Pith Number

pith:5VNQ6CAX

pith:2026:5VNQ6CAXI2JMBMSQQISPOU4LGO

not attested not anchored not stored refs pending

Isometric Invariant Quantification of Gaussian Divergence over Poincare Disc

Levent Ali Meng\"ut\"urk

The L2-embedded hyperbolic isometric invariant on the Poincaré disc equals the spherical squared-Hellinger distance for Gaussian measures.

arxiv:2602.17159 v5 · 2026-02-19 · cs.IT · math.IT · math.PR

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\usepackage{pith}
\pithnumber{5VNQ6CAXI2JMBMSQQISPOU4LGO}

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Record completeness

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2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications 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

presents a geometric duality between the spherical squared-Hellinger distance and a hyperbolic isometric invariant of the Poincare disc under the action of the general Mobius group

C2weakest assumption

That the L2-embedded hyperbolic isometric invariant provides a practically useful and distinct quantification of divergence between Gaussian measures beyond existing methods.

C3one line summary

Geometric duality connects squared-Hellinger distance to a Mobius-invariant hyperbolic quantity on the Poincare disc, proposed as a new divergence for Gaussians.

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-20T00:03:06.131913Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ed5b0f08174692c0b2508224f7538b33ae30b7fdc80ba4caf681069edefddf20

Aliases

arxiv: 2602.17159 · arxiv_version: 2602.17159v5 · doi: 10.48550/arxiv.2602.17159 · pith_short_12: 5VNQ6CAXI2JM · pith_short_16: 5VNQ6CAXI2JMBMSQ · pith_short_8: 5VNQ6CAX

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/5VNQ6CAXI2JMBMSQQISPOU4LGO \
  | 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: ed5b0f08174692c0b2508224f7538b33ae30b7fdc80ba4caf681069edefddf20

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0e79519df7c294cf78cda58c19695e6d148e43895386184d21b225e3653e52e6",
    "cross_cats_sorted": [
      "math.IT",
      "math.PR"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.IT",
    "submitted_at": "2026-02-19T08:14:56Z",
    "title_canon_sha256": "b67872e0334159d44c294581e6ec7c4850123d129b86c5ad3188b9e87549b70d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2602.17159",
    "kind": "arxiv",
    "version": 5
  }
}