Pith Number

pith:35C3CB56

pith:2011:35C3CB56BJIQAC53ZOVLWDK242

not attested not anchored not stored refs pending

Lower bounds of Growth of Hopf algebras

D.-G. Wang, G. Zhuang, J.J. Zhang

arxiv:1101.1116 v2 · 2011-01-05 · 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{35C3CB56BJIQAC53ZOVLWDK242}

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	2026-05-18T03:58:49.166233Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

df45b107be0a51000bbbcbaabb0d5ae6a05acfea25894647abf4fa0fd6a7253a

Aliases

arxiv: 1101.1116 · arxiv_version: 1101.1116v2 · doi: 10.48550/arxiv.1101.1116 · pith_short_12: 35C3CB56BJIQ · pith_short_16: 35C3CB56BJIQAC53 · pith_short_8: 35C3CB56

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/35C3CB56BJIQAC53ZOVLWDK242 \
  | 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: df45b107be0a51000bbbcbaabb0d5ae6a05acfea25894647abf4fa0fd6a7253a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a6a5dee3dce2d55830c3ec94a6b3ccb1f2db751620bff5c6f7f77ac691616b20",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.RA",
    "submitted_at": "2011-01-05T23:46:52Z",
    "title_canon_sha256": "246e50e65f7164c8fc828928fcc0171f3bed8259669955cde9ee2a449fe046c1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1101.1116",
    "kind": "arxiv",
    "version": 2
  }
}