{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:TWEYV4SK3NSBXNBFWKLXY3OPYV","short_pith_number":"pith:TWEYV4SK","canonical_record":{"source":{"id":"1602.01246","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2016-02-03T10:11:19Z","cross_cats_sorted":[],"title_canon_sha256":"357e49e8880ec55e2c732cc70cdae814284cc4e5f0263ab4dcc8affc593eb199","abstract_canon_sha256":"cbf2ff659b7592185b78cd6b2369cc560662c5498ec1ea23e6a9c94dbecbd784"},"schema_version":"1.0"},"canonical_sha256":"9d898af24adb641bb425b2977c6dcfc54151a9ed150c3da7c9e3b3cba3644e2e","source":{"kind":"arxiv","id":"1602.01246","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.01246","created_at":"2026-05-18T01:04:28Z"},{"alias_kind":"arxiv_version","alias_value":"1602.01246v2","created_at":"2026-05-18T01:04:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.01246","created_at":"2026-05-18T01:04:28Z"},{"alias_kind":"pith_short_12","alias_value":"TWEYV4SK3NSB","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_16","alias_value":"TWEYV4SK3NSBXNBF","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_8","alias_value":"TWEYV4SK","created_at":"2026-05-18T12:30:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:TWEYV4SK3NSBXNBFWKLXY3OPYV","target":"record","payload":{"canonical_record":{"source":{"id":"1602.01246","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2016-02-03T10:11:19Z","cross_cats_sorted":[],"title_canon_sha256":"357e49e8880ec55e2c732cc70cdae814284cc4e5f0263ab4dcc8affc593eb199","abstract_canon_sha256":"cbf2ff659b7592185b78cd6b2369cc560662c5498ec1ea23e6a9c94dbecbd784"},"schema_version":"1.0"},"canonical_sha256":"9d898af24adb641bb425b2977c6dcfc54151a9ed150c3da7c9e3b3cba3644e2e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:04:28.116027Z","signature_b64":"7wMU0oibxdunJgTNN7+uPu6CRdgL/TxpvWrYgdIyXAWmGD4xAxdCTR+SfX5W/TdlRPyg0i8K/7VdvqvxFMWrCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9d898af24adb641bb425b2977c6dcfc54151a9ed150c3da7c9e3b3cba3644e2e","last_reissued_at":"2026-05-18T01:04:28.115309Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:04:28.115309Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1602.01246","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":"2026-05-18T01:04:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"N8FdJPhSZfMYo8GR+uuovdvhT/JzfvPsF/AK9GFcWGtFKDLHUkcCYZkcdmEh+jS9fyvg5IVTkMlDeZNlzfcBAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T19:21:02.795021Z"},"content_sha256":"646f22451a1730f1d2909afd7e39e6b8dda2f80152013ebf1caf3a1e6759d17f","schema_version":"1.0","event_id":"sha256:646f22451a1730f1d2909afd7e39e6b8dda2f80152013ebf1caf3a1e6759d17f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:TWEYV4SK3NSBXNBFWKLXY3OPYV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Computing with quasiseparable matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.SC","authors_text":"ARIC), Clement Pernet (UGA","submitted_at":"2016-02-03T10:11:19Z","abstract_excerpt":"The class of quasiseparable matrices is defined by a pair of bounds, called the quasiseparable orders, on the ranks of the maximal sub-matrices entirely located in their strictly lower and upper triangular parts. These arise naturally in applications, as e.g. the inverse of band matrices, and are widely used for they admit structured representations allowing to compute with them in time linear in the dimension and quadratic with the quasiseparable order. We show, in this paper, the connection between the notion of quasisepa-rability and the rank profile matrix invariant, presented in [Dumas \\&"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.01246","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":"2026-05-18T01:04:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cMRLd1TjOHQ4g5gz0iaEePVMyU2nsdaYwTQY92ypHZkQp2/7zZQUO4PrR1oynbB5h88elAYmsHQWLlSciN8NBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T19:21:02.795737Z"},"content_sha256":"935956bffac9f80d5a7f186695cac504d2c0754a5f3772043e7b7c654b1db331","schema_version":"1.0","event_id":"sha256:935956bffac9f80d5a7f186695cac504d2c0754a5f3772043e7b7c654b1db331"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TWEYV4SK3NSBXNBFWKLXY3OPYV/bundle.json","state_url":"https://pith.science/pith/TWEYV4SK3NSBXNBFWKLXY3OPYV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TWEYV4SK3NSBXNBFWKLXY3OPYV/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":"2026-06-09T19:21:02Z","links":{"resolver":"https://pith.science/pith/TWEYV4SK3NSBXNBFWKLXY3OPYV","bundle":"https://pith.science/pith/TWEYV4SK3NSBXNBFWKLXY3OPYV/bundle.json","state":"https://pith.science/pith/TWEYV4SK3NSBXNBFWKLXY3OPYV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TWEYV4SK3NSBXNBFWKLXY3OPYV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:TWEYV4SK3NSBXNBFWKLXY3OPYV","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":"cbf2ff659b7592185b78cd6b2369cc560662c5498ec1ea23e6a9c94dbecbd784","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2016-02-03T10:11:19Z","title_canon_sha256":"357e49e8880ec55e2c732cc70cdae814284cc4e5f0263ab4dcc8affc593eb199"},"schema_version":"1.0","source":{"id":"1602.01246","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.01246","created_at":"2026-05-18T01:04:28Z"},{"alias_kind":"arxiv_version","alias_value":"1602.01246v2","created_at":"2026-05-18T01:04:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.01246","created_at":"2026-05-18T01:04:28Z"},{"alias_kind":"pith_short_12","alias_value":"TWEYV4SK3NSB","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_16","alias_value":"TWEYV4SK3NSBXNBF","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_8","alias_value":"TWEYV4SK","created_at":"2026-05-18T12:30:46Z"}],"graph_snapshots":[{"event_id":"sha256:935956bffac9f80d5a7f186695cac504d2c0754a5f3772043e7b7c654b1db331","target":"graph","created_at":"2026-05-18T01:04:28Z","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":"The class of quasiseparable matrices is defined by a pair of bounds, called the quasiseparable orders, on the ranks of the maximal sub-matrices entirely located in their strictly lower and upper triangular parts. These arise naturally in applications, as e.g. the inverse of band matrices, and are widely used for they admit structured representations allowing to compute with them in time linear in the dimension and quadratic with the quasiseparable order. We show, in this paper, the connection between the notion of quasisepa-rability and the rank profile matrix invariant, presented in [Dumas \\&","authors_text":"ARIC), Clement Pernet (UGA","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2016-02-03T10:11:19Z","title":"Computing with quasiseparable matrices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.01246","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":"sha256:646f22451a1730f1d2909afd7e39e6b8dda2f80152013ebf1caf3a1e6759d17f","target":"record","created_at":"2026-05-18T01:04:28Z","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":"cbf2ff659b7592185b78cd6b2369cc560662c5498ec1ea23e6a9c94dbecbd784","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2016-02-03T10:11:19Z","title_canon_sha256":"357e49e8880ec55e2c732cc70cdae814284cc4e5f0263ab4dcc8affc593eb199"},"schema_version":"1.0","source":{"id":"1602.01246","kind":"arxiv","version":2}},"canonical_sha256":"9d898af24adb641bb425b2977c6dcfc54151a9ed150c3da7c9e3b3cba3644e2e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9d898af24adb641bb425b2977c6dcfc54151a9ed150c3da7c9e3b3cba3644e2e","first_computed_at":"2026-05-18T01:04:28.115309Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:04:28.115309Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7wMU0oibxdunJgTNN7+uPu6CRdgL/TxpvWrYgdIyXAWmGD4xAxdCTR+SfX5W/TdlRPyg0i8K/7VdvqvxFMWrCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:04:28.116027Z","signed_message":"canonical_sha256_bytes"},"source_id":"1602.01246","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:646f22451a1730f1d2909afd7e39e6b8dda2f80152013ebf1caf3a1e6759d17f","sha256:935956bffac9f80d5a7f186695cac504d2c0754a5f3772043e7b7c654b1db331"],"state_sha256":"53e6347fcbda72578cf9c2d8ddaa27a762d5739743cb5a530cc5856b102173ec"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+YeRiSNtPaxO+UC1z6P/zfHpFgmS87glXC+3fiLdYKwcWeEnE3RzA3Kjs1jFXYTNbgV9qg2qOiSDnJsuG9TDDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T19:21:02.799961Z","bundle_sha256":"f66e0fecc5b9bb5a2834743dd7ead3aaedd882dceffaeb2724ab5f972504bbfb"}}