Pith Number

pith:ZY5OLGDD

pith:2015:ZY5OLGDDZNOVLUIEAG2VHS7526

not attested not anchored not stored refs pending

A simple solution to the word problem for virtual braid groups

Bruno Aaron Cisneros de La Cruz (IMB), Luis Paris (IMB), Paolo Bellingeri (LMNO)

arxiv:1506.05283 v2 · 2015-06-17 · math.GR · 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{ZY5OLGDDZNOVLUIEAG2VHS7526}

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	2026-05-18T01:19:38.713214Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ce3ae59863cb5d55d10401b553cbfdd7b426876e0d7fae34702e8e70a6ae2920

Aliases

arxiv: 1506.05283 · arxiv_version: 1506.05283v2 · doi: 10.48550/arxiv.1506.05283 · pith_short_12: ZY5OLGDDZNOV · pith_short_16: ZY5OLGDDZNOVLUIE · pith_short_8: ZY5OLGDD

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/ZY5OLGDDZNOVLUIEAG2VHS7526 \
  | 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: ce3ae59863cb5d55d10401b553cbfdd7b426876e0d7fae34702e8e70a6ae2920

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "da55011a645c8b5519e7e91920f011fb170cda8fb7636258207323559a3333cf",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2015-06-17T11:27:31Z",
    "title_canon_sha256": "c324614b3368df0a982e739ef3ffef28fb6458c26cceb17a3cc31d3081f4644d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1506.05283",
    "kind": "arxiv",
    "version": 2
  }
}