{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:5NNYJYJ3LDITJ6SRNCZMXGJ4QB","short_pith_number":"pith:5NNYJYJ3","canonical_record":{"source":{"id":"1608.06613","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-08-23T19:33:23Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"87a9ece3df5d743fb3981e2a475be03f740bb8e863cd75c7e13cc211ae7ce8e8","abstract_canon_sha256":"da655a490401a8bfb8ead219b32f6521fda2228ffbd55016b20c51067dd28290"},"schema_version":"1.0"},"canonical_sha256":"eb5b84e13b58d134fa5168b2cb993c804295c620779bc8e3ddc881f60c7a2b34","source":{"kind":"arxiv","id":"1608.06613","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.06613","created_at":"2026-05-18T01:06:20Z"},{"alias_kind":"arxiv_version","alias_value":"1608.06613v2","created_at":"2026-05-18T01:06:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.06613","created_at":"2026-05-18T01:06:20Z"},{"alias_kind":"pith_short_12","alias_value":"5NNYJYJ3LDIT","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_16","alias_value":"5NNYJYJ3LDITJ6SR","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_8","alias_value":"5NNYJYJ3","created_at":"2026-05-18T12:30:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:5NNYJYJ3LDITJ6SRNCZMXGJ4QB","target":"record","payload":{"canonical_record":{"source":{"id":"1608.06613","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-08-23T19:33:23Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"87a9ece3df5d743fb3981e2a475be03f740bb8e863cd75c7e13cc211ae7ce8e8","abstract_canon_sha256":"da655a490401a8bfb8ead219b32f6521fda2228ffbd55016b20c51067dd28290"},"schema_version":"1.0"},"canonical_sha256":"eb5b84e13b58d134fa5168b2cb993c804295c620779bc8e3ddc881f60c7a2b34","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:06:20.320190Z","signature_b64":"GGXIWzL9p9Jp+pyaViSgZqCjYGbWX0a1KZUGfpjHcM7U1zWvOAVtfMDQWNoGqNLDGR4vy/2QG8VeBZ66WPA4AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"eb5b84e13b58d134fa5168b2cb993c804295c620779bc8e3ddc881f60c7a2b34","last_reissued_at":"2026-05-18T01:06:20.319556Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:06:20.319556Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1608.06613","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:06:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0kO6VmpMng8Ca5cnoLRcYCheh7u52OL7V4TttuGJxF3KmHwXhGp7P9GjLDQgHaHOpGQmPvaxXtj++rZ0noGoDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T19:02:02.775674Z"},"content_sha256":"3d2a53a2dd7b0492a2306c494bf80af28f4d161fbcb297bc9af4462b1fb7c166","schema_version":"1.0","event_id":"sha256:3d2a53a2dd7b0492a2306c494bf80af28f4d161fbcb297bc9af4462b1fb7c166"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:5NNYJYJ3LDITJ6SRNCZMXGJ4QB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Diagonality Measures of Hermitian Positive-Definite Matrices with Application to the Approximate Joint Diagonalization Problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Khaled Alyani, Maher Moakher, Marco Congedo","submitted_at":"2016-08-23T19:33:23Z","abstract_excerpt":"In this paper, we introduce properly-invariant diagonality measures of Hermitian positive-definite matrices. These diagonality measures are defined as distances or divergences between a given positive-definite matrix and its diagonal part. We then give closed-form expressions of these diagonality measures and discuss their invariance properties. The diagonality measure based on the log-determinant $\\alpha$-divergence is general enough as it includes a diagonality criterion used by the signal processing community as a special case. These diagonality measures are then used to formulate minimizat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.06613","kind":"arxiv","version":2},"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":"2026-05-18T01:06:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fEDQ0ExwUCjMZXpCnYm1c+xpxfAd+uAvA3o5S/CLZdPrjZYlW544e77ePKLr6e38LcaNoW00Het4uHb2VuinDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T19:02:02.776019Z"},"content_sha256":"a5badc43f147277b1d9929fb1498bb4f95071d3b893ed1691eb34827d3d70dbb","schema_version":"1.0","event_id":"sha256:a5badc43f147277b1d9929fb1498bb4f95071d3b893ed1691eb34827d3d70dbb"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5NNYJYJ3LDITJ6SRNCZMXGJ4QB/bundle.json","state_url":"https://pith.science/pith/5NNYJYJ3LDITJ6SRNCZMXGJ4QB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5NNYJYJ3LDITJ6SRNCZMXGJ4QB/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":"2026-06-29T19:02:02Z","links":{"resolver":"https://pith.science/pith/5NNYJYJ3LDITJ6SRNCZMXGJ4QB","bundle":"https://pith.science/pith/5NNYJYJ3LDITJ6SRNCZMXGJ4QB/bundle.json","state":"https://pith.science/pith/5NNYJYJ3LDITJ6SRNCZMXGJ4QB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5NNYJYJ3LDITJ6SRNCZMXGJ4QB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:5NNYJYJ3LDITJ6SRNCZMXGJ4QB","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":"da655a490401a8bfb8ead219b32f6521fda2228ffbd55016b20c51067dd28290","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-08-23T19:33:23Z","title_canon_sha256":"87a9ece3df5d743fb3981e2a475be03f740bb8e863cd75c7e13cc211ae7ce8e8"},"schema_version":"1.0","source":{"id":"1608.06613","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.06613","created_at":"2026-05-18T01:06:20Z"},{"alias_kind":"arxiv_version","alias_value":"1608.06613v2","created_at":"2026-05-18T01:06:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.06613","created_at":"2026-05-18T01:06:20Z"},{"alias_kind":"pith_short_12","alias_value":"5NNYJYJ3LDIT","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_16","alias_value":"5NNYJYJ3LDITJ6SR","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_8","alias_value":"5NNYJYJ3","created_at":"2026-05-18T12:30:01Z"}],"graph_snapshots":[{"event_id":"sha256:a5badc43f147277b1d9929fb1498bb4f95071d3b893ed1691eb34827d3d70dbb","target":"graph","created_at":"2026-05-18T01:06:20Z","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":"In this paper, we introduce properly-invariant diagonality measures of Hermitian positive-definite matrices. These diagonality measures are defined as distances or divergences between a given positive-definite matrix and its diagonal part. We then give closed-form expressions of these diagonality measures and discuss their invariance properties. The diagonality measure based on the log-determinant $\\alpha$-divergence is general enough as it includes a diagonality criterion used by the signal processing community as a special case. These diagonality measures are then used to formulate minimizat","authors_text":"Khaled Alyani, Maher Moakher, Marco Congedo","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-08-23T19:33:23Z","title":"Diagonality Measures of Hermitian Positive-Definite Matrices with Application to the Approximate Joint Diagonalization Problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.06613","kind":"arxiv","version":2},"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":"sha256:3d2a53a2dd7b0492a2306c494bf80af28f4d161fbcb297bc9af4462b1fb7c166","target":"record","created_at":"2026-05-18T01:06:20Z","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":"da655a490401a8bfb8ead219b32f6521fda2228ffbd55016b20c51067dd28290","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-08-23T19:33:23Z","title_canon_sha256":"87a9ece3df5d743fb3981e2a475be03f740bb8e863cd75c7e13cc211ae7ce8e8"},"schema_version":"1.0","source":{"id":"1608.06613","kind":"arxiv","version":2}},"canonical_sha256":"eb5b84e13b58d134fa5168b2cb993c804295c620779bc8e3ddc881f60c7a2b34","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"eb5b84e13b58d134fa5168b2cb993c804295c620779bc8e3ddc881f60c7a2b34","first_computed_at":"2026-05-18T01:06:20.319556Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:06:20.319556Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GGXIWzL9p9Jp+pyaViSgZqCjYGbWX0a1KZUGfpjHcM7U1zWvOAVtfMDQWNoGqNLDGR4vy/2QG8VeBZ66WPA4AA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:06:20.320190Z","signed_message":"canonical_sha256_bytes"},"source_id":"1608.06613","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3d2a53a2dd7b0492a2306c494bf80af28f4d161fbcb297bc9af4462b1fb7c166","sha256:a5badc43f147277b1d9929fb1498bb4f95071d3b893ed1691eb34827d3d70dbb"],"state_sha256":"5007b2322b74607c486e3bebb067b582787bb328f5a13fb532abd42853b52dfb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"koZzZdPj+F8QLGqwKaHOEZK6udI9l70GZjDC+kjRV9nwmCSe0KQXQ8lWtENjDaIimKyW7dCzvFq11Q/SOQrLDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-29T19:02:02.777850Z","bundle_sha256":"38e8ffca2ae553e2c69291b9b2a3ebf4f560185f75f1fb6e1cd0fab1e81e5eeb"}}