{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:PI5EYIIQN6D7BIXWIBOIKGAIZ6","short_pith_number":"pith:PI5EYIIQ","canonical_record":{"source":{"id":"2312.01715","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2023-12-04T08:14:23Z","cross_cats_sorted":["math.CO","math.OA"],"title_canon_sha256":"8170c867c1f88000c3a564a12429de1a197c2987a4145d449caa6a4af6cbbf59","abstract_canon_sha256":"f10635c0e9791675abab6b225c96081a1f3acab0335bda8217c57a17f44aa9fe"},"schema_version":"1.0"},"canonical_sha256":"7a3a4c21106f87f0a2f6405c851808cf8fcb770715c9a0e77245bce9dac01243","source":{"kind":"arxiv","id":"2312.01715","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2312.01715","created_at":"2026-07-05T10:51:03Z"},{"alias_kind":"arxiv_version","alias_value":"2312.01715v2","created_at":"2026-07-05T10:51:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2312.01715","created_at":"2026-07-05T10:51:03Z"},{"alias_kind":"pith_short_12","alias_value":"PI5EYIIQN6D7","created_at":"2026-07-05T10:51:03Z"},{"alias_kind":"pith_short_16","alias_value":"PI5EYIIQN6D7BIXW","created_at":"2026-07-05T10:51:03Z"},{"alias_kind":"pith_short_8","alias_value":"PI5EYIIQ","created_at":"2026-07-05T10:51:03Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:PI5EYIIQN6D7BIXWIBOIKGAIZ6","target":"record","payload":{"canonical_record":{"source":{"id":"2312.01715","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2023-12-04T08:14:23Z","cross_cats_sorted":["math.CO","math.OA"],"title_canon_sha256":"8170c867c1f88000c3a564a12429de1a197c2987a4145d449caa6a4af6cbbf59","abstract_canon_sha256":"f10635c0e9791675abab6b225c96081a1f3acab0335bda8217c57a17f44aa9fe"},"schema_version":"1.0"},"canonical_sha256":"7a3a4c21106f87f0a2f6405c851808cf8fcb770715c9a0e77245bce9dac01243","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:51:03.359640Z","signature_b64":"0CtM4t46drq1D/+TYF2SN/fxAPJhfEzTA91rhCKeWwPlxS7KkehqRuFI6IiSFRHD6Q0EiuEH4tERfOwrCyv1BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7a3a4c21106f87f0a2f6405c851808cf8fcb770715c9a0e77245bce9dac01243","last_reissued_at":"2026-07-05T10:51:03.359140Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:51:03.359140Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2312.01715","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":"2026-07-05T10:51:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"u7qVZXoihR3ZHTtOKw4tqP2stNLX2btTBez6D3V8AJ/colc85yrfXY58xU8NdUl8EMDBJS2ug3aHr40zK0E8DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T05:54:17.101258Z"},"content_sha256":"734a6e3084bd096e8309fecaca2961457e60179d25b29e6eceeec6519df60edc","schema_version":"1.0","event_id":"sha256:734a6e3084bd096e8309fecaca2961457e60179d25b29e6eceeec6519df60edc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:PI5EYIIQN6D7BIXWIBOIKGAIZ6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Interlacing Polynomial Method for Matrix Approximation via Generalized Column and Row Selection","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.OA"],"primary_cat":"math.FA","authors_text":"Jian-Feng Cai, Zhiqiang Xu, Zili Xu","submitted_at":"2023-12-04T08:14:23Z","abstract_excerpt":"This paper delves into the spectral norm aspect of the Generalized Column and Row Subset Selection (GCRSS) problem. Given a target matrix $\\mathbf{A}\\in \\mathbb{R}^{n\\times d}$, the objective of GCRSS is to select a column submatrix $\\mathbf{B}_{:,S}\\in\\mathbb{R}^{n\\times k}$ from the source matrix $\\mathbf{B}\\in\\mathbb{R}^{n\\times d_B}$ and a row submatrix $\\mathbf{C}_{R,:}\\in\\mathbb{R}^{r\\times d}$ from the source matrix $\\mathbf{C}\\in\\mathbb{R}^{n_C\\times d}$, such that the residual matrix $(\\mathbf{I}_n-\\mathbf{B}_{:,S}\\mathbf{B}_{:,S}^{\\dagger})\\mathbf{A}(\\mathbf{I}_d-\\mathbf{C}_{R,:}^{\\d"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2312.01715","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2312.01715/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":"2026-07-05T10:51:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hcJPtTy35bQ7IA6O3XhYNx5Gc52pQCds7NQrZYrZ+xxOVI/U9Rbh1ID5GN0cHGTZO0HvN0VC7rSBXcm3fCBVAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T05:54:17.101764Z"},"content_sha256":"a696223d63cfa045e9bb0b114da7234242b246a597add15e64723672ec40f9e1","schema_version":"1.0","event_id":"sha256:a696223d63cfa045e9bb0b114da7234242b246a597add15e64723672ec40f9e1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PI5EYIIQN6D7BIXWIBOIKGAIZ6/bundle.json","state_url":"https://pith.science/pith/PI5EYIIQN6D7BIXWIBOIKGAIZ6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PI5EYIIQN6D7BIXWIBOIKGAIZ6/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":"2026-08-05T05:54:17Z","links":{"resolver":"https://pith.science/pith/PI5EYIIQN6D7BIXWIBOIKGAIZ6","bundle":"https://pith.science/pith/PI5EYIIQN6D7BIXWIBOIKGAIZ6/bundle.json","state":"https://pith.science/pith/PI5EYIIQN6D7BIXWIBOIKGAIZ6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PI5EYIIQN6D7BIXWIBOIKGAIZ6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:PI5EYIIQN6D7BIXWIBOIKGAIZ6","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":"f10635c0e9791675abab6b225c96081a1f3acab0335bda8217c57a17f44aa9fe","cross_cats_sorted":["math.CO","math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2023-12-04T08:14:23Z","title_canon_sha256":"8170c867c1f88000c3a564a12429de1a197c2987a4145d449caa6a4af6cbbf59"},"schema_version":"1.0","source":{"id":"2312.01715","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2312.01715","created_at":"2026-07-05T10:51:03Z"},{"alias_kind":"arxiv_version","alias_value":"2312.01715v2","created_at":"2026-07-05T10:51:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2312.01715","created_at":"2026-07-05T10:51:03Z"},{"alias_kind":"pith_short_12","alias_value":"PI5EYIIQN6D7","created_at":"2026-07-05T10:51:03Z"},{"alias_kind":"pith_short_16","alias_value":"PI5EYIIQN6D7BIXW","created_at":"2026-07-05T10:51:03Z"},{"alias_kind":"pith_short_8","alias_value":"PI5EYIIQ","created_at":"2026-07-05T10:51:03Z"}],"graph_snapshots":[{"event_id":"sha256:a696223d63cfa045e9bb0b114da7234242b246a597add15e64723672ec40f9e1","target":"graph","created_at":"2026-07-05T10:51:03Z","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/2312.01715/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This paper delves into the spectral norm aspect of the Generalized Column and Row Subset Selection (GCRSS) problem. Given a target matrix $\\mathbf{A}\\in \\mathbb{R}^{n\\times d}$, the objective of GCRSS is to select a column submatrix $\\mathbf{B}_{:,S}\\in\\mathbb{R}^{n\\times k}$ from the source matrix $\\mathbf{B}\\in\\mathbb{R}^{n\\times d_B}$ and a row submatrix $\\mathbf{C}_{R,:}\\in\\mathbb{R}^{r\\times d}$ from the source matrix $\\mathbf{C}\\in\\mathbb{R}^{n_C\\times d}$, such that the residual matrix $(\\mathbf{I}_n-\\mathbf{B}_{:,S}\\mathbf{B}_{:,S}^{\\dagger})\\mathbf{A}(\\mathbf{I}_d-\\mathbf{C}_{R,:}^{\\d","authors_text":"Jian-Feng Cai, Zhiqiang Xu, Zili Xu","cross_cats":["math.CO","math.OA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2023-12-04T08:14:23Z","title":"Interlacing Polynomial Method for Matrix Approximation via Generalized Column and Row Selection"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2312.01715","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":"sha256:734a6e3084bd096e8309fecaca2961457e60179d25b29e6eceeec6519df60edc","target":"record","created_at":"2026-07-05T10:51:03Z","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":"f10635c0e9791675abab6b225c96081a1f3acab0335bda8217c57a17f44aa9fe","cross_cats_sorted":["math.CO","math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2023-12-04T08:14:23Z","title_canon_sha256":"8170c867c1f88000c3a564a12429de1a197c2987a4145d449caa6a4af6cbbf59"},"schema_version":"1.0","source":{"id":"2312.01715","kind":"arxiv","version":2}},"canonical_sha256":"7a3a4c21106f87f0a2f6405c851808cf8fcb770715c9a0e77245bce9dac01243","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7a3a4c21106f87f0a2f6405c851808cf8fcb770715c9a0e77245bce9dac01243","first_computed_at":"2026-07-05T10:51:03.359140Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:51:03.359140Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0CtM4t46drq1D/+TYF2SN/fxAPJhfEzTA91rhCKeWwPlxS7KkehqRuFI6IiSFRHD6Q0EiuEH4tERfOwrCyv1BQ==","signature_status":"signed_v1","signed_at":"2026-07-05T10:51:03.359640Z","signed_message":"canonical_sha256_bytes"},"source_id":"2312.01715","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:734a6e3084bd096e8309fecaca2961457e60179d25b29e6eceeec6519df60edc","sha256:a696223d63cfa045e9bb0b114da7234242b246a597add15e64723672ec40f9e1"],"state_sha256":"e77384fec2fa477efb46918107256a5599c8bea0ca20c634f661a62eb84cb2ce"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MGWhDp6aGWQCVWrL3HyLUIY/BYdGk0EdcXLaGLd9eTeEeGDOvbrdgKJm9DWFwTiNNaqXYkwOsyJTKlv6ortuDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-05T05:54:17.107405Z","bundle_sha256":"4bfb5efb6331ae5db44fc39f63663149382ce1061b87f798dd2779b8289e008c"}}