Pith Number

pith:ARY63B44

pith:2026:ARY63B44E6NMJHQDJFTNEXKYCM

not attested not anchored not stored refs pending

Higher (gauged) Wess--Zumino--Witten terms based on Lie crossed modules

Danhua Song

For differential crossed modules the pure-gauge higher WZW term vanishes identically while the gauged term is exact.

arxiv:2604.10416 v2 · 2026-04-12 · math-ph · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ARY63B44E6NMJHQDJFTNEXKYCM}

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 prove that, for the symmetric invariant polynomial associated with differential crossed modules, the pure-gauge higher WZW term vanishes identically, whereas the higher gWZW term is exact. Consequently, the higher CS action is higher-gauge invariant on closed manifolds, and on manifolds with boundary all gauge dependence is encoded in boundary terms.

C2weakest assumption

The derivation assumes that strict Lie 2-groups are presented by Lie crossed modules and that a symmetric invariant polynomial exists for the associated differential crossed modules, allowing the Cartan homotopy formula to produce the required transgression forms.

C3one line summary

Higher WZW terms vanish and gauged versions are exact for symmetric invariant polynomials on differential crossed modules, making higher CS actions gauge-invariant on closed manifolds with boundary dependence isolated.

Receipt and verification

First computed	2026-05-26T01:03:29.866376Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0471ed879c279ac49e034966d25d58131821d284b8f22fff353c58593da2c713

Aliases

arxiv: 2604.10416 · arxiv_version: 2604.10416v2 · doi: 10.48550/arxiv.2604.10416 · pith_short_12: ARY63B44E6NM · pith_short_16: ARY63B44E6NMJHQD · pith_short_8: ARY63B44

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/ARY63B44E6NMJHQDJFTNEXKYCM \
  | 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: 0471ed879c279ac49e034966d25d58131821d284b8f22fff353c58593da2c713

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "815764f159b35cb5fdfc2557dff443028845af2407d1e8d1c98f224717bf1b2a",
    "cross_cats_sorted": [
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2026-04-12T02:20:01Z",
    "title_canon_sha256": "f9cf41e1f2b1b7f833c83fdbece7630162644c0e3ac68ba7a05bc52ebb5c762a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.10416",
    "kind": "arxiv",
    "version": 2
  }
}