{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:P2DLSXS4KC2GMDFZEGRYBEBGVT","short_pith_number":"pith:P2DLSXS4","canonical_record":{"source":{"id":"2306.07047","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2023-06-12T11:52:11Z","cross_cats_sorted":["math.ST","stat.TH"],"title_canon_sha256":"adb4895310d05531e6472b4e5ca0e4fa360845a62d662512c7448ab32bf7a46f","abstract_canon_sha256":"503105f00226bc13cabed5a63cd53ea8438a918991e61171bae703da8ce84688"},"schema_version":"1.0"},"canonical_sha256":"7e86b95e5c50b4660cb921a3809026acfe4e9ace51aa157ca85514c71ad9abb4","source":{"kind":"arxiv","id":"2306.07047","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2306.07047","created_at":"2026-07-05T07:57:40Z"},{"alias_kind":"arxiv_version","alias_value":"2306.07047v3","created_at":"2026-07-05T07:57:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2306.07047","created_at":"2026-07-05T07:57:40Z"},{"alias_kind":"pith_short_12","alias_value":"P2DLSXS4KC2G","created_at":"2026-07-05T07:57:40Z"},{"alias_kind":"pith_short_16","alias_value":"P2DLSXS4KC2GMDFZ","created_at":"2026-07-05T07:57:40Z"},{"alias_kind":"pith_short_8","alias_value":"P2DLSXS4","created_at":"2026-07-05T07:57:40Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:P2DLSXS4KC2GMDFZEGRYBEBGVT","target":"record","payload":{"canonical_record":{"source":{"id":"2306.07047","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2023-06-12T11:52:11Z","cross_cats_sorted":["math.ST","stat.TH"],"title_canon_sha256":"adb4895310d05531e6472b4e5ca0e4fa360845a62d662512c7448ab32bf7a46f","abstract_canon_sha256":"503105f00226bc13cabed5a63cd53ea8438a918991e61171bae703da8ce84688"},"schema_version":"1.0"},"canonical_sha256":"7e86b95e5c50b4660cb921a3809026acfe4e9ace51aa157ca85514c71ad9abb4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:57:40.944474Z","signature_b64":"1F1d0ydiG8zvfZeYhv3+bICdIs00sxUnZ6GVKUp84DdBmnWd+FFg/Ngt3ULFcTSxpXYSN4gk+WVLfTtqN7K1AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7e86b95e5c50b4660cb921a3809026acfe4e9ace51aa157ca85514c71ad9abb4","last_reissued_at":"2026-07-05T07:57:40.944122Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:57:40.944122Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2306.07047","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T07:57:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"09SJweY/6yU80M/TGXfCqy3v58XbG0vBdKfemMrfs6OxujtboruOaGoCcHlB7MhySMRNXTLsuIP1khO9z6brAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-09T01:24:34.951071Z"},"content_sha256":"f834656f5ca63640199425fd630a4586d810e0cb2b79043cddbdc37321db273d","schema_version":"1.0","event_id":"sha256:f834656f5ca63640199425fd630a4586d810e0cb2b79043cddbdc37321db273d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:P2DLSXS4KC2GMDFZEGRYBEBGVT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Foundations of Causal Discovery on Groups of Variables","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.ST","stat.TH"],"primary_cat":"stat.ME","authors_text":"Jakob Runge, Jonas Wahl, Urmi Ninad","submitted_at":"2023-06-12T11:52:11Z","abstract_excerpt":"Discovering causal relationships from observational data is a challenging task that relies on assumptions connecting statistical quantities to graphical or algebraic causal models. In this work, we focus on widely employed assumptions for causal discovery when objects of interest are (multivariate) groups of random variables rather than individual (univariate) random variables, as is the case in a variety of problems in scientific domains such as climate science or neuroscience. If the group-level causal models are derived from partitioning a micro-level model into groups, we explore the relat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2306.07047","kind":"arxiv","version":3},"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/2306.07047/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":"2026-07-05T07:57:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZzIfaWIGjDI+DMAVRbobCpht3F3cE1TY+Fcffswh6dQXh8eWHimLILkeIifZx6dpluq44evXmFtJlJj4u8f9Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-09T01:24:34.951495Z"},"content_sha256":"b9fe9d6abaea8ab7c096014c62bcd6893b48b42fc1059d4c3c929e9df2fcb042","schema_version":"1.0","event_id":"sha256:b9fe9d6abaea8ab7c096014c62bcd6893b48b42fc1059d4c3c929e9df2fcb042"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/P2DLSXS4KC2GMDFZEGRYBEBGVT/bundle.json","state_url":"https://pith.science/pith/P2DLSXS4KC2GMDFZEGRYBEBGVT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/P2DLSXS4KC2GMDFZEGRYBEBGVT/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":"2026-07-09T01:24:34Z","links":{"resolver":"https://pith.science/pith/P2DLSXS4KC2GMDFZEGRYBEBGVT","bundle":"https://pith.science/pith/P2DLSXS4KC2GMDFZEGRYBEBGVT/bundle.json","state":"https://pith.science/pith/P2DLSXS4KC2GMDFZEGRYBEBGVT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/P2DLSXS4KC2GMDFZEGRYBEBGVT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:P2DLSXS4KC2GMDFZEGRYBEBGVT","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":"503105f00226bc13cabed5a63cd53ea8438a918991e61171bae703da8ce84688","cross_cats_sorted":["math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2023-06-12T11:52:11Z","title_canon_sha256":"adb4895310d05531e6472b4e5ca0e4fa360845a62d662512c7448ab32bf7a46f"},"schema_version":"1.0","source":{"id":"2306.07047","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2306.07047","created_at":"2026-07-05T07:57:40Z"},{"alias_kind":"arxiv_version","alias_value":"2306.07047v3","created_at":"2026-07-05T07:57:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2306.07047","created_at":"2026-07-05T07:57:40Z"},{"alias_kind":"pith_short_12","alias_value":"P2DLSXS4KC2G","created_at":"2026-07-05T07:57:40Z"},{"alias_kind":"pith_short_16","alias_value":"P2DLSXS4KC2GMDFZ","created_at":"2026-07-05T07:57:40Z"},{"alias_kind":"pith_short_8","alias_value":"P2DLSXS4","created_at":"2026-07-05T07:57:40Z"}],"graph_snapshots":[{"event_id":"sha256:b9fe9d6abaea8ab7c096014c62bcd6893b48b42fc1059d4c3c929e9df2fcb042","target":"graph","created_at":"2026-07-05T07:57:40Z","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/2306.07047/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Discovering causal relationships from observational data is a challenging task that relies on assumptions connecting statistical quantities to graphical or algebraic causal models. In this work, we focus on widely employed assumptions for causal discovery when objects of interest are (multivariate) groups of random variables rather than individual (univariate) random variables, as is the case in a variety of problems in scientific domains such as climate science or neuroscience. If the group-level causal models are derived from partitioning a micro-level model into groups, we explore the relat","authors_text":"Jakob Runge, Jonas Wahl, Urmi Ninad","cross_cats":["math.ST","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2023-06-12T11:52:11Z","title":"Foundations of Causal Discovery on Groups of Variables"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2306.07047","kind":"arxiv","version":3},"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:f834656f5ca63640199425fd630a4586d810e0cb2b79043cddbdc37321db273d","target":"record","created_at":"2026-07-05T07:57:40Z","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":"503105f00226bc13cabed5a63cd53ea8438a918991e61171bae703da8ce84688","cross_cats_sorted":["math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2023-06-12T11:52:11Z","title_canon_sha256":"adb4895310d05531e6472b4e5ca0e4fa360845a62d662512c7448ab32bf7a46f"},"schema_version":"1.0","source":{"id":"2306.07047","kind":"arxiv","version":3}},"canonical_sha256":"7e86b95e5c50b4660cb921a3809026acfe4e9ace51aa157ca85514c71ad9abb4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7e86b95e5c50b4660cb921a3809026acfe4e9ace51aa157ca85514c71ad9abb4","first_computed_at":"2026-07-05T07:57:40.944122Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T07:57:40.944122Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1F1d0ydiG8zvfZeYhv3+bICdIs00sxUnZ6GVKUp84DdBmnWd+FFg/Ngt3ULFcTSxpXYSN4gk+WVLfTtqN7K1AQ==","signature_status":"signed_v1","signed_at":"2026-07-05T07:57:40.944474Z","signed_message":"canonical_sha256_bytes"},"source_id":"2306.07047","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f834656f5ca63640199425fd630a4586d810e0cb2b79043cddbdc37321db273d","sha256:b9fe9d6abaea8ab7c096014c62bcd6893b48b42fc1059d4c3c929e9df2fcb042"],"state_sha256":"38fe6f97e8a7fdef9500e44781dfd3bbac39f9600c5d3de2035eed84ae1e1b35"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HqeUUOMVEPYVf/Rf3OtMfmpK9tHq5HC38tELywViZYuG1ez3z1Hb4DrwNccQCbGJLZr6ib0P6Xt41JdwbA7ECQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-09T01:24:34.953572Z","bundle_sha256":"39b444a30b8ea9f86f794c4e2b5ac156cd7eb33df5622015d872d244686d8e8c"}}