Pith Number

pith:X2QK4UDB

pith:1999:X2QK4UDBRZURWP3CVPT5SQZPPX

not attested not anchored not stored refs pending

Multiplicative structure of Kauffman bracket skein module quantizations

Doug Bullock, Jozef H. Przytycki

arxiv:math/9902117 v1 · 1999-02-20 · math.QA

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{X2QK4UDBRZURWP3CVPT5SQZPPX}

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.

Cited by

1 paper in Pith

Kauffman bracket skein module of the connected sum of two solid tori

Receipt and verification

First computed	2026-07-04T14:40:58.316850Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bea0ae50618e691b3f62abe7d9432f7de6137e86e13f05541af0ba845a7a4388

Aliases

arxiv: math/9902117 · arxiv_version: math/9902117v1 · doi: 10.48550/arxiv.math/9902117 · pith_short_12: X2QK4UDBRZUR · pith_short_16: X2QK4UDBRZURWP3C · pith_short_8: X2QK4UDB

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/X2QK4UDBRZURWP3CVPT5SQZPPX \
  | 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: bea0ae50618e691b3f62abe7d9432f7de6137e86e13f05541af0ba845a7a4388

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3c33c579a98aedd84ebe6839f4c9b986ab6cd3094d5e1f958040875c3269a045",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.QA",
    "submitted_at": "1999-02-20T00:16:28Z",
    "title_canon_sha256": "853d85fbac1b0bdf18406285ee071d2a8113f8f237b41169e07fa2a6ea286666"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/9902117",
    "kind": "arxiv",
    "version": 1
  }
}