{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:WKWPRKFNVZYE7KUUMYPVKUQBOP","short_pith_number":"pith:WKWPRKFN","canonical_record":{"source":{"id":"2308.15106","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2023-08-29T08:14:11Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"fb3b60138f6fa47775fe66a7aee0456d98255df2e721a586ce88e9604f417af8","abstract_canon_sha256":"2ac638d8be6fb8c84a923b1ce994d1ea7b1320331246ea52585a2d6f0a1b93d4"},"schema_version":"1.0"},"canonical_sha256":"b2acf8a8adae704faa94661f55520173d116385750e252e38b6fe7677023dc3a","source":{"kind":"arxiv","id":"2308.15106","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2308.15106","created_at":"2026-07-05T06:45:43Z"},{"alias_kind":"arxiv_version","alias_value":"2308.15106v1","created_at":"2026-07-05T06:45:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2308.15106","created_at":"2026-07-05T06:45:43Z"},{"alias_kind":"pith_short_12","alias_value":"WKWPRKFNVZYE","created_at":"2026-07-05T06:45:43Z"},{"alias_kind":"pith_short_16","alias_value":"WKWPRKFNVZYE7KUU","created_at":"2026-07-05T06:45:43Z"},{"alias_kind":"pith_short_8","alias_value":"WKWPRKFN","created_at":"2026-07-05T06:45:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:WKWPRKFNVZYE7KUUMYPVKUQBOP","target":"record","payload":{"canonical_record":{"source":{"id":"2308.15106","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2023-08-29T08:14:11Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"fb3b60138f6fa47775fe66a7aee0456d98255df2e721a586ce88e9604f417af8","abstract_canon_sha256":"2ac638d8be6fb8c84a923b1ce994d1ea7b1320331246ea52585a2d6f0a1b93d4"},"schema_version":"1.0"},"canonical_sha256":"b2acf8a8adae704faa94661f55520173d116385750e252e38b6fe7677023dc3a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:45:43.600614Z","signature_b64":"W1GtkY4pCs38IfCpCSF1kJ+wm9mw9uO+rC1iSkFW4w7IWNncXuVM4zTxtHowfvZcbplrmnVlStxQg1XtEOnLDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b2acf8a8adae704faa94661f55520173d116385750e252e38b6fe7677023dc3a","last_reissued_at":"2026-07-05T06:45:43.600048Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:45:43.600048Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2308.15106","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":"2026-07-05T06:45:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TZaSWgNbhcS+o/YK8ubBX5aElc/2Dvi1Xx5xEyeZMePjqVc4rJ//sOk1fthQvLme6WVpQSvHqNCAHALuBCaWBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T08:57:17.295600Z"},"content_sha256":"daaacdbc1de1258eca309f968a11318d3c3e6ddfcb6b99e2d2ca609060831182","schema_version":"1.0","event_id":"sha256:daaacdbc1de1258eca309f968a11318d3c3e6ddfcb6b99e2d2ca609060831182"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:WKWPRKFNVZYE7KUUMYPVKUQBOP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On factorization of rank-one auto-correlation matrix polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"David Brie (CRAN), Julien Flamant (CRAN), Konstantin Usevich (CRAN), Marianne Clausel (IECL)","submitted_at":"2023-08-29T08:14:11Z","abstract_excerpt":"This article characterizes the rank-one factorization of auto-correlation matrix polynomials.  We establish a sufficient and necessary uniqueness condition for uniqueness of the factorization based on the greatest common divisor (GCD) of multiple polynomials.  In the unique case, we show that the factorization can be carried out explicitly using GCDs. In the non-unique case, the number of non-trivially different factorizations is given and all solutions are enumerated."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2308.15106","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2308.15106/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":"2026-07-05T06:45:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Nx0TUEPy93OYCORDZbzWQSQIri4ylIZJTqfm4wqJbWFzn/ABfOCj/vqh4GS/DnRYnXtPsRDTK9ccxEjhe+UBDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T08:57:17.296436Z"},"content_sha256":"a98d7ad2b980e90fd228b9fa582a594f71bc83fc86e22c4667257bbdae477461","schema_version":"1.0","event_id":"sha256:a98d7ad2b980e90fd228b9fa582a594f71bc83fc86e22c4667257bbdae477461"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WKWPRKFNVZYE7KUUMYPVKUQBOP/bundle.json","state_url":"https://pith.science/pith/WKWPRKFNVZYE7KUUMYPVKUQBOP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WKWPRKFNVZYE7KUUMYPVKUQBOP/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":"2026-08-14T08:57:17Z","links":{"resolver":"https://pith.science/pith/WKWPRKFNVZYE7KUUMYPVKUQBOP","bundle":"https://pith.science/pith/WKWPRKFNVZYE7KUUMYPVKUQBOP/bundle.json","state":"https://pith.science/pith/WKWPRKFNVZYE7KUUMYPVKUQBOP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WKWPRKFNVZYE7KUUMYPVKUQBOP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:WKWPRKFNVZYE7KUUMYPVKUQBOP","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":"2ac638d8be6fb8c84a923b1ce994d1ea7b1320331246ea52585a2d6f0a1b93d4","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2023-08-29T08:14:11Z","title_canon_sha256":"fb3b60138f6fa47775fe66a7aee0456d98255df2e721a586ce88e9604f417af8"},"schema_version":"1.0","source":{"id":"2308.15106","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2308.15106","created_at":"2026-07-05T06:45:43Z"},{"alias_kind":"arxiv_version","alias_value":"2308.15106v1","created_at":"2026-07-05T06:45:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2308.15106","created_at":"2026-07-05T06:45:43Z"},{"alias_kind":"pith_short_12","alias_value":"WKWPRKFNVZYE","created_at":"2026-07-05T06:45:43Z"},{"alias_kind":"pith_short_16","alias_value":"WKWPRKFNVZYE7KUU","created_at":"2026-07-05T06:45:43Z"},{"alias_kind":"pith_short_8","alias_value":"WKWPRKFN","created_at":"2026-07-05T06:45:43Z"}],"graph_snapshots":[{"event_id":"sha256:a98d7ad2b980e90fd228b9fa582a594f71bc83fc86e22c4667257bbdae477461","target":"graph","created_at":"2026-07-05T06:45:43Z","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/2308.15106/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This article characterizes the rank-one factorization of auto-correlation matrix polynomials.  We establish a sufficient and necessary uniqueness condition for uniqueness of the factorization based on the greatest common divisor (GCD) of multiple polynomials.  In the unique case, we show that the factorization can be carried out explicitly using GCDs. In the non-unique case, the number of non-trivially different factorizations is given and all solutions are enumerated.","authors_text":"David Brie (CRAN), Julien Flamant (CRAN), Konstantin Usevich (CRAN), Marianne Clausel (IECL)","cross_cats":["cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2023-08-29T08:14:11Z","title":"On factorization of rank-one auto-correlation matrix polynomials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2308.15106","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:daaacdbc1de1258eca309f968a11318d3c3e6ddfcb6b99e2d2ca609060831182","target":"record","created_at":"2026-07-05T06:45:43Z","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":"2ac638d8be6fb8c84a923b1ce994d1ea7b1320331246ea52585a2d6f0a1b93d4","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2023-08-29T08:14:11Z","title_canon_sha256":"fb3b60138f6fa47775fe66a7aee0456d98255df2e721a586ce88e9604f417af8"},"schema_version":"1.0","source":{"id":"2308.15106","kind":"arxiv","version":1}},"canonical_sha256":"b2acf8a8adae704faa94661f55520173d116385750e252e38b6fe7677023dc3a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b2acf8a8adae704faa94661f55520173d116385750e252e38b6fe7677023dc3a","first_computed_at":"2026-07-05T06:45:43.600048Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:45:43.600048Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"W1GtkY4pCs38IfCpCSF1kJ+wm9mw9uO+rC1iSkFW4w7IWNncXuVM4zTxtHowfvZcbplrmnVlStxQg1XtEOnLDw==","signature_status":"signed_v1","signed_at":"2026-07-05T06:45:43.600614Z","signed_message":"canonical_sha256_bytes"},"source_id":"2308.15106","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:daaacdbc1de1258eca309f968a11318d3c3e6ddfcb6b99e2d2ca609060831182","sha256:a98d7ad2b980e90fd228b9fa582a594f71bc83fc86e22c4667257bbdae477461"],"state_sha256":"8a42769f710c62a07a8253cd352a7c0759d727bfe6feb4cab88e1030d32a9266"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"r7dy+JwN5no4naDn1VwLIkVE5v1S7StsyAlgI6I0KxfBcirzti+7qb4ptN5ljSpJTg5aC2NPKQloKD+vQHevAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-14T08:57:17.303606Z","bundle_sha256":"461dc66ae0d34cc1edb93a153d3b1f0ea99f424c694c71c9020a8289a6b032d5"}}