Pith Number

pith:CUZQONL2

pith:2010:CUZQONL2BCJO7XDFYR4FVSFBRL

not attested not anchored not stored refs pending

A Functorial Map from Virtual Knots to Classical Knots and Generalisations of Parity

Vassily Olegovich Manturov

arxiv:1011.4640 v4 · 2010-11-21 · 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{CUZQONL2BCJO7XDFYR4FVSFBRL}

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	2026-05-18T03:46:31.966122Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

153307357a0892efdc65c4785ac8a18acd8c32e2bca207ea977fadfa6c4f3f79

Aliases

arxiv: 1011.4640 · arxiv_version: 1011.4640v4 · doi: 10.48550/arxiv.1011.4640 · pith_short_12: CUZQONL2BCJO · pith_short_16: CUZQONL2BCJO7XDF · pith_short_8: CUZQONL2

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/CUZQONL2BCJO7XDFYR4FVSFBRL \
  | 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: 153307357a0892efdc65c4785ac8a18acd8c32e2bca207ea977fadfa6c4f3f79

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ce6c688f5771eafb957e7087e80b2fc650572585e6677da6aac42586283c7bab",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2010-11-21T05:49:44Z",
    "title_canon_sha256": "9a9ffee43497c376f1e2e77097593371fc38d62d7c33d2a22dd44dc0697188b0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1011.4640",
    "kind": "arxiv",
    "version": 4
  }
}