{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:4DQEJ3KGJG4G2GIQM6YC76YIQI","short_pith_number":"pith:4DQEJ3KG","canonical_record":{"source":{"id":"1508.03530","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CL","submitted_at":"2015-07-30T03:10:18Z","cross_cats_sorted":["physics.data-an","physics.soc-ph"],"title_canon_sha256":"1f4fe3ec6f112a390ad11df2e3dec3250d4bc9afe31836d8108251259cb37091","abstract_canon_sha256":"274f616540bff2947247e6ea29d9f8f065fe5b4d9d7416646d960053add83d2f"},"schema_version":"1.0"},"canonical_sha256":"e0e044ed4649b86d191067b02ffb08823745b28384e116a67da0bbe95df655c0","source":{"kind":"arxiv","id":"1508.03530","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.03530","created_at":"2026-05-18T01:34:15Z"},{"alias_kind":"arxiv_version","alias_value":"1508.03530v1","created_at":"2026-05-18T01:34:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.03530","created_at":"2026-05-18T01:34:15Z"},{"alias_kind":"pith_short_12","alias_value":"4DQEJ3KGJG4G","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_16","alias_value":"4DQEJ3KGJG4G2GIQ","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_8","alias_value":"4DQEJ3KG","created_at":"2026-05-18T12:29:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:4DQEJ3KGJG4G2GIQM6YC76YIQI","target":"record","payload":{"canonical_record":{"source":{"id":"1508.03530","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CL","submitted_at":"2015-07-30T03:10:18Z","cross_cats_sorted":["physics.data-an","physics.soc-ph"],"title_canon_sha256":"1f4fe3ec6f112a390ad11df2e3dec3250d4bc9afe31836d8108251259cb37091","abstract_canon_sha256":"274f616540bff2947247e6ea29d9f8f065fe5b4d9d7416646d960053add83d2f"},"schema_version":"1.0"},"canonical_sha256":"e0e044ed4649b86d191067b02ffb08823745b28384e116a67da0bbe95df655c0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:34:15.046335Z","signature_b64":"3/PyiQfJDMGTBM7uK4y+CNDxnIl8Dbs8Y3IFXE1bLKUoI4aDDFo4R14Ne2eTRWcKMb/+PoGAAka8fLD5zzOMAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e0e044ed4649b86d191067b02ffb08823745b28384e116a67da0bbe95df655c0","last_reissued_at":"2026-05-18T01:34:15.045636Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:34:15.045636Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1508.03530","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":"2026-05-18T01:34:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"C6URuW3YTmzj58fTyMa9+YGuiPpqBaHgQns9nM+Sg6+sKKMJHZu0I/LOoyeBNwVzIN9tdvT728wTS3POFvY+Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T15:23:00.387156Z"},"content_sha256":"8a2685bffafbcda97338a1e53b7fd92eb70a06d3be5ba2333f5c4c9ea12b96fa","schema_version":"1.0","event_id":"sha256:8a2685bffafbcda97338a1e53b7fd92eb70a06d3be5ba2333f5c4c9ea12b96fa"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:4DQEJ3KGJG4G2GIQM6YC76YIQI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Information-theoretical analysis of the statistical dependencies among three variables: Applications to written language","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["physics.data-an","physics.soc-ph"],"primary_cat":"cs.CL","authors_text":"Dami\\'an G. Hern\\'andez, Dami\\'an H. Zanette, In\\'es Samengo","submitted_at":"2015-07-30T03:10:18Z","abstract_excerpt":"We develop the information-theoretical concepts required to study the statistical dependencies among three variables. Some of such dependencies are pure triple interactions, in the sense that they cannot be explained in terms of a combination of pairwise correlations. We derive bounds for triple dependencies, and characterize the shape of the joint probability distribution of three binary variables with high triple interaction. The analysis also allows us to quantify the amount of redundancy in the mutual information between pairs of variables, and to assess whether the information between two"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.03530","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":"2026-05-18T01:34:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"O0gSAxiu8rwsJdc+CLNXME/2mVpDvt4p5zDWHPx99+rm1F3tB0oqsyEnrUckzzHHfO2wteiulUxWJkZ7/PnrAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T15:23:00.387537Z"},"content_sha256":"17008185a8fcc60a16b04c5c6d7a728e2fad3a9151b6e6e18ca7f535b6c28d4a","schema_version":"1.0","event_id":"sha256:17008185a8fcc60a16b04c5c6d7a728e2fad3a9151b6e6e18ca7f535b6c28d4a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4DQEJ3KGJG4G2GIQM6YC76YIQI/bundle.json","state_url":"https://pith.science/pith/4DQEJ3KGJG4G2GIQM6YC76YIQI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4DQEJ3KGJG4G2GIQM6YC76YIQI/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":"2026-06-09T15:23:00Z","links":{"resolver":"https://pith.science/pith/4DQEJ3KGJG4G2GIQM6YC76YIQI","bundle":"https://pith.science/pith/4DQEJ3KGJG4G2GIQM6YC76YIQI/bundle.json","state":"https://pith.science/pith/4DQEJ3KGJG4G2GIQM6YC76YIQI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4DQEJ3KGJG4G2GIQM6YC76YIQI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:4DQEJ3KGJG4G2GIQM6YC76YIQI","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":"274f616540bff2947247e6ea29d9f8f065fe5b4d9d7416646d960053add83d2f","cross_cats_sorted":["physics.data-an","physics.soc-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CL","submitted_at":"2015-07-30T03:10:18Z","title_canon_sha256":"1f4fe3ec6f112a390ad11df2e3dec3250d4bc9afe31836d8108251259cb37091"},"schema_version":"1.0","source":{"id":"1508.03530","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.03530","created_at":"2026-05-18T01:34:15Z"},{"alias_kind":"arxiv_version","alias_value":"1508.03530v1","created_at":"2026-05-18T01:34:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.03530","created_at":"2026-05-18T01:34:15Z"},{"alias_kind":"pith_short_12","alias_value":"4DQEJ3KGJG4G","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_16","alias_value":"4DQEJ3KGJG4G2GIQ","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_8","alias_value":"4DQEJ3KG","created_at":"2026-05-18T12:29:05Z"}],"graph_snapshots":[{"event_id":"sha256:17008185a8fcc60a16b04c5c6d7a728e2fad3a9151b6e6e18ca7f535b6c28d4a","target":"graph","created_at":"2026-05-18T01:34:15Z","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 develop the information-theoretical concepts required to study the statistical dependencies among three variables. Some of such dependencies are pure triple interactions, in the sense that they cannot be explained in terms of a combination of pairwise correlations. We derive bounds for triple dependencies, and characterize the shape of the joint probability distribution of three binary variables with high triple interaction. The analysis also allows us to quantify the amount of redundancy in the mutual information between pairs of variables, and to assess whether the information between two","authors_text":"Dami\\'an G. Hern\\'andez, Dami\\'an H. Zanette, In\\'es Samengo","cross_cats":["physics.data-an","physics.soc-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CL","submitted_at":"2015-07-30T03:10:18Z","title":"Information-theoretical analysis of the statistical dependencies among three variables: Applications to written language"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.03530","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":"sha256:8a2685bffafbcda97338a1e53b7fd92eb70a06d3be5ba2333f5c4c9ea12b96fa","target":"record","created_at":"2026-05-18T01:34:15Z","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":"274f616540bff2947247e6ea29d9f8f065fe5b4d9d7416646d960053add83d2f","cross_cats_sorted":["physics.data-an","physics.soc-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CL","submitted_at":"2015-07-30T03:10:18Z","title_canon_sha256":"1f4fe3ec6f112a390ad11df2e3dec3250d4bc9afe31836d8108251259cb37091"},"schema_version":"1.0","source":{"id":"1508.03530","kind":"arxiv","version":1}},"canonical_sha256":"e0e044ed4649b86d191067b02ffb08823745b28384e116a67da0bbe95df655c0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e0e044ed4649b86d191067b02ffb08823745b28384e116a67da0bbe95df655c0","first_computed_at":"2026-05-18T01:34:15.045636Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:34:15.045636Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3/PyiQfJDMGTBM7uK4y+CNDxnIl8Dbs8Y3IFXE1bLKUoI4aDDFo4R14Ne2eTRWcKMb/+PoGAAka8fLD5zzOMAA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:34:15.046335Z","signed_message":"canonical_sha256_bytes"},"source_id":"1508.03530","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8a2685bffafbcda97338a1e53b7fd92eb70a06d3be5ba2333f5c4c9ea12b96fa","sha256:17008185a8fcc60a16b04c5c6d7a728e2fad3a9151b6e6e18ca7f535b6c28d4a"],"state_sha256":"870056148ee41fe4c1640531f6d54377d6433887a4e565ce4cf7458d3bb5caed"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hw9kTTp5PtqvWz/Ot8QAeVl5A65wR00SGCFx/93cYtwh7AgLHuPs/2RLUH+6F8p4eRIRVvcguhuS5AzLde8mCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T15:23:00.389576Z","bundle_sha256":"d4e34c95ed0993d6900608c5441fbb0ea111d00b4f38abe76e00bba3c30ab235"}}