Pith Number

pith:QPZIAFU7

pith:2011:QPZIAFU7NRZ4TAZM6NJWGRWAAJ

not attested not anchored not stored refs pending

Dual Garside structure and reducibility of braids

Matthieu Calvez

arxiv:1105.3675 v2 · 2011-05-18 · 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{QPZIAFU7NRZ4TAZM6NJWGRWAAJ}

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	2026-05-18T02:21:59.334604Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

83f280169f6c73c9832cf3536346c002733c75155445b031804f5c2c262b5294

Aliases

arxiv: 1105.3675 · arxiv_version: 1105.3675v2 · doi: 10.48550/arxiv.1105.3675 · pith_short_12: QPZIAFU7NRZ4 · pith_short_16: QPZIAFU7NRZ4TAZM · pith_short_8: QPZIAFU7

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/QPZIAFU7NRZ4TAZM6NJWGRWAAJ \
  | 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: 83f280169f6c73c9832cf3536346c002733c75155445b031804f5c2c262b5294

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "956d290604512600da15b43507176f53d256c3fd6de081be81badf38594e668d",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2011-05-18T16:06:57Z",
    "title_canon_sha256": "fdec92373f0aa5f344a8af1bf9cac90ece9222f47e94d594d1def9e1d414db33"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1105.3675",
    "kind": "arxiv",
    "version": 2
  }
}