Pith Number

pith:YGAFQULI

pith:2026:YGAFQULITMDM63SIJ4QJCVVNUL

not attested not anchored not stored refs resolved

Diagrammatic technique for Vogel's universality

A. Sleptsov, D. Khudoteplov

The diagrammatic technique in Vogel's Λ-algebra enables universal computations for Lie algebra quantities.

arxiv:2605.12911 v2 · 2026-05-13 · math.QA · hep-th · math-ph · math.GT · math.MP · math.RT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{YGAFQULITMDM63SIJ4QJCVVNUL}

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.

Claims

C1strongest claim

We revive the diagrammatic technique grounded in Vogel's Λ-algebra and show that it enables truly universal computations. We examine numerous examples and discuss them.

C2weakest assumption

That the diagrammatic operations in Vogel's Λ-algebra faithfully capture the universal properties hypothesized in 1999 without hidden dependence on specific representation-theoretic data or post-hoc adjustments for each example.

C3one line summary

Vogel's diagrammatic Lambda-algebra enables truly universal computations of Lie-theoretic quantities, demonstrated via multiple examples.

References

39 extracted · 39 resolved · 5 Pith anchors

[1] The universal Lie algebra 1999

[2] Casimir eigenvalues for universal Lie algebra 2012 · arXiv:1105.0115

[3] Split Casimir operator and solutions of the Yang–Baxter equation for the and Lie superalgebras, higher Casimir operators, and the Vogel parameters 2022

[4] On universal quantum dimensions 2017

[5] Universality in Chern-Simons theory 2012

Receipt and verification

First computed	2026-05-18T03:09:10.483881Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c1805851689b06cf6e484f209156ada2d38dd77d7cbeaf914eae46242510b7ea

Aliases

arxiv: 2605.12911 · arxiv_version: 2605.12911v2 · doi: 10.48550/arxiv.2605.12911 · pith_short_12: YGAFQULITMDM · pith_short_16: YGAFQULITMDM63SI · pith_short_8: YGAFQULI

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/YGAFQULITMDM63SIJ4QJCVVNUL \
  | 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: c1805851689b06cf6e484f209156ada2d38dd77d7cbeaf914eae46242510b7ea

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "42caa79e15f4dda4a3293e5be98ba9fb62487dc3f6de0db02047497fbaa66d41",
    "cross_cats_sorted": [
      "hep-th",
      "math-ph",
      "math.GT",
      "math.MP",
      "math.RT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.QA",
    "submitted_at": "2026-05-13T02:36:58Z",
    "title_canon_sha256": "4eb0a60c6dc450b1f9288b212baf85f935e5b6d995a13298e58932f242cddc94"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.12911",
    "kind": "arxiv",
    "version": 2
  }
}