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Privacy-preserving verification using zk-SNARKs can operate across a multi-party chain where each party proves the correctness of their computation without revealing private inputs to other parties. https://w3id.org/sciencelive/np/RALDaVTP30wEYZBlpQKCTojxtYEkRCZbjjWRB2KBLN6i4 https://w3id.org/np/o/ntemplate/wasCreatedFromTemplate https://w3id.org/np/RALmXhDw3rHcMveTgbv8VtWxijUHwnSqhCmtJFIPKWVaA https://w3id.org/sciencelive/np/RALDaVTP30wEYZBlpQKCTojxtYEkRCZbjjWRB2KBLN6i4/sig http://purl.org/nanopub/x/hasAlgorithm RSA https://w3id.org/sciencelive/np/RALDaVTP30wEYZBlpQKCTojxtYEkRCZbjjWRB2KBLN6i4/sig http://purl.org/nanopub/x/hasPublicKey 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http://purl.org/aida/zk-SNARK%20proofs%20are%20compact%20enough%20to%20be%20bundled%20with%20standard%20compliance%20reports%20without%20significant%20overhead%20regardless%20of%20the%20number%20of%20input%20measurements. https://w3id.org/sciencelive/np/RAkqwTImAu9TAMBcsA4mR58dX_nocCDyE7gS1p100VNtI http://purl.org/nanopub/x/wasCreatedAt https://platform.sciencelive4all.org https://w3id.org/sciencelive/np/RAkqwTImAu9TAMBcsA4mR58dX_nocCDyE7gS1p100VNtI http://www.w3.org/1999/02/22-rdf-syntax-ns#type http://purl.org/nanopub/x/ExampleNanopub https://w3id.org/sciencelive/np/RAkqwTImAu9TAMBcsA4mR58dX_nocCDyE7gS1p100VNtI http://www.w3.org/2000/01/rdf-schema#label AIDA sentence: zk-SNARK proofs are compact enough to be bundled with standard compliance reports without significant overhead regardless of the number of input measurements. https://w3id.org/sciencelive/np/RAkqwTImAu9TAMBcsA4mR58dX_nocCDyE7gS1p100VNtI https://w3id.org/np/o/ntemplate/wasCreatedFromTemplate 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For instance, in an automobile manufacturing supply chain, motor part manufacturers would not want to disclose where their factories are or some of the metrics regarding the production of their products. https://doi.org/10.48550/arXiv.2506.16347 http://www.w3.org/2000/01/rdf-schema#comment We believe this multi-party approach is directly relevant to cross-border biodiversity monitoring networks where national nodes need to contribute to aggregated EU-level reporting without exposing raw data that is subject to national data sovereignty constraints. https://w3id.org/np/o/ntemplate/CREATOR http://purl.org/spar/cito/quotes https://doi.org/10.48550/arXiv.2506.16347 https://w3id.org/sciencelive/np/RAwKU8so5QbWzDKm1E1Zc0yh4HOfIx3eYszmO9Lv7v4Ng/provenance https://w3id.org/sciencelive/np/RAwKU8so5QbWzDKm1E1Zc0yh4HOfIx3eYszmO9Lv7v4Ng/assertion http://www.w3.org/ns/prov#wasAttributedTo https://orcid.org/0000-0002-1784-2920 https://w3id.org/sciencelive/np/RAwKU8so5QbWzDKm1E1Zc0yh4HOfIx3eYszmO9Lv7v4Ng/pubinfo https://orcid.org/0000-0002-1784-2920 http://xmlns.com/foaf/0.1/name Anne Fouilloux https://w3id.org/sciencelive/np/RAwKU8so5QbWzDKm1E1Zc0yh4HOfIx3eYszmO9Lv7v4Ng http://purl.org/dc/terms/created 2026-04-13T17:39:50.993Z https://w3id.org/sciencelive/np/RAwKU8so5QbWzDKm1E1Zc0yh4HOfIx3eYszmO9Lv7v4Ng http://purl.org/dc/terms/creator https://orcid.org/0000-0002-1784-2920 https://w3id.org/sciencelive/np/RAwKU8so5QbWzDKm1E1Zc0yh4HOfIx3eYszmO9Lv7v4Ng http://purl.org/dc/terms/license https://creativecommons.org/licenses/by/4.0/ https://w3id.org/sciencelive/np/RAwKU8so5QbWzDKm1E1Zc0yh4HOfIx3eYszmO9Lv7v4Ng http://purl.org/nanopub/x/hasNanopubType http://purl.org/spar/cito/cites https://w3id.org/sciencelive/np/RAwKU8so5QbWzDKm1E1Zc0yh4HOfIx3eYszmO9Lv7v4Ng http://purl.org/nanopub/x/wasCreatedAt https://platform.sciencelive4all.org https://w3id.org/sciencelive/np/RAwKU8so5QbWzDKm1E1Zc0yh4HOfIx3eYszmO9Lv7v4Ng http://www.w3.org/1999/02/22-rdf-syntax-ns#type http://purl.org/nanopub/x/ExampleNanopub https://w3id.org/sciencelive/np/RAwKU8so5QbWzDKm1E1Zc0yh4HOfIx3eYszmO9Lv7v4Ng http://www.w3.org/2000/01/rdf-schema#label Paper annotation: The approach can also be used in other industries. 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http://purl.org/aida/Zero-knowledge%20proofs%20based%20on%20zk-SNARKs%20can%20verify%20that%20environmental%20sensor%20readings%20satisfy%20regulatory%20compliance%20thresholds%20without%20revealing%20the%20underlying%20measurement%20values. https://w3id.org/sciencelive/np/RAaP8oA9UUXgvkk2NXIbFwacWPdtpUc1rxFE6fWFlZf7w http://purl.org/nanopub/x/wasCreatedAt https://platform.sciencelive4all.org https://w3id.org/sciencelive/np/RAaP8oA9UUXgvkk2NXIbFwacWPdtpUc1rxFE6fWFlZf7w http://www.w3.org/1999/02/22-rdf-syntax-ns#type http://purl.org/nanopub/x/ExampleNanopub https://w3id.org/sciencelive/np/RAaP8oA9UUXgvkk2NXIbFwacWPdtpUc1rxFE6fWFlZf7w http://www.w3.org/2000/01/rdf-schema#label AIDA sentence: Zero-knowledge proofs based on zk-SNARKs can verify that environmental sensor readings satisfy regulatory compliance thresholds without revealing the underlying measurement values. https://w3id.org/sciencelive/np/RAaP8oA9UUXgvkk2NXIbFwacWPdtpUc1rxFE6fWFlZf7w 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https://w3id.org/sciencelive/np/RAsVhVgy2R6IUCAKyVIwrvrVIktqNIzxKXvPJ7LWtvhDc/assertion https://doi.org/10.48550/arXiv.2506.16347 http://purl.org/spar/cito/hasQuotedText A zk-SNARK then allows a cloud provider to prove that there is a valid signature chain for every meter reading and every carbon intensity figure used in the emissions accounting, but without disclosing the value of those meter readings, the identity of the electricity supplier, or any other internals that might be sensitive. https://doi.org/10.48550/arXiv.2506.16347 http://www.w3.org/2000/01/rdf-schema#comment I believe this approach can be generalised beyond carbon emissions accounting to environmental biodiversity monitoring, where sensor data from protected areas such as Natura 2000 sites must be reported to regulators without revealing exact readings or locations that could endanger species or compromise data sovereignty across national LifeWatch ERIC nodes. https://w3id.org/np/o/ntemplate/CREATOR 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https://w3id.org/sciencelive/np/RAFHcBby77Kge_n8Beyigx_caeW8lPb7vgiJkq5mHFxdY/assertion https://w3id.org/sciencelive/np/RAFHcBby77Kge_n8Beyigx_caeW8lPb7vgiJkq5mHFxdY/odrl-outcome-walkthrough http://schema.org/endDate 2026-04-11 https://w3id.org/sciencelive/np/RAFHcBby77Kge_n8Beyigx_caeW8lPb7vgiJkq5mHFxdY/odrl-outcome-walkthrough http://www.w3.org/1999/02/22-rdf-syntax-ns#type https://w3id.org/sciencelive/o/terms/FORRT-Replication-Outcome https://w3id.org/sciencelive/np/RAFHcBby77Kge_n8Beyigx_caeW8lPb7vgiJkq5mHFxdY/odrl-outcome-walkthrough http://www.w3.org/2000/01/rdf-schema#label ODRL automated access control: claim fully supported https://w3id.org/sciencelive/np/RAFHcBby77Kge_n8Beyigx_caeW8lPb7vgiJkq5mHFxdY/odrl-outcome-walkthrough https://w3id.org/sciencelive/o/terms/hasConclusionDescription The claim that ODRL policies published as signed nanopublications enable fully automated, cryptographically verifiable access control is fully supported. The end-to-end walkthrough demonstrates every step — from policy creation through automated evaluation to key wrapping and decryption — using production-ready code, with sub-second policy evaluation and complete auditability via nanopublications. https://w3id.org/sciencelive/np/RAFHcBby77Kge_n8Beyigx_caeW8lPb7vgiJkq5mHFxdY/odrl-outcome-walkthrough https://w3id.org/sciencelive/o/terms/hasConfidenceLevel https://w3id.org/sciencelive/o/terms/VeryHighConfidence https://w3id.org/sciencelive/np/RAFHcBby77Kge_n8Beyigx_caeW8lPb7vgiJkq5mHFxdY/odrl-outcome-walkthrough https://w3id.org/sciencelive/o/terms/hasEvidenceDescription The walkthrough exercises the full FAIR2Adapt access control pipeline against a synthetic biodiversity dataset: (1) ODRL policy correctly enforced the Public Benefit purpose constraint, permitting use/reproduce while blocking commercialise/sell, (2) ECDH key wrapping produced a 428-byte envelope that only the consumer's EC P-256 private key could unwrap, (3) AES-256-GCM decryption recovered all 20 rows with byte-perfect integrity, (4) every decision (policy, grant) is recorded as a signed, immutable nanopublication independently verifiable on the nanopub network. The same code paths are used in production for the Hamburg urban pluvial flood risk dataset. https://w3id.org/sciencelive/np/RAFHcBby77Kge_n8Beyigx_caeW8lPb7vgiJkq5mHFxdY/odrl-outcome-walkthrough https://w3id.org/sciencelive/o/terms/hasLimitationsDescription The walkthrough uses synthetic data (20 rows, ~3KB) rather than a large real-world dataset, so performance at scale is not tested. The consumer DID is a walkthrough identity hosted on GitHub Pages, not a real institutional DID infrastructure. The access request is simulated locally rather than through the automated GitHub Actions workflow used in production. 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http://www.w3.org/ns/prov#wasAttributedTo https://orcid.org/0000-0002-1784-2920 https://w3id.org/sciencelive/np/RAFHcBby77Kge_n8Beyigx_caeW8lPb7vgiJkq5mHFxdY/pubinfo https://orcid.org/0000-0002-1784-2920 http://xmlns.com/foaf/0.1/name Anne Fouilloux https://w3id.org/sciencelive/np/RAFHcBby77Kge_n8Beyigx_caeW8lPb7vgiJkq5mHFxdY http://purl.org/dc/terms/created 2026-04-12T09:35:48.363Z https://w3id.org/sciencelive/np/RAFHcBby77Kge_n8Beyigx_caeW8lPb7vgiJkq5mHFxdY http://purl.org/dc/terms/creator https://orcid.org/0000-0002-1784-2920 https://w3id.org/sciencelive/np/RAFHcBby77Kge_n8Beyigx_caeW8lPb7vgiJkq5mHFxdY http://purl.org/dc/terms/license https://creativecommons.org/licenses/by/4.0/ https://w3id.org/sciencelive/np/RAFHcBby77Kge_n8Beyigx_caeW8lPb7vgiJkq5mHFxdY http://purl.org/nanopub/x/introduces https://w3id.org/sciencelive/np/RAFHcBby77Kge_n8Beyigx_caeW8lPb7vgiJkq5mHFxdY/odrl-outcome-walkthrough https://w3id.org/sciencelive/np/RAFHcBby77Kge_n8Beyigx_caeW8lPb7vgiJkq5mHFxdY 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data. 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At mid-latitudes (+48°), 98% of pixels are assigned to a different cell. This demonstrates that sphere-based HEALPix indexing is unsuitable for European Earth observation data (Copernicus/Sentinel, 45-65°N). https://w3id.org/sciencelive/np/RANLZSWPo1AXNszhQDilv20UB6wM32Gp6WzbUhTCfzUK4/healpix-wgs84 https://w3id.org/sciencelive/o/terms/hasConfidenceLevel https://w3id.org/sciencelive/o/terms/HighConfidence https://w3id.org/sciencelive/np/RANLZSWPo1AXNszhQDilv20UB6wM32Gp6WzbUhTCfzUK4/healpix-wgs84 https://w3id.org/sciencelive/o/terms/hasEvidenceDescription ELLIPSOID ANALYSIS (HEALPix depth 9, sphere vs WGS84): | Region | Center lat | Pixels in different cell | Jaccard similarity | |---------------|------------|--------------------------|-------------------| | Equatorial | 0° | 26.6% | 0.9951 | | Mid-latitude | +48° | 98.4% | 0.9844 | | High-latitude | +62° | 90.8% | 0.9868 | | Arctic | +78° | 52.6% | 0.9908 | At mid-latitudes (Mediterranean, +48°), nearly every pixel (98.4%) is assigned to a different HEALPix cell when using sphere vs WGS84 ellipsoid. Polygon coverage Jaccard similarity drops to 0.9844, indicating measurable differences in spatial coverage. 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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/np/RAXyttjp7732efY5f-_Sdl8mMflMBdCH2Y1w_ZvhLPLtA/healpix-outcome https://w3id.org/sciencelive/o/terms/hasConfidenceLevel https://w3id.org/sciencelive/o/terms/HighConfidence https://w3id.org/sciencelive/np/RAXyttjp7732efY5f-_Sdl8mMflMBdCH2Y1w_ZvhLPLtA/healpix-outcome 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/np/RAXyttjp7732efY5f-_Sdl8mMflMBdCH2Y1w_ZvhLPLtA/healpix-outcome 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/np/RAXyttjp7732efY5f-_Sdl8mMflMBdCH2Y1w_ZvhLPLtA/healpix-outcome 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Vector benchmark: Voronoi polygons, dissolve by value, polyfill to HEALPix cells, join on cell ID, 7-bit classification. Raster benchmark: Gaussian-smoothed layers, pre-indexed pixel-to-cell mapping, aggregate and classify. Ellipsoid analysis: compares sphere vs WGS84 cell assignments across equatorial (0°), Mediterranean (+48°), Scandinavian (+62°), and Arctic (+78°) regions. Environment: Python 3.11, healpix-geo 0.1.1, Docker containerized, seeded RNG (seed=42). https://w3id.org/sciencelive/np/RAQv81flnEBHM1kunkUavJgGtU3zWB-ZhTW7F5CfYE5OA/healpix-replication https://w3id.org/sciencelive/o/terms/hasScopeDescription Replicates both vector and raster benchmarks from Law & Ardo (2024) using HEALPix indexing via the healpix-geo library (Rust-based) instead of H3. 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