Pith Number

pith:FO4QVYVV

pith:2012:FO4QVYVVTTLTJWUYOUTKMIJ5PE

not attested not anchored not stored refs pending

A Graphical Construction of the sl(3) Invariant for Virtual Knots

Louis Hirsch Kauffman, Vassily Olegovich Manturov

arxiv:1207.0719 v3 · 2012-07-03 · math.GT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{FO4QVYVVTTLTJWUYOUTKMIJ5PE}

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	2026-05-18T02:48:55.112171Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2bb90ae2b59cd734da987526a6213d79253178dd5e4fb235e9f7d63c8174394c

Aliases

arxiv: 1207.0719 · arxiv_version: 1207.0719v3 · doi: 10.48550/arxiv.1207.0719 · pith_short_12: FO4QVYVVTTLT · pith_short_16: FO4QVYVVTTLTJWUY · pith_short_8: FO4QVYVV

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/FO4QVYVVTTLTJWUYOUTKMIJ5PE \
  | 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: 2bb90ae2b59cd734da987526a6213d79253178dd5e4fb235e9f7d63c8174394c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "687a0b8210150ea0ba28b44545388dd1812b176c48f926e8f61555e0f9632598",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2012-07-03T15:34:43Z",
    "title_canon_sha256": "5b33406d24ff6a163044768bb4cd03433e927ced5b7f690f92869693d86842ad"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1207.0719",
    "kind": "arxiv",
    "version": 3
  }
}