Pith Number

pith:N2J7TDU5

pith:2010:N2J7TDU5QGEE6LP6JUJVV35QBU

not attested not anchored not stored refs pending

Preantipodes for dual-quasi bialgebras

Alessandro Ardizzoni, Alice Pavarin

arxiv:1012.1956 v1 · 2010-12-09 · math.QA · 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{N2J7TDU5QGEE6LP6JUJVV35QBU}

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	2026-05-18T04:33:49.265832Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6e93f98e9d81884f2dfe4d135aefb00d0fa6332397e74063f1e1e1aae46d73ee

Aliases

arxiv: 1012.1956 · arxiv_version: 1012.1956v1 · doi: 10.48550/arxiv.1012.1956 · pith_short_12: N2J7TDU5QGEE · pith_short_16: N2J7TDU5QGEE6LP6 · pith_short_8: N2J7TDU5

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/N2J7TDU5QGEE6LP6JUJVV35QBU \
  | 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: 6e93f98e9d81884f2dfe4d135aefb00d0fa6332397e74063f1e1e1aae46d73ee

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a91b81f238a476e0fe38e73faacfb7c90537acde3d4539ef0ea4ea56f41e5455",
    "cross_cats_sorted": [
      "math.RA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.QA",
    "submitted_at": "2010-12-09T09:35:42Z",
    "title_canon_sha256": "20cf921d5b581aa92911d7a38ad1e87b975265be5480c25acb9739cf5baee538"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1012.1956",
    "kind": "arxiv",
    "version": 1
  }
}