{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:4ESXSB7PQ4P76MFLBXCDHYSZMV","short_pith_number":"pith:4ESXSB7P","canonical_record":{"source":{"id":"1202.3779","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2012-02-14T16:41:17Z","cross_cats_sorted":["stat.ML"],"title_canon_sha256":"4b785f1384e441d06a3026f84daf00d20727de72f6466a9089c7b41f994ea161","abstract_canon_sha256":"8734bd91b539ceccb074777d90e0ec51e592e895a15ce1ec9ace228b6272f7f5"},"schema_version":"1.0"},"canonical_sha256":"e1257907ef871fff30ab0dc433e259656ec72a50627c9650368634039469787c","source":{"kind":"arxiv","id":"1202.3779","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.3779","created_at":"2026-05-18T04:02:02Z"},{"alias_kind":"arxiv_version","alias_value":"1202.3779v1","created_at":"2026-05-18T04:02:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.3779","created_at":"2026-05-18T04:02:02Z"},{"alias_kind":"pith_short_12","alias_value":"4ESXSB7PQ4P7","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_16","alias_value":"4ESXSB7PQ4P76MFL","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_8","alias_value":"4ESXSB7P","created_at":"2026-05-18T12:26:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:4ESXSB7PQ4P76MFLBXCDHYSZMV","target":"record","payload":{"canonical_record":{"source":{"id":"1202.3779","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2012-02-14T16:41:17Z","cross_cats_sorted":["stat.ML"],"title_canon_sha256":"4b785f1384e441d06a3026f84daf00d20727de72f6466a9089c7b41f994ea161","abstract_canon_sha256":"8734bd91b539ceccb074777d90e0ec51e592e895a15ce1ec9ace228b6272f7f5"},"schema_version":"1.0"},"canonical_sha256":"e1257907ef871fff30ab0dc433e259656ec72a50627c9650368634039469787c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:02:02.810699Z","signature_b64":"9GN4sXqGH1l/0//dwkg7nLbUCTDRpcUjQKTz6Zg7uAx8aV5b99TrfMIF2s2Azd+dE1F6siqJI5XbB0j3iqHHBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e1257907ef871fff30ab0dc433e259656ec72a50627c9650368634039469787c","last_reissued_at":"2026-05-18T04:02:02.810122Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:02:02.810122Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1202.3779","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":"2026-05-18T04:02:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WiwECYisU1AvRF3Y8fKUyuwhMWe4IPfvk+YCzsR5S1tSOwMGTwouFh8TDqQbnuAEsOBqR4FC1Z1U/+Cv67vxBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T16:11:21.951785Z"},"content_sha256":"c4eb0d9203ad2bbb62a88080f0bdc2c3b63727f6067ff5d9c01cff6d6fc4bd22","schema_version":"1.0","event_id":"sha256:c4eb0d9203ad2bbb62a88080f0bdc2c3b63727f6067ff5d9c01cff6d6fc4bd22"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:4ESXSB7PQ4P76MFLBXCDHYSZMV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Testing whether linear equations are causal: A free probability theory approach","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ML"],"primary_cat":"cs.LG","authors_text":"Dominik Janzing, Jakob Zscheischler, Kun Zhang","submitted_at":"2012-02-14T16:41:17Z","abstract_excerpt":"We propose a method that infers whether linear relations between two high-dimensional variables X and Y are due to a causal influence from X to Y or from Y to X. The earlier proposed so-called Trace Method is extended to the regime where the dimension of the observed variables exceeds the sample size. Based on previous work, we postulate conditions that characterize a causal relation between X and Y. Moreover, we describe a statistical test and argue that both causal directions are typically rejected if there is a common cause. A full theoretical analysis is presented for the deterministic cas"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.3779","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":""},"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":"2026-05-18T04:02:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"42enHf5ucAX/NbM3ej3c2YrkBW1Ka++5XaJtggsWhocKW5GUdM16f8TXadJpKupurzX/CoZEpZW037UbnYPKDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T16:11:21.952499Z"},"content_sha256":"9197b185fb55ad1ef3dee98fb01d8c8bb653deba423698e572e73cea5c1a6d68","schema_version":"1.0","event_id":"sha256:9197b185fb55ad1ef3dee98fb01d8c8bb653deba423698e572e73cea5c1a6d68"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4ESXSB7PQ4P76MFLBXCDHYSZMV/bundle.json","state_url":"https://pith.science/pith/4ESXSB7PQ4P76MFLBXCDHYSZMV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4ESXSB7PQ4P76MFLBXCDHYSZMV/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":"2026-05-25T16:11:21Z","links":{"resolver":"https://pith.science/pith/4ESXSB7PQ4P76MFLBXCDHYSZMV","bundle":"https://pith.science/pith/4ESXSB7PQ4P76MFLBXCDHYSZMV/bundle.json","state":"https://pith.science/pith/4ESXSB7PQ4P76MFLBXCDHYSZMV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4ESXSB7PQ4P76MFLBXCDHYSZMV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:4ESXSB7PQ4P76MFLBXCDHYSZMV","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":"8734bd91b539ceccb074777d90e0ec51e592e895a15ce1ec9ace228b6272f7f5","cross_cats_sorted":["stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2012-02-14T16:41:17Z","title_canon_sha256":"4b785f1384e441d06a3026f84daf00d20727de72f6466a9089c7b41f994ea161"},"schema_version":"1.0","source":{"id":"1202.3779","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.3779","created_at":"2026-05-18T04:02:02Z"},{"alias_kind":"arxiv_version","alias_value":"1202.3779v1","created_at":"2026-05-18T04:02:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.3779","created_at":"2026-05-18T04:02:02Z"},{"alias_kind":"pith_short_12","alias_value":"4ESXSB7PQ4P7","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_16","alias_value":"4ESXSB7PQ4P76MFL","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_8","alias_value":"4ESXSB7P","created_at":"2026-05-18T12:26:53Z"}],"graph_snapshots":[{"event_id":"sha256:9197b185fb55ad1ef3dee98fb01d8c8bb653deba423698e572e73cea5c1a6d68","target":"graph","created_at":"2026-05-18T04:02:02Z","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"},"paper":{"abstract_excerpt":"We propose a method that infers whether linear relations between two high-dimensional variables X and Y are due to a causal influence from X to Y or from Y to X. The earlier proposed so-called Trace Method is extended to the regime where the dimension of the observed variables exceeds the sample size. Based on previous work, we postulate conditions that characterize a causal relation between X and Y. Moreover, we describe a statistical test and argue that both causal directions are typically rejected if there is a common cause. A full theoretical analysis is presented for the deterministic cas","authors_text":"Dominik Janzing, Jakob Zscheischler, Kun Zhang","cross_cats":["stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2012-02-14T16:41:17Z","title":"Testing whether linear equations are causal: A free probability theory approach"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.3779","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:c4eb0d9203ad2bbb62a88080f0bdc2c3b63727f6067ff5d9c01cff6d6fc4bd22","target":"record","created_at":"2026-05-18T04:02:02Z","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":"8734bd91b539ceccb074777d90e0ec51e592e895a15ce1ec9ace228b6272f7f5","cross_cats_sorted":["stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2012-02-14T16:41:17Z","title_canon_sha256":"4b785f1384e441d06a3026f84daf00d20727de72f6466a9089c7b41f994ea161"},"schema_version":"1.0","source":{"id":"1202.3779","kind":"arxiv","version":1}},"canonical_sha256":"e1257907ef871fff30ab0dc433e259656ec72a50627c9650368634039469787c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e1257907ef871fff30ab0dc433e259656ec72a50627c9650368634039469787c","first_computed_at":"2026-05-18T04:02:02.810122Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:02:02.810122Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9GN4sXqGH1l/0//dwkg7nLbUCTDRpcUjQKTz6Zg7uAx8aV5b99TrfMIF2s2Azd+dE1F6siqJI5XbB0j3iqHHBg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:02:02.810699Z","signed_message":"canonical_sha256_bytes"},"source_id":"1202.3779","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c4eb0d9203ad2bbb62a88080f0bdc2c3b63727f6067ff5d9c01cff6d6fc4bd22","sha256:9197b185fb55ad1ef3dee98fb01d8c8bb653deba423698e572e73cea5c1a6d68"],"state_sha256":"055d999eb58c3fc0404b4c029f82e642e67aa5f30ae57893d5ae40e000ebf284"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IjUuwbfT8kU0kLLRQZ3wkw1OSBR+b8xhHvRuVyBNsR15ptd+NFTZ/3gYQD24sF4LDI4TWuNhJdvPBzMW/C7VDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T16:11:21.956393Z","bundle_sha256":"08bd8f3dbf2b681db948c058066861b03c44ec3ae16a046f09a18bd764ee7eb8"}}