Pith Number

pith:SHSAQXP3

pith:2010:SHSAQXP3LQFY4R55ZW6UJC2WOQ

not attested not anchored not stored refs pending

Commutative Hopf structures over a loop

Gongxiang Liu, Hua-Lin Huang, Yu Ye

arxiv:1002.0405 v1 · 2010-02-02 · 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{SHSAQXP3LQFY4R55ZW6UJC2WOQ}

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	2026-07-04T17:20:46.297926Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

91e4085dfb5c0b8e47bdcdbd448b5674364c6515ddc2129a52ebeeb5c46c667d

Aliases

arxiv: 1002.0405 · arxiv_version: 1002.0405v1 · doi: 10.48550/arxiv.1002.0405 · pith_short_12: SHSAQXP3LQFY · pith_short_16: SHSAQXP3LQFY4R55 · pith_short_8: SHSAQXP3

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/SHSAQXP3LQFY4R55ZW6UJC2WOQ \
  | 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: 91e4085dfb5c0b8e47bdcdbd448b5674364c6515ddc2129a52ebeeb5c46c667d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fe3cb614a7ba97cb0190db3bff92b7e74351369e54c8199dff9fb14b756beab8",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.RA",
    "submitted_at": "2010-02-02T16:19:46Z",
    "title_canon_sha256": "576f1a0254f8857e82910a4cb9a41121fc24362a7ba9ce22bb9f3fa29a81600c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1002.0405",
    "kind": "arxiv",
    "version": 1
  }
}