Pith Number

pith:VCD5O6E3

pith:2007:VCD5O6E3CVPLV2JW2OXTYXX57V

not attested not anchored not stored refs pending

Invariants of Welded Virtual Knots Via Crossed Module Invariants of Knotted Surfaces

Jo\~ao Faria Martins, Louis H. Kauffman

arxiv:0704.1246 v2 · 2007-04-10 · math.GT · hep-th · math.QA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VCD5O6E3CVPLV2JW2OXTYXX57V}

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	2026-05-18T00:44:10.587293Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a887d7789b155ebae936d3af3c5efdfd4bcbe5db980a77c4c7e493c5796dd87b

Aliases

arxiv: 0704.1246 · arxiv_version: 0704.1246v2 · doi: 10.48550/arxiv.0704.1246 · pith_short_12: VCD5O6E3CVPL · pith_short_16: VCD5O6E3CVPLV2JW · pith_short_8: VCD5O6E3

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/VCD5O6E3CVPLV2JW2OXTYXX57V \
  | 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: a887d7789b155ebae936d3af3c5efdfd4bcbe5db980a77c4c7e493c5796dd87b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a330bae79014956886140d7c7105e4ea02c5115f17caf4cdfafd3dfdda06e52e",
    "cross_cats_sorted": [
      "hep-th",
      "math.QA"
    ],
    "license": "",
    "primary_cat": "math.GT",
    "submitted_at": "2007-04-10T15:32:19Z",
    "title_canon_sha256": "83967c014bce50ddca757237b1a87fecdfe530e554850e83334516049e4a5665"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0704.1246",
    "kind": "arxiv",
    "version": 2
  }
}