{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:S5RQ44RORBIK7625AS6TBX5MAV","short_pith_number":"pith:S5RQ44RO","canonical_record":{"source":{"id":"1609.09493","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2016-09-29T11:49:35Z","cross_cats_sorted":["math.NA"],"title_canon_sha256":"e8c8d42e79feb2776b33e5daec5d647e9174eef352bd16a8e1cafdae0dae19bc","abstract_canon_sha256":"41c8a6a5cb82119739f9eca5c26d9f23c816eda17cdbd580e976ffd0c1313d6b"},"schema_version":"1.0"},"canonical_sha256":"97630e722e8850affb5d04bd30dfac055a98d6be2e9fb09be3be96fd9db5c751","source":{"kind":"arxiv","id":"1609.09493","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.09493","created_at":"2026-05-18T00:49:42Z"},{"alias_kind":"arxiv_version","alias_value":"1609.09493v3","created_at":"2026-05-18T00:49:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.09493","created_at":"2026-05-18T00:49:42Z"},{"alias_kind":"pith_short_12","alias_value":"S5RQ44RORBIK","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_16","alias_value":"S5RQ44RORBIK7625","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_8","alias_value":"S5RQ44RO","created_at":"2026-05-18T12:30:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:S5RQ44RORBIK7625AS6TBX5MAV","target":"record","payload":{"canonical_record":{"source":{"id":"1609.09493","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2016-09-29T11:49:35Z","cross_cats_sorted":["math.NA"],"title_canon_sha256":"e8c8d42e79feb2776b33e5daec5d647e9174eef352bd16a8e1cafdae0dae19bc","abstract_canon_sha256":"41c8a6a5cb82119739f9eca5c26d9f23c816eda17cdbd580e976ffd0c1313d6b"},"schema_version":"1.0"},"canonical_sha256":"97630e722e8850affb5d04bd30dfac055a98d6be2e9fb09be3be96fd9db5c751","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:49:42.056322Z","signature_b64":"p04KomkulTfH1zk5aXyG5jgLJO8GmxDBKp4pD8Ia3FcddkJ1znUyja5AeIOdHWqAExtgZPYvNs1DuxI3ny3tDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"97630e722e8850affb5d04bd30dfac055a98d6be2e9fb09be3be96fd9db5c751","last_reissued_at":"2026-05-18T00:49:42.055865Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:49:42.055865Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1609.09493","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:49:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pZuxbNTCKkMAiNa+Nkm9IV1V5LHqw8pO7DpqRSV5x6qf8SgHphbYgp/ZZFq8QmPOGuiQAzE5ijJazk06KtIGDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-05T07:08:26.819210Z"},"content_sha256":"4a6ba76e0fcb6f3d825e8ff7b142c3d3ed404a7a22737a73c828e25355257a6a","schema_version":"1.0","event_id":"sha256:4a6ba76e0fcb6f3d825e8ff7b142c3d3ed404a7a22737a73c828e25355257a6a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:S5RQ44RORBIK7625AS6TBX5MAV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On vector spaces of linearizations for matrix polynomials in orthogonal bases","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NA"],"primary_cat":"math.RA","authors_text":"Heike Fa{\\ss}bender, Philip Saltenberger","submitted_at":"2016-09-29T11:49:35Z","abstract_excerpt":"Matrix polynomials given in an orthogonal basis are considered. Following the ideas of Mackey et al. \"Vector spaces of Linearizations for Matrix Polynomials\" (2006), the vec- tor spaces, called M1(P), M2(P) and DM(P), of potential linearizations for P are analyzed. All pencils in M1(P) are characterized concisely. Moreover, several easy to check criteria whether a pencil in M1(P) is a (strong) linearization of P are given. The equivalence of some of them to the Z-rank-condition (see Mackey et al. 2006) is pointed out. Results on the vector space dimensions, the genericity of linearizations in "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.09493","kind":"arxiv","version":3},"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":"2026-05-18T00:49:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"h7Xi20EYmQjsr8w6P/t3Pw2ryZGeV1dcN5czfGnz6ZpawBrPHxpaaAPnB8WIBF2RouGaawGx8VotPO6c7E19CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-05T07:08:26.819571Z"},"content_sha256":"39c83bf12a5c4e73d05432db5b05992c80dcb9e3bc409b82255ef7fcfa048771","schema_version":"1.0","event_id":"sha256:39c83bf12a5c4e73d05432db5b05992c80dcb9e3bc409b82255ef7fcfa048771"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/S5RQ44RORBIK7625AS6TBX5MAV/bundle.json","state_url":"https://pith.science/pith/S5RQ44RORBIK7625AS6TBX5MAV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/S5RQ44RORBIK7625AS6TBX5MAV/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":"2026-07-05T07:08:26Z","links":{"resolver":"https://pith.science/pith/S5RQ44RORBIK7625AS6TBX5MAV","bundle":"https://pith.science/pith/S5RQ44RORBIK7625AS6TBX5MAV/bundle.json","state":"https://pith.science/pith/S5RQ44RORBIK7625AS6TBX5MAV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/S5RQ44RORBIK7625AS6TBX5MAV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:S5RQ44RORBIK7625AS6TBX5MAV","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":"41c8a6a5cb82119739f9eca5c26d9f23c816eda17cdbd580e976ffd0c1313d6b","cross_cats_sorted":["math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2016-09-29T11:49:35Z","title_canon_sha256":"e8c8d42e79feb2776b33e5daec5d647e9174eef352bd16a8e1cafdae0dae19bc"},"schema_version":"1.0","source":{"id":"1609.09493","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.09493","created_at":"2026-05-18T00:49:42Z"},{"alias_kind":"arxiv_version","alias_value":"1609.09493v3","created_at":"2026-05-18T00:49:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.09493","created_at":"2026-05-18T00:49:42Z"},{"alias_kind":"pith_short_12","alias_value":"S5RQ44RORBIK","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_16","alias_value":"S5RQ44RORBIK7625","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_8","alias_value":"S5RQ44RO","created_at":"2026-05-18T12:30:41Z"}],"graph_snapshots":[{"event_id":"sha256:39c83bf12a5c4e73d05432db5b05992c80dcb9e3bc409b82255ef7fcfa048771","target":"graph","created_at":"2026-05-18T00:49:42Z","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":"Matrix polynomials given in an orthogonal basis are considered. Following the ideas of Mackey et al. \"Vector spaces of Linearizations for Matrix Polynomials\" (2006), the vec- tor spaces, called M1(P), M2(P) and DM(P), of potential linearizations for P are analyzed. All pencils in M1(P) are characterized concisely. Moreover, several easy to check criteria whether a pencil in M1(P) is a (strong) linearization of P are given. The equivalence of some of them to the Z-rank-condition (see Mackey et al. 2006) is pointed out. Results on the vector space dimensions, the genericity of linearizations in ","authors_text":"Heike Fa{\\ss}bender, Philip Saltenberger","cross_cats":["math.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2016-09-29T11:49:35Z","title":"On vector spaces of linearizations for matrix polynomials in orthogonal bases"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.09493","kind":"arxiv","version":3},"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":"sha256:4a6ba76e0fcb6f3d825e8ff7b142c3d3ed404a7a22737a73c828e25355257a6a","target":"record","created_at":"2026-05-18T00:49:42Z","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":"41c8a6a5cb82119739f9eca5c26d9f23c816eda17cdbd580e976ffd0c1313d6b","cross_cats_sorted":["math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2016-09-29T11:49:35Z","title_canon_sha256":"e8c8d42e79feb2776b33e5daec5d647e9174eef352bd16a8e1cafdae0dae19bc"},"schema_version":"1.0","source":{"id":"1609.09493","kind":"arxiv","version":3}},"canonical_sha256":"97630e722e8850affb5d04bd30dfac055a98d6be2e9fb09be3be96fd9db5c751","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"97630e722e8850affb5d04bd30dfac055a98d6be2e9fb09be3be96fd9db5c751","first_computed_at":"2026-05-18T00:49:42.055865Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:49:42.055865Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"p04KomkulTfH1zk5aXyG5jgLJO8GmxDBKp4pD8Ia3FcddkJ1znUyja5AeIOdHWqAExtgZPYvNs1DuxI3ny3tDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:49:42.056322Z","signed_message":"canonical_sha256_bytes"},"source_id":"1609.09493","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4a6ba76e0fcb6f3d825e8ff7b142c3d3ed404a7a22737a73c828e25355257a6a","sha256:39c83bf12a5c4e73d05432db5b05992c80dcb9e3bc409b82255ef7fcfa048771"],"state_sha256":"c26aa59457901223dd1298a361f9e6e8ba4cd7379411ce4a2cc94843752bdfd9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Dn7xBK86vYLtgXvtNlpYI7TChNKPBsVFP8whcqcK91VUqDXcyDjfvwM/SnMRckxhl7SeFLMoSO8tDm4fgsN1Bg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-05T07:08:26.821434Z","bundle_sha256":"55256404dcf26e6827f555cf47fb7d5662087f3a903d7bccb342121f707b3348"}}