Pith Number

pith:H725NTO6

pith:2010:H725NTO643IZOI4IEFOAGPM62J

not attested not anchored not stored refs pending

R-smash products of Hopf quasigroups

Tomasz Brzezi\'nski, Zhengming Jiao

arxiv:1010.1656 v1 · 2010-10-08 · math.QA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{H725NTO643IZOI4IEFOAGPM62J}

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	2026-05-18T04:39:39.960809Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3ff5d6cddee6d1972388215c033d9ed27b48f9b96396067962f3dde3741c7158

Aliases

arxiv: 1010.1656 · arxiv_version: 1010.1656v1 · doi: 10.48550/arxiv.1010.1656 · pith_short_12: H725NTO643IZ · pith_short_16: H725NTO643IZOI4I · pith_short_8: H725NTO6

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/H725NTO643IZOI4IEFOAGPM62J \
  | 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: 3ff5d6cddee6d1972388215c033d9ed27b48f9b96396067962f3dde3741c7158

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "48b0fd0f8661fb2b2129828e1a528d2469d1875ca55e5189e4dbcac9000df4e4",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.QA",
    "submitted_at": "2010-10-08T10:47:36Z",
    "title_canon_sha256": "753fa84fdd12fe22bf854b353df6ee9df69a03f0f8cf911394313835bcee5229"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1010.1656",
    "kind": "arxiv",
    "version": 1
  }
}