Pith Number

pith:4ZUJGYG7

pith:2012:4ZUJGYG7N2CL2IPDW7JYH5LZZ7

not attested not anchored not stored refs pending

Lawrence-Krammer-Bigelow representations and dual Garside length of braids

Bert Wiest (IRMAR), Tetsuya Ito

arxiv:1201.0957 v1 · 2012-01-04 · 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{4ZUJGYG7N2CL2IPDW7JYH5LZZ7}

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	2026-05-18T01:22:26.991640Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e6689360df6e84bd21e3b7d383f579cff5f0a26e2a493b08116201905fd10d38

Aliases

arxiv: 1201.0957 · arxiv_version: 1201.0957v1 · doi: 10.48550/arxiv.1201.0957 · pith_short_12: 4ZUJGYG7N2CL · pith_short_16: 4ZUJGYG7N2CL2IPD · pith_short_8: 4ZUJGYG7

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/4ZUJGYG7N2CL2IPDW7JYH5LZZ7 \
  | 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: e6689360df6e84bd21e3b7d383f579cff5f0a26e2a493b08116201905fd10d38

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e06e285e1280e7406c3ce0f1c76ca3ff8a67fe079a67e4490e422dbbc4064f25",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2012-01-04T18:35:33Z",
    "title_canon_sha256": "3109707b9c926ef4c7fe43b5a9c0bf1bb912bc1ad83d0159a0c3b01b075550d7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1201.0957",
    "kind": "arxiv",
    "version": 1
  }
}