{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:ECYSRC32BZZZQ376X2H7SCD3EM","short_pith_number":"pith:ECYSRC32","canonical_record":{"source":{"id":"2409.13506","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"physics.data-an","submitted_at":"2024-09-20T13:48:03Z","cross_cats_sorted":[],"title_canon_sha256":"2b4dbda928b97981bf1283c56ad933f9948fe660b454c075ae58e25569f7c191","abstract_canon_sha256":"832ec4d9ff371b1a759c17cda08992d36d9d801a6fc9fa521fa9e0c74d19343a"},"schema_version":"1.0"},"canonical_sha256":"20b1288b7a0e73986ffebe8ff9087b2317ae73823a4f78348635bcf9bc25f51d","source":{"kind":"arxiv","id":"2409.13506","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2409.13506","created_at":"2026-07-05T09:09:36Z"},{"alias_kind":"arxiv_version","alias_value":"2409.13506v1","created_at":"2026-07-05T09:09:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2409.13506","created_at":"2026-07-05T09:09:36Z"},{"alias_kind":"pith_short_12","alias_value":"ECYSRC32BZZZ","created_at":"2026-07-05T09:09:36Z"},{"alias_kind":"pith_short_16","alias_value":"ECYSRC32BZZZQ376","created_at":"2026-07-05T09:09:36Z"},{"alias_kind":"pith_short_8","alias_value":"ECYSRC32","created_at":"2026-07-05T09:09:36Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:ECYSRC32BZZZQ376X2H7SCD3EM","target":"record","payload":{"canonical_record":{"source":{"id":"2409.13506","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"physics.data-an","submitted_at":"2024-09-20T13:48:03Z","cross_cats_sorted":[],"title_canon_sha256":"2b4dbda928b97981bf1283c56ad933f9948fe660b454c075ae58e25569f7c191","abstract_canon_sha256":"832ec4d9ff371b1a759c17cda08992d36d9d801a6fc9fa521fa9e0c74d19343a"},"schema_version":"1.0"},"canonical_sha256":"20b1288b7a0e73986ffebe8ff9087b2317ae73823a4f78348635bcf9bc25f51d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:09:36.590918Z","signature_b64":"Ca2rVlnihU9sB2ewUm1Ll7E3EWi+asR62v2wbXoqyEnvrXKcJ7LfCBiDYIdkj5K8izBq55DUp4ihuVWxb/lwDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"20b1288b7a0e73986ffebe8ff9087b2317ae73823a4f78348635bcf9bc25f51d","last_reissued_at":"2026-07-05T09:09:36.590382Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:09:36.590382Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2409.13506","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":"2026-07-05T09:09:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DU5liArv1o6hj57QSBBQOIqcfj4WILpAFaNiVumivw+ydBy6sNt4AMjhW07kfpawfbTUsKQs9ySA7M6hPiW5BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T22:22:47.746050Z"},"content_sha256":"0ca3334a09292c4e34e9de8b741556d4301a6921360c74ab0cde41cb1d11ad66","schema_version":"1.0","event_id":"sha256:0ca3334a09292c4e34e9de8b741556d4301a6921360c74ab0cde41cb1d11ad66"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:ECYSRC32BZZZQ376X2H7SCD3EM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Partial information decomposition for mixed discrete and continuous random variables","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"physics.data-an","authors_text":"Chiara Bar\\`a, Ivan Lazic, Luca Faes, Marta Iovino, Yuri Antonacci","submitted_at":"2024-09-20T13:48:03Z","abstract_excerpt":"The framework of Partial Information Decomposition (PID) unveils complex nonlinear interactions in network systems by dissecting the mutual information (MI) between a target variable and several source variables. While PID measures have been formulated mostly for discrete variables, with only recent extensions to continuous systems, the case of mixed variables where the target is discrete and the sources are continuous is not yet covered properly. Here, we introduce a PID scheme whereby the MI between a specific state of the discrete target and (subsets of) the continuous sources is expressed "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2409.13506","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/2409.13506/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":"2026-07-05T09:09:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TfBN/uLDur8wVZCPli9Qp685yD8F08xz2ib5Ls8QIO7WTpE661KXJnE20i4Gq4FKbNnhgA/JdZ3cvVEOuS/oCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T22:22:47.746449Z"},"content_sha256":"a26efb8c11aab56f9668ca58bbd1fdc4d846712560861dd5ee161064d183fb46","schema_version":"1.0","event_id":"sha256:a26efb8c11aab56f9668ca58bbd1fdc4d846712560861dd5ee161064d183fb46"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ECYSRC32BZZZQ376X2H7SCD3EM/bundle.json","state_url":"https://pith.science/pith/ECYSRC32BZZZQ376X2H7SCD3EM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ECYSRC32BZZZQ376X2H7SCD3EM/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":"2026-08-12T22:22:47Z","links":{"resolver":"https://pith.science/pith/ECYSRC32BZZZQ376X2H7SCD3EM","bundle":"https://pith.science/pith/ECYSRC32BZZZQ376X2H7SCD3EM/bundle.json","state":"https://pith.science/pith/ECYSRC32BZZZQ376X2H7SCD3EM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ECYSRC32BZZZQ376X2H7SCD3EM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:ECYSRC32BZZZQ376X2H7SCD3EM","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":"832ec4d9ff371b1a759c17cda08992d36d9d801a6fc9fa521fa9e0c74d19343a","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"physics.data-an","submitted_at":"2024-09-20T13:48:03Z","title_canon_sha256":"2b4dbda928b97981bf1283c56ad933f9948fe660b454c075ae58e25569f7c191"},"schema_version":"1.0","source":{"id":"2409.13506","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2409.13506","created_at":"2026-07-05T09:09:36Z"},{"alias_kind":"arxiv_version","alias_value":"2409.13506v1","created_at":"2026-07-05T09:09:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2409.13506","created_at":"2026-07-05T09:09:36Z"},{"alias_kind":"pith_short_12","alias_value":"ECYSRC32BZZZ","created_at":"2026-07-05T09:09:36Z"},{"alias_kind":"pith_short_16","alias_value":"ECYSRC32BZZZQ376","created_at":"2026-07-05T09:09:36Z"},{"alias_kind":"pith_short_8","alias_value":"ECYSRC32","created_at":"2026-07-05T09:09:36Z"}],"graph_snapshots":[{"event_id":"sha256:a26efb8c11aab56f9668ca58bbd1fdc4d846712560861dd5ee161064d183fb46","target":"graph","created_at":"2026-07-05T09:09:36Z","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/2409.13506/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The framework of Partial Information Decomposition (PID) unveils complex nonlinear interactions in network systems by dissecting the mutual information (MI) between a target variable and several source variables. While PID measures have been formulated mostly for discrete variables, with only recent extensions to continuous systems, the case of mixed variables where the target is discrete and the sources are continuous is not yet covered properly. Here, we introduce a PID scheme whereby the MI between a specific state of the discrete target and (subsets of) the continuous sources is expressed ","authors_text":"Chiara Bar\\`a, Ivan Lazic, Luca Faes, Marta Iovino, Yuri Antonacci","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"physics.data-an","submitted_at":"2024-09-20T13:48:03Z","title":"Partial information decomposition for mixed discrete and continuous random variables"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2409.13506","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":"sha256:0ca3334a09292c4e34e9de8b741556d4301a6921360c74ab0cde41cb1d11ad66","target":"record","created_at":"2026-07-05T09:09:36Z","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":"832ec4d9ff371b1a759c17cda08992d36d9d801a6fc9fa521fa9e0c74d19343a","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"physics.data-an","submitted_at":"2024-09-20T13:48:03Z","title_canon_sha256":"2b4dbda928b97981bf1283c56ad933f9948fe660b454c075ae58e25569f7c191"},"schema_version":"1.0","source":{"id":"2409.13506","kind":"arxiv","version":1}},"canonical_sha256":"20b1288b7a0e73986ffebe8ff9087b2317ae73823a4f78348635bcf9bc25f51d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"20b1288b7a0e73986ffebe8ff9087b2317ae73823a4f78348635bcf9bc25f51d","first_computed_at":"2026-07-05T09:09:36.590382Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:09:36.590382Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Ca2rVlnihU9sB2ewUm1Ll7E3EWi+asR62v2wbXoqyEnvrXKcJ7LfCBiDYIdkj5K8izBq55DUp4ihuVWxb/lwDQ==","signature_status":"signed_v1","signed_at":"2026-07-05T09:09:36.590918Z","signed_message":"canonical_sha256_bytes"},"source_id":"2409.13506","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0ca3334a09292c4e34e9de8b741556d4301a6921360c74ab0cde41cb1d11ad66","sha256:a26efb8c11aab56f9668ca58bbd1fdc4d846712560861dd5ee161064d183fb46"],"state_sha256":"9b43ad7a656768ed315bd04091611e98f374c05f0bba5d6dc7f057d0304025b3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zaa4e1wXcU9hYotRMLkm54DUhyCmNlM+5vnyP2wLtFu3CEDo28DSF+9vJ6b1RwQRdW0MEDX31RNTD9ZgOMO9Cw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-12T22:22:47.749339Z","bundle_sha256":"e01118a5026aaaf963012f45c661d04208b309a25456195aabb8d86578f41bf1"}}