLW6BK7KXUDYKTQ \
  | 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: 7b39a5e231b38d55dbc157d57a0f0a9c170e47824b317e1a5083e2ce9765b2e0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "42ec0fd2f936416eda148185a843bac854d02dc636f8e9a1d58d4d8d431adb09",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.RA",
    "submitted_at": "2014-09-18T03:45:54Z",
    "title_canon_sha256": "4ce6e8b9989b2383f1660be577892d2e40a98c25af345dc284a0e1d0ac65ee8e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1409.5184",
    "kind": "arxiv",
    "version": 1
  }
}