Pith Number

pith:64H5E4GO

pith:2026:64H5E4GOCWZTYWHRITJDY25NPB

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GL-racks and coloring invariants of Legendrian knots

Zhiyi He, Zhiyun Cheng

Every finite GL-rack decomposes canonically into permutation and block types, so Legendrian knots with the same classical invariants have equivalent coloring invariants under any such rack.

arxiv:2605.16968 v1 · 2026-05-16 · math.GT

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Claims

C1strongest claim

As a corollary, we verify that two Legendrian knots with the same classical invariants share equivalent coloring invariants with respect to any given finite GL-rack.

C2weakest assumption

The canonical decomposition of finite GL-racks into permutation and block types holds for every finite GL-rack and directly implies the equivalence of their induced coloring invariants on Legendrian knots.

C3one line summary

Finite GL-racks decompose canonically into permutation and block GL-racks, implying that Legendrian knots with identical classical invariants have equivalent coloring invariants for any finite GL-rack.

References

21 extracted · 21 resolved · 1 Pith anchors

[1] From racks to pointed Hopf algebras.Adv 2003

[2] Holonomy braidings, biquandles and quantum invariants of links with SL 2(C) flat connections.Selecta Math 2020

[3] Scott Carter, Daniel Jelsovsky, Seiichi Kamada, Laurel Langford, and Masahico Saito 2003

[4] Legendrian rack invariants of Legendrian knots 2021

[5] Fundamental generalized Legendrian rack and classical invariants.Internat 2026

Receipt and verification

First computed	2026-05-20T00:03:33.552524Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f70fd270ce15b33c58f144d23c6bad787245a046fa6e78faf97b1ee052014ac5

Aliases

arxiv: 2605.16968 · arxiv_version: 2605.16968v1 · doi: 10.48550/arxiv.2605.16968 · pith_short_12: 64H5E4GOCWZT · pith_short_16: 64H5E4GOCWZTYWHR · pith_short_8: 64H5E4GO

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/64H5E4GOCWZTYWHRITJDY25NPB \
  | 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: f70fd270ce15b33c58f144d23c6bad787245a046fa6e78faf97b1ee052014ac5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "85ffe83b406b3fd070dd376150f3283d6efd62a09e1b2c5f3a696400ed7236f7",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2026-05-16T12:42:35Z",
    "title_canon_sha256": "8a4640fdbc70cf8d35ee080b4c96cb6f334b49ccce8d8d7b68e91de8f660b1c5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.16968",
    "kind": "arxiv",
    "version": 1
  }
}