{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:3LHBCINDTUJVU3NXNBJD5RSOQV","short_pith_number":"pith:3LHBCIND","canonical_record":{"source":{"id":"2112.05071","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2021-12-09T17:53:12Z","cross_cats_sorted":[],"title_canon_sha256":"f945019f79e0b4efe1c0651c3891e1a18d3be8538a8603a3333a62d1399a22e7","abstract_canon_sha256":"99313c82de691dbeb0dc3b7cfb7e7ca23ae985d55bc2fa9c7506f9b7d0e20b67"},"schema_version":"1.0"},"canonical_sha256":"dace1121a39d135a6db768523ec64e85707f01c2b9212ad6e8a32cbb42f536a4","source":{"kind":"arxiv","id":"2112.05071","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2112.05071","created_at":"2026-07-05T05:22:05Z"},{"alias_kind":"arxiv_version","alias_value":"2112.05071v1","created_at":"2026-07-05T05:22:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2112.05071","created_at":"2026-07-05T05:22:05Z"},{"alias_kind":"pith_short_12","alias_value":"3LHBCINDTUJV","created_at":"2026-07-05T05:22:05Z"},{"alias_kind":"pith_short_16","alias_value":"3LHBCINDTUJVU3NX","created_at":"2026-07-05T05:22:05Z"},{"alias_kind":"pith_short_8","alias_value":"3LHBCIND","created_at":"2026-07-05T05:22:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:3LHBCINDTUJVU3NXNBJD5RSOQV","target":"record","payload":{"canonical_record":{"source":{"id":"2112.05071","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2021-12-09T17:53:12Z","cross_cats_sorted":[],"title_canon_sha256":"f945019f79e0b4efe1c0651c3891e1a18d3be8538a8603a3333a62d1399a22e7","abstract_canon_sha256":"99313c82de691dbeb0dc3b7cfb7e7ca23ae985d55bc2fa9c7506f9b7d0e20b67"},"schema_version":"1.0"},"canonical_sha256":"dace1121a39d135a6db768523ec64e85707f01c2b9212ad6e8a32cbb42f536a4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:22:05.147840Z","signature_b64":"j+kcy08gXDvQMcMLG6Hm1yfj07I+u9O8CNc2u5EOGlIn5rfnkjyklv2qFVItUBVD21ZD1Bnx+WBf6qQOUnotBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dace1121a39d135a6db768523ec64e85707f01c2b9212ad6e8a32cbb42f536a4","last_reissued_at":"2026-07-05T05:22:05.147336Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:22:05.147336Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2112.05071","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T05:22:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KlE0UhJeCHBi7S8AQIJetwkEWovTPYYtjhqDeCMuBF7+RTLBdzCui6+m3ITx4IFlYPMHxVxrBDFhSzwJm6tRCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T00:50:22.176097Z"},"content_sha256":"3a230630a9e35edc9e3ec809596ffa45e5e0427b194c68b109ed725c299bad02","schema_version":"1.0","event_id":"sha256:3a230630a9e35edc9e3ec809596ffa45e5e0427b194c68b109ed725c299bad02"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:3LHBCINDTUJVU3NXNBJD5RSOQV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Novel Tropical Geometry-based Interpretable Machine Learning Method: Application in Prognosis of Advanced Heart Failure","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Harm Derksen, Heming Yao, Jessica R. Golbus, Jonathan Gryak, Justin Zhang, Kayvan Najarian, Keith D. Aaronson","submitted_at":"2021-12-09T17:53:12Z","abstract_excerpt":"A model's interpretability is essential to many practical applications such as clinical decision support systems. In this paper, a novel interpretable machine learning method is presented, which can model the relationship between input variables and responses in humanly understandable rules. The method is built by applying tropical geometry to fuzzy inference systems, wherein variable encoding functions and salient rules can be discovered by supervised learning. Experiments using synthetic datasets were conducted to investigate the performance and capacity of the proposed algorithm in classifi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2112.05071","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2112.05071/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T05:22:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wKsI8A4KjJJjew2qNG9XU/Ks0avNlr1/EgHUev0qAETxD5w29IbfjFZqpLrSI29kH+jIdRgRNaRAnocY9Q0FDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T00:50:22.176633Z"},"content_sha256":"a90112ad6a0780fc155d33f1cc961915a187a41211254180b205922c11723c55","schema_version":"1.0","event_id":"sha256:a90112ad6a0780fc155d33f1cc961915a187a41211254180b205922c11723c55"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3LHBCINDTUJVU3NXNBJD5RSOQV/bundle.json","state_url":"https://pith.science/pith/3LHBCINDTUJVU3NXNBJD5RSOQV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3LHBCINDTUJVU3NXNBJD5RSOQV/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-11T00:50:22Z","links":{"resolver":"https://pith.science/pith/3LHBCINDTUJVU3NXNBJD5RSOQV","bundle":"https://pith.science/pith/3LHBCINDTUJVU3NXNBJD5RSOQV/bundle.json","state":"https://pith.science/pith/3LHBCINDTUJVU3NXNBJD5RSOQV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3LHBCINDTUJVU3NXNBJD5RSOQV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:3LHBCINDTUJVU3NXNBJD5RSOQV","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"99313c82de691dbeb0dc3b7cfb7e7ca23ae985d55bc2fa9c7506f9b7d0e20b67","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2021-12-09T17:53:12Z","title_canon_sha256":"f945019f79e0b4efe1c0651c3891e1a18d3be8538a8603a3333a62d1399a22e7"},"schema_version":"1.0","source":{"id":"2112.05071","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2112.05071","created_at":"2026-07-05T05:22:05Z"},{"alias_kind":"arxiv_version","alias_value":"2112.05071v1","created_at":"2026-07-05T05:22:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2112.05071","created_at":"2026-07-05T05:22:05Z"},{"alias_kind":"pith_short_12","alias_value":"3LHBCINDTUJV","created_at":"2026-07-05T05:22:05Z"},{"alias_kind":"pith_short_16","alias_value":"3LHBCINDTUJVU3NX","created_at":"2026-07-05T05:22:05Z"},{"alias_kind":"pith_short_8","alias_value":"3LHBCIND","created_at":"2026-07-05T05:22:05Z"}],"graph_snapshots":[{"event_id":"sha256:a90112ad6a0780fc155d33f1cc961915a187a41211254180b205922c11723c55","target":"graph","created_at":"2026-07-05T05:22:05Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2112.05071/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"A model's interpretability is essential to many practical applications such as clinical decision support systems. In this paper, a novel interpretable machine learning method is presented, which can model the relationship between input variables and responses in humanly understandable rules. The method is built by applying tropical geometry to fuzzy inference systems, wherein variable encoding functions and salient rules can be discovered by supervised learning. Experiments using synthetic datasets were conducted to investigate the performance and capacity of the proposed algorithm in classifi","authors_text":"Harm Derksen, Heming Yao, Jessica R. Golbus, Jonathan Gryak, Justin Zhang, Kayvan Najarian, Keith D. Aaronson","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2021-12-09T17:53:12Z","title":"A Novel Tropical Geometry-based Interpretable Machine Learning Method: Application in Prognosis of Advanced Heart Failure"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2112.05071","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:3a230630a9e35edc9e3ec809596ffa45e5e0427b194c68b109ed725c299bad02","target":"record","created_at":"2026-07-05T05:22:05Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"99313c82de691dbeb0dc3b7cfb7e7ca23ae985d55bc2fa9c7506f9b7d0e20b67","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2021-12-09T17:53:12Z","title_canon_sha256":"f945019f79e0b4efe1c0651c3891e1a18d3be8538a8603a3333a62d1399a22e7"},"schema_version":"1.0","source":{"id":"2112.05071","kind":"arxiv","version":1}},"canonical_sha256":"dace1121a39d135a6db768523ec64e85707f01c2b9212ad6e8a32cbb42f536a4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dace1121a39d135a6db768523ec64e85707f01c2b9212ad6e8a32cbb42f536a4","first_computed_at":"2026-07-05T05:22:05.147336Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:22:05.147336Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"j+kcy08gXDvQMcMLG6Hm1yfj07I+u9O8CNc2u5EOGlIn5rfnkjyklv2qFVItUBVD21ZD1Bnx+WBf6qQOUnotBQ==","signature_status":"signed_v1","signed_at":"2026-07-05T05:22:05.147840Z","signed_message":"canonical_sha256_bytes"},"source_id":"2112.05071","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3a230630a9e35edc9e3ec809596ffa45e5e0427b194c68b109ed725c299bad02","sha256:a90112ad6a0780fc155d33f1cc961915a187a41211254180b205922c11723c55"],"state_sha256":"0b9cb44e55597930531f3a77fcc06c782b11acf50f535685eeadd52d128c037f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MvModwbZ6WVn+dvflYGABsVcooF1+KgZUspGu05bnN5MMe45aecSLbjS7CNKFtrJduaqD2ramj6l7S+SNsToCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-11T00:50:22.182051Z","bundle_sha256":"4e63150fb12f64a75547deb6eb722bcb3782e80dc4d7b8cec59a7c76d9f13dd5"}}