Pith Number

pith:Q22HT5Z7

pith:2025:Q22HT5Z7PFVYZB4OU7YHGS37QW

not attested not anchored not stored refs pending

Normalizing Flows on Quotient Manifolds via Boundary Quotients

Benjamin Cai, William Ghanem

Normalizing flows on the 3-sphere can be pushed forward via the covering map to approximate distributions on lens spaces.

arxiv:2511.22882 v3 · 2025-11-28 · cs.LG · math.PR

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3 Author claim open · sign in to claim

4 Citations open

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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 construct pushforward distributions via the universal covering map rho: S^3 -> L(p;q) with the goal of approximating these distributions using flows on L(p;q). We highlight that our method deletes redundancies in the case of a symmetric S^3 distribution.

C2weakest assumption

That flows trained on the covering space S^3 can be pushed forward to produce accurate approximations on L(p;q) without significant distortion or loss of expressivity due to the quotient map.

C3one line summary

Approximates pushforwards of distributions on lens spaces by using normalizing flows on the covering 3-sphere, deleting redundancies for symmetric cases, and demonstrates on von Mises-Fisher densities plus a Z_12-symmetric benzene model.

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-27T00:04:24.373086Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

86b479f73f796b8c878ea7f0734b7f85be7921e947c9a847fdeb4aa7b2f57fe4

Aliases

arxiv: 2511.22882 · arxiv_version: 2511.22882v3 · doi: 10.48550/arxiv.2511.22882 · pith_short_12: Q22HT5Z7PFVY · pith_short_16: Q22HT5Z7PFVYZB4O · pith_short_8: Q22HT5Z7

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/Q22HT5Z7PFVYZB4OU7YHGS37QW \
  | 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: 86b479f73f796b8c878ea7f0734b7f85be7921e947c9a847fdeb4aa7b2f57fe4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7240311be62c20d084d193e035cfdce4d782a75804ef932c41378c1e92f32500",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2025-11-28T05:12:27Z",
    "title_canon_sha256": "d5170e0e0e0bb43a94d198eb48bd35706a40f3e21479e956a73c76c918c0a986"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2511.22882",
    "kind": "arxiv",
    "version": 3
  }
}