{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2007:QDSU5ZA3SI6LRH5XRFJSFB6G3A","short_pith_number":"pith:QDSU5ZA3","canonical_record":{"source":{"id":"math-ph/0702002","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math-ph","submitted_at":"2007-02-01T08:19:02Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"9d7b052703dcfc640d7496be209366105ab93c35f9c96f496165150805a70d28","abstract_canon_sha256":"11df70b8acfd2144d7ccb07300b9f06f2bd1c7fbd351327badd67c14de5412a5"},"schema_version":"1.0"},"canonical_sha256":"80e54ee41b923cb89fb789532287c6d80faf3dda700b430d265223108e0407f1","source":{"kind":"arxiv","id":"math-ph/0702002","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math-ph/0702002","created_at":"2026-05-18T01:23:13Z"},{"alias_kind":"arxiv_version","alias_value":"math-ph/0702002v1","created_at":"2026-05-18T01:23:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math-ph/0702002","created_at":"2026-05-18T01:23:13Z"},{"alias_kind":"pith_short_12","alias_value":"QDSU5ZA3SI6L","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_16","alias_value":"QDSU5ZA3SI6LRH5X","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_8","alias_value":"QDSU5ZA3","created_at":"2026-05-18T12:25:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2007:QDSU5ZA3SI6LRH5XRFJSFB6G3A","target":"record","payload":{"canonical_record":{"source":{"id":"math-ph/0702002","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math-ph","submitted_at":"2007-02-01T08:19:02Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"9d7b052703dcfc640d7496be209366105ab93c35f9c96f496165150805a70d28","abstract_canon_sha256":"11df70b8acfd2144d7ccb07300b9f06f2bd1c7fbd351327badd67c14de5412a5"},"schema_version":"1.0"},"canonical_sha256":"80e54ee41b923cb89fb789532287c6d80faf3dda700b430d265223108e0407f1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:23:13.154777Z","signature_b64":"u5H7Q6MHW2Lhh0sT5VgNWBzzRfzriK0b39/wjvKtBxYGWLUlTxU9Zdq9U5Hq4u1Nv/O6xgLglCm0ynrCmtMfCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"80e54ee41b923cb89fb789532287c6d80faf3dda700b430d265223108e0407f1","last_reissued_at":"2026-05-18T01:23:13.154297Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:23:13.154297Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math-ph/0702002","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":"2026-05-18T01:23:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vcITmpc5P28VDk6SrNvBHXfehY+wFjX0IGFNWfDiLGLaO2jsec7PxMY1D+GcWgQYV4hhV18ipUeItsHxuJ7GBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T01:30:13.228879Z"},"content_sha256":"5571e92ee2e12139d7a9093640f035a986513a0723492a55d9e0a9df3830aa27","schema_version":"1.0","event_id":"sha256:5571e92ee2e12139d7a9093640f035a986513a0723492a55d9e0a9df3830aa27"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2007:QDSU5ZA3SI6LRH5XRFJSFB6G3A","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Maximizing Multi-Information","license":"","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Andreas Knauf, Nihat Ay","submitted_at":"2007-02-01T08:19:02Z","abstract_excerpt":"Stochastic interdependence of a probablility distribution on a product space is measured by its Kullback-Leibler distance from the exponential family of product distributions (called multi-information). Here we investigate low-dimensional exponential families that contain the maximizers of stochastic interdependence in their closure.\n  Based on a detailed description of the structure of probablility distributions with globally maximal multi-information we obtain our main result: The exponential family of pure pair-interactions contains all global maximizers of the multi-information in its clos"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0702002","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":"2026-05-18T01:23:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"97YAKBcOkVRdSy6UtS4u78CaV9iBMhKgQpXWDyjvXtsMHxM/D/T7PWn2BvKtvm0zIuB/WjM/9roo+G9C7aJHDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T01:30:13.229223Z"},"content_sha256":"8ff358dcc0dcc5cd99c392a8ae994cdd4a0c9640c2320e33ef238f32bfe79e0b","schema_version":"1.0","event_id":"sha256:8ff358dcc0dcc5cd99c392a8ae994cdd4a0c9640c2320e33ef238f32bfe79e0b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QDSU5ZA3SI6LRH5XRFJSFB6G3A/bundle.json","state_url":"https://pith.science/pith/QDSU5ZA3SI6LRH5XRFJSFB6G3A/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QDSU5ZA3SI6LRH5XRFJSFB6G3A/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":"2026-06-03T01:30:13Z","links":{"resolver":"https://pith.science/pith/QDSU5ZA3SI6LRH5XRFJSFB6G3A","bundle":"https://pith.science/pith/QDSU5ZA3SI6LRH5XRFJSFB6G3A/bundle.json","state":"https://pith.science/pith/QDSU5ZA3SI6LRH5XRFJSFB6G3A/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QDSU5ZA3SI6LRH5XRFJSFB6G3A/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:QDSU5ZA3SI6LRH5XRFJSFB6G3A","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":"11df70b8acfd2144d7ccb07300b9f06f2bd1c7fbd351327badd67c14de5412a5","cross_cats_sorted":["math.MP"],"license":"","primary_cat":"math-ph","submitted_at":"2007-02-01T08:19:02Z","title_canon_sha256":"9d7b052703dcfc640d7496be209366105ab93c35f9c96f496165150805a70d28"},"schema_version":"1.0","source":{"id":"math-ph/0702002","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math-ph/0702002","created_at":"2026-05-18T01:23:13Z"},{"alias_kind":"arxiv_version","alias_value":"math-ph/0702002v1","created_at":"2026-05-18T01:23:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math-ph/0702002","created_at":"2026-05-18T01:23:13Z"},{"alias_kind":"pith_short_12","alias_value":"QDSU5ZA3SI6L","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_16","alias_value":"QDSU5ZA3SI6LRH5X","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_8","alias_value":"QDSU5ZA3","created_at":"2026-05-18T12:25:55Z"}],"graph_snapshots":[{"event_id":"sha256:8ff358dcc0dcc5cd99c392a8ae994cdd4a0c9640c2320e33ef238f32bfe79e0b","target":"graph","created_at":"2026-05-18T01:23:13Z","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":"Stochastic interdependence of a probablility distribution on a product space is measured by its Kullback-Leibler distance from the exponential family of product distributions (called multi-information). Here we investigate low-dimensional exponential families that contain the maximizers of stochastic interdependence in their closure.\n  Based on a detailed description of the structure of probablility distributions with globally maximal multi-information we obtain our main result: The exponential family of pure pair-interactions contains all global maximizers of the multi-information in its clos","authors_text":"Andreas Knauf, Nihat Ay","cross_cats":["math.MP"],"headline":"","license":"","primary_cat":"math-ph","submitted_at":"2007-02-01T08:19:02Z","title":"Maximizing Multi-Information"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0702002","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":"sha256:5571e92ee2e12139d7a9093640f035a986513a0723492a55d9e0a9df3830aa27","target":"record","created_at":"2026-05-18T01:23:13Z","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":"11df70b8acfd2144d7ccb07300b9f06f2bd1c7fbd351327badd67c14de5412a5","cross_cats_sorted":["math.MP"],"license":"","primary_cat":"math-ph","submitted_at":"2007-02-01T08:19:02Z","title_canon_sha256":"9d7b052703dcfc640d7496be209366105ab93c35f9c96f496165150805a70d28"},"schema_version":"1.0","source":{"id":"math-ph/0702002","kind":"arxiv","version":1}},"canonical_sha256":"80e54ee41b923cb89fb789532287c6d80faf3dda700b430d265223108e0407f1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"80e54ee41b923cb89fb789532287c6d80faf3dda700b430d265223108e0407f1","first_computed_at":"2026-05-18T01:23:13.154297Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:23:13.154297Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"u5H7Q6MHW2Lhh0sT5VgNWBzzRfzriK0b39/wjvKtBxYGWLUlTxU9Zdq9U5Hq4u1Nv/O6xgLglCm0ynrCmtMfCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:23:13.154777Z","signed_message":"canonical_sha256_bytes"},"source_id":"math-ph/0702002","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5571e92ee2e12139d7a9093640f035a986513a0723492a55d9e0a9df3830aa27","sha256:8ff358dcc0dcc5cd99c392a8ae994cdd4a0c9640c2320e33ef238f32bfe79e0b"],"state_sha256":"0605c7fb760b99e8e90154608ccce2cd90c0567a6ac32ac421487f4186fe8e98"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gf3009YVSUfLOkUZU7fJc0Ha8lFfToagx3fkfWRdlVDBfQfnHgTP39Si6RSTOA2KhSy4SI8w0v3myArnNptGBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T01:30:13.231208Z","bundle_sha256":"7d07d82266ad0ba890ec2733e50870752112a8451e5e62c6bf2259849412b73e"}}