Pith Number

pith:467DWYAD

pith:2007:467DWYADUQ4G72TPWHJ24XBU54

not attested not anchored not stored refs pending

A Note on Kasparov Product and Duality

Hyun Ho Lee

arxiv:0712.1842 v2 · 2007-12-11 · math.OA · math.KT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{467DWYADUQ4G72TPWHJ24XBU54}

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	2026-05-18T04:41:04.061228Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e7be3b6003a4386fea6fb1d3ae5c34ef323e442480e8be0412b8975bc6a6874f

Aliases

arxiv: 0712.1842 · arxiv_version: 0712.1842v2 · doi: 10.48550/arxiv.0712.1842 · pith_short_12: 467DWYADUQ4G · pith_short_16: 467DWYADUQ4G72TP · pith_short_8: 467DWYAD

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/467DWYADUQ4G72TPWHJ24XBU54 \
  | 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: e7be3b6003a4386fea6fb1d3ae5c34ef323e442480e8be0412b8975bc6a6874f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6373a4dbc082ed53b95e1fed2bc40bf53a03958ee5da6c4baa5f54bdfef2d783",
    "cross_cats_sorted": [
      "math.KT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2007-12-11T22:53:13Z",
    "title_canon_sha256": "168f4c19720cc6bffa5c3fb6bb95499a0e7023d1c2af0d266f32aaacf385643e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0712.1842",
    "kind": "arxiv",
    "version": 2
  }
}