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  "official_claim": "Theorem 4.9 proves standard message-passing GNNs fail any-dimensional universality because their pointwise nonlinearities are discontinuous in the cut metric, since a pointwise map is continuous with respect to the cut norm only if it is linear (Theorem 4.9, Section 4.2).",
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    "domain": "graph-signed",
    "title_hint": "Any-dimensional invariant universality",
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    "forest_diag_mean": 0.25978390573855853,
    "claim_sha14": "fb928c2f170f33",
    "claim_snippet": "Theorem 4.9 proves standard message-passing GNNs fail any-dimensional universality because their pointwise nonlinearities are discontinuous in the cut metric, since a pointwise map is continuous with respect to the cu..."
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  "orid": "wRVTDcEMv8",
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  "repaired_at": "2026-07-27T19:05:00.342688+00:00"
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