Pith Number

pith:LYTVRZOQ

pith:2009:LYTVRZOQW2T5K7HPZ7SQBHD2U4

not attested not anchored not stored refs pending

The quandle and group for higher-dimensional and virtual knots

Blake Winter

arxiv:0905.3948 v1 · 2009-05-25 · math.GT · 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{LYTVRZOQW2T5K7HPZ7SQBHD2U4}

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

Fundamental Quandles Do Not Determine the First Postnikov Invariant of 2-Knots

Receipt and verification

First computed	2026-07-04T15:42:53.533548Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5e2758e5d0b6a7d57cefcfe5009c7aa71b3356e9cca9a56f4010b378115f325d

Aliases

arxiv: 0905.3948 · arxiv_version: 0905.3948v1 · doi: 10.48550/arxiv.0905.3948 · pith_short_12: LYTVRZOQW2T5 · pith_short_16: LYTVRZOQW2T5K7HP · pith_short_8: LYTVRZOQ

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/LYTVRZOQW2T5K7HPZ7SQBHD2U4 \
  | 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: 5e2758e5d0b6a7d57cefcfe5009c7aa71b3356e9cca9a56f4010b378115f325d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d61bb60a5d09294fc08f397a851d934b3ac5660894767ebf8b4814fb3a3f02d9",
    "cross_cats_sorted": [
      "math.QA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2009-05-25T05:36:21Z",
    "title_canon_sha256": "351600edb12a2f5508ffc0acd1a9bb479d1a5b5d1e6d16f3e3b5169b5c05f5a8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0905.3948",
    "kind": "arxiv",
    "version": 1
  }
}