@prefix this: <https://w3id.org/np/RAaxbCLR3IGRKsixYvjynG2kKbjAwr0ZE-YYhqztgIBuo> .
@prefix sub: <https://w3id.org/np/RAaxbCLR3IGRKsixYvjynG2kKbjAwr0ZE-YYhqztgIBuo/> .
@prefix np: <http://www.nanopub.org/nschema#> .
@prefix rdf: <http://www.w3.org/1999/02/22-rdf-syntax-ns#> .
@prefix prov: <http://www.w3.org/ns/prov#> .
@prefix npx: <http://purl.org/nanopub/x/> .
@prefix dc: <http://purl.org/dc/terms/> .
@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .

sub:Head {
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    np:hasAssertion sub:assertion;
    np:hasProvenance sub:provenance;
    np:hasPublicationInfo sub:pubinfo .
}

sub:assertion {
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    dc:description "That effects can be more symmetric than their causes is directly demonstrable both mathematically and empirically in crystal physics: any second-rank symmetric tensor (optical indicatrix, electrical conductivity, thermal expansion) in a cubic crystal has full spherical symmetry ∞∞m, which is strictly higher than the cubic point group of the crystal lattice. Furthermore, acentric crystals with accidental or vanishingly small piezoelectric coefficients show zero response despite lacking inversion symmetry. Public tensor databases such as the Materials Project verify this across thousands of compounds immediately.";
    dc:subject <https://w3id.org/delphi/resource/concept/dataset-resolvability-0.2.0>;
    <http://www.w3.org/2000/01/rdf-schema#comment> "Proposed test with existing data: Compare the symmetry group G_effect of second-rank and fourth-rank physical property tensors (such as dielectric permittivity, magnetic susceptibility, thermal expansion, or optical refractivity) against the crystallographic point group G_crystal of the host crystal. Confirm that G_effect can strictly contain G_crystal (G_crystal ⊂ G_effect) by verifying, for example, that every cubic crystal (point groups 23, m-3, 432, -43m, m-3m) exhibits a fully isotropic spherical O(3) second-rank dielectric or refractive index tensor.";
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    prov:wasAttributedTo <https://w3id.org/delphi/resource/agent/delphisci-resolvability-assessor-gemini-4-argon-medium>;
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  <https://w3id.org/delphi/resource/evidence/curie1894-03--gemini--dataset-1> a <https://w3id.org/delphi/ontology/EvidenceItem>;
    dc:description "Supplies dielectric, refractive, piezoelectric, and elastic tensors across all crystal systems, demonstrating higher tensor symmetry than crystal point-group symmetry.";
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    prov:wasDerivedFrom <https://materialsproject.org/> .
  
  <https://w3id.org/delphi/resource/model/gemini-4-argon-medium> a <https://w3id.org/delphi/ontology/LanguageModel>;
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}

sub:provenance {
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  sub:assessmentPlan prov:hadPlan <https://github.com/fractastical/delphisci/blob/5241dc54170fa807613109d52197d32342021641/claim-sources/crystals-and-form/README.md> .
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sub:pubinfo {
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  this: dc:created "2026-11-07T03:18:24.087Z"^^xsd:dateTime;
    dc:creator <https://orcid.org/0009-0007-4948-9192>;
    dc:license <https://creativecommons.org/licenses/by/4.0/>;
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    npx:introduces <https://w3id.org/delphi/resource/assessment/curie1894-03--gemini>;
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    <https://w3id.org/delphi/ontology/domain> <https://w3id.org/delphi/resource/domain/crystals-and-form> .
  
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