Pith Number

pith:T6TIXJDB

pith:2011:T6TIXJDBIC45WWR53ZK46DGCVB

not attested not anchored not stored refs pending

The Pure Virtual Braid Group Is Quadratic

Peter Lee

arxiv:1110.2356 v4 · 2011-10-11 · math.QA · 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{T6TIXJDBIC45WWR53ZK46DGCVB}

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	2026-05-18T03:39:53.193156Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9fa68ba46140b9db5a3dde55cf0cc2a87dde58a4ddd259a3b6d28d36ce7d6f93

Aliases

arxiv: 1110.2356 · arxiv_version: 1110.2356v4 · doi: 10.48550/arxiv.1110.2356 · pith_short_12: T6TIXJDBIC45 · pith_short_16: T6TIXJDBIC45WWR5 · pith_short_8: T6TIXJDB

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/T6TIXJDBIC45WWR53ZK46DGCVB \
  | 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: 9fa68ba46140b9db5a3dde55cf0cc2a87dde58a4ddd259a3b6d28d36ce7d6f93

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "45f8aa62acc1d908376a4355e923592cacbfc68485564fcfbfe312e504681017",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.QA",
    "submitted_at": "2011-10-11T12:48:49Z",
    "title_canon_sha256": "dd3ecd0e8070dc6c15c0f4d99902efb7e8eaacad9e1510e94f92a326b582d0a5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1110.2356",
    "kind": "arxiv",
    "version": 4
  }
}