Pith Number

pith:GNAAXPFP

pith:2011:GNAAXPFPAPCXSLLVMGXNLI7GP4

not attested not anchored not stored refs pending

A Categorical Model for the Virtual Braid Group

Louis H. Kauffman, Sofia Lambropoulou

arxiv:1103.3158 v3 · 2011-03-16 · 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{GNAAXPFPAPCXSLLVMGXNLI7GP4}

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	2026-05-18T02:22:18.826407Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

33400bbcaf03c5792d7561aed5a3e67f15f83c3b35b79468bffa18644e07aa27

Aliases

arxiv: 1103.3158 · arxiv_version: 1103.3158v3 · doi: 10.48550/arxiv.1103.3158 · pith_short_12: GNAAXPFPAPCX · pith_short_16: GNAAXPFPAPCXSLLV · pith_short_8: GNAAXPFP

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/GNAAXPFPAPCXSLLVMGXNLI7GP4 \
  | 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: 33400bbcaf03c5792d7561aed5a3e67f15f83c3b35b79468bffa18644e07aa27

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "793e1aba8e864759820dc1ceef8561f1614a37b1890c9a9c6fbaa586c5831fee",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2011-03-16T12:31:51Z",
    "title_canon_sha256": "4a3ab7163a13e0870b39ae092e398d495eeb9eb98109117a8050b8fd36af3bbd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1103.3158",
    "kind": "arxiv",
    "version": 3
  }
}