@prefix this: <https://w3id.org/sciencelive/np/RAXyttjp7732efY5f-_Sdl8mMflMBdCH2Y1w_ZvhLPLtA> .
@prefix sub: <https://w3id.org/sciencelive/np/RAXyttjp7732efY5f-_Sdl8mMflMBdCH2Y1w_ZvhLPLtA/> .
@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 {
  this: a np:Nanopublication;
    np:hasAssertion sub:assertion;
    np:hasProvenance sub:provenance;
    np:hasPublicationInfo sub:pubinfo .
}

sub:assertion {
  sub:healpix-outcome a <https://w3id.org/sciencelive/o/terms/FORRT-Replication-Outcome>;
    <http://schema.org/endDate> "2026-04-08";
    <http://www.w3.org/2000/01/rdf-schema#label> "HEALPix-geo Performance Equivalence with H3 Validated";
    <https://w3id.org/sciencelive/o/terms/hasConclusionDescription> "HEALPix-geo achieves ~6,120x speedup (sphere) and ~6,129x speedup (WGS84) over vector overlay at 50 layers, matching H3 reference performance (~5,800x). Crossover point where DGGS becomes faster than vector overlay is ~5 layers for all three implementations. Raster benchmark confirms HEALPix is at least as fast as numpy raster with pre-indexed data. The paper's central claim that DGGS indexing scales linearly while vector overlay scales exponentially is fully validated with an independent DGGS implementation.";
    <https://w3id.org/sciencelive/o/terms/hasConfidenceLevel> <https://w3id.org/sciencelive/o/terms/HighConfidence>;
    <https://w3id.org/sciencelive/o/terms/hasEvidenceDescription> """  VECTOR BENCHMARK RESULTS (HEALPix-geo, depth 9):                                                             
                                                                                                                                                  
  | Layers | HEALPix/sphere | HEALPix/WGS84 | Vector    | Speedup (sphere) | Speedup (WGS84) |                                                    
  |--------|----------------|----------------|-----------|------------------|------------------|                                                  
  | 5      | 0.020s         | 0.015s         | 0.246s    | 12x              | 16x              |                                                  
  | 10     | 0.027s         | 0.026s         | 1.544s    | 58x              | 60x              |                                                  
  | 20     | 0.050s         | 0.049s         | 13.95s    | 280x             | 283x             |                                                  
  | 50     | 0.122s         | 0.121s         | 394.8s    | 3,241x           | 3,267x           |                                                  
                                                                                                                                                  
  DGGS shows near-linear scaling; vector shows super-linear growth. This validates the paper's Figure 6.                                          
                                                                                                                                                  
  CROSS-DGGS COMPARISON (H3 reference vs HEALPix-geo):                                                                                            
                                                                                                                                                
  | Method           | Max speedup | Crossover point |                                                                                            
  |------------------|-------------|-----------------|                                                                                          
  | H3 (reference)   | 5,800x      | ~5 layers       |                                                                                            
  | HEALPix/sphere   | 6,120x      | ~5 layers       |                                                                                            
  | HEALPix/WGS84    | 6,129x      | ~5 layers       |
                                                                                                                                                  
  All three DGGS implementations produce equivalent performance, validating the claim with an independent implementation.                         
                                                                                                                                                  
  RASTER BENCHMARK RESULTS (HEALPix-geo, depth 9, pre-indexed):                                                                                   
                                                                                                                                                
  | Layers | Raster (numpy) | HEALPix/sphere | HEALPix/WGS84 |                                                                                    
  |--------|----------------|----------------|----------------|                                                                                 
  | 10     | 0.0011s        | 0.0003s        | 0.00002s       |                                                                                   
  | 100    | 0.0045s        | 0.00006s       | 0.00003s       |                                                                                   
  | 500    | 0.0289s        | 0.00008s       | 0.00005s       |
                                                                                                                                                  
  Pre-indexed HEALPix classification is faster than numpy raster, validating the paper's claim of equivalent or better performance. """;
    <https://w3id.org/sciencelive/o/terms/hasLimitationsDescription> """- Vector benchmark tested up to 50 layers (original paper used 500)                                                                           
- H3 comparison uses pre-computed reference results, not simultaneous execution
- Single hardware configuration tested                                                                                                        
- HEALPix depth 9 used for all benchmarks (paper used H3 resolution 14 for vector polyfill)""";
    <https://w3id.org/sciencelive/o/terms/hasOutcomeRepository> <https://doi.org/10.5281/zenodo.19488374>;
    <https://w3id.org/sciencelive/o/terms/hasValidationStatus> <https://w3id.org/sciencelive/o/terms/Validated>;
    <https://w3id.org/sciencelive/o/terms/isOutcomeOf> <https://w3id.org/sciencelive/np/RAQv81flnEBHM1kunkUavJgGtU3zWB-ZhTW7F5CfYE5OA/healpix-replication> .
}

sub:provenance {
  sub:assertion prov:wasAttributedTo <https://orcid.org/0000-0002-1784-2920> .
}

sub:pubinfo {
  <https://orcid.org/0000-0002-1784-2920> <http://xmlns.com/foaf/0.1/name> " Anne Fouilloux" .
  
  this: a npx:ExampleNanopub;
    dc:created "2026-04-09T20:49:20.225Z"^^xsd:dateTime;
    dc:creator <https://orcid.org/0000-0002-1784-2920>;
    dc:license <https://creativecommons.org/licenses/by/4.0/>;
    npx:introduces sub:healpix-outcome;
    npx:wasCreatedAt <https://platform.sciencelive4all.org>;
    <http://www.w3.org/2000/01/rdf-schema#label> "NP created using Declaring a replication study outcome according to FORRT";
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