{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:KLFVBWFYUEDR67LDXFHPCBWLHM","short_pith_number":"pith:KLFVBWFY","canonical_record":{"source":{"id":"1309.1773","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-09-06T20:32:20Z","cross_cats_sorted":[],"title_canon_sha256":"9aa5279886cd1ef9667be0cb88dfe3fd59ff56abfc077fca2dd6e95f65720434","abstract_canon_sha256":"54dac60555a02cdfa95d026d360a819dce7e944da7de7ac79ba0c6d15d626948"},"schema_version":"1.0"},"canonical_sha256":"52cb50d8b8a1071f7d63b94ef106cb3b21db35e50c01fb6b17a4189145e32065","source":{"kind":"arxiv","id":"1309.1773","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.1773","created_at":"2026-05-18T01:26:58Z"},{"alias_kind":"arxiv_version","alias_value":"1309.1773v3","created_at":"2026-05-18T01:26:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.1773","created_at":"2026-05-18T01:26:58Z"},{"alias_kind":"pith_short_12","alias_value":"KLFVBWFYUEDR","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_16","alias_value":"KLFVBWFYUEDR67LD","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_8","alias_value":"KLFVBWFY","created_at":"2026-05-18T12:27:51Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:KLFVBWFYUEDR67LDXFHPCBWLHM","target":"record","payload":{"canonical_record":{"source":{"id":"1309.1773","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-09-06T20:32:20Z","cross_cats_sorted":[],"title_canon_sha256":"9aa5279886cd1ef9667be0cb88dfe3fd59ff56abfc077fca2dd6e95f65720434","abstract_canon_sha256":"54dac60555a02cdfa95d026d360a819dce7e944da7de7ac79ba0c6d15d626948"},"schema_version":"1.0"},"canonical_sha256":"52cb50d8b8a1071f7d63b94ef106cb3b21db35e50c01fb6b17a4189145e32065","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:26:58.560038Z","signature_b64":"rx9uM7a92iIJUmYBfYuRt8JQF428od/X91O0/E8AM+9r6j9TwXjWJzDZmTvxMln8GhayIazw+pzT57SEktLGCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"52cb50d8b8a1071f7d63b94ef106cb3b21db35e50c01fb6b17a4189145e32065","last_reissued_at":"2026-05-18T01:26:58.559450Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:26:58.559450Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1309.1773","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":"2026-05-18T01:26:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"l/g70VV7GGLOl+K+/x00j4MpbEoy7QVfEruTnUi0j5ITyjWtGEsumvbNMw35vkWi5v6k0FopcgZ+86m3S5XDBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T16:28:55.582343Z"},"content_sha256":"ae9341fc832114e06ba4ab18c150c7cbf01fe82fb5bbc85578c049d3ee6a1b12","schema_version":"1.0","event_id":"sha256:ae9341fc832114e06ba4ab18c150c7cbf01fe82fb5bbc85578c049d3ee6a1b12"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:KLFVBWFYUEDR67LDXFHPCBWLHM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Iterative representing set selection for nested cross approximation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"A. Yu Mikhalev, I. V. Oseledets","submitted_at":"2013-09-06T20:32:20Z","abstract_excerpt":"A new fast algebraic method for obtaining an $\\mathcal{H}^2$-approximation of a matrix from its entries is presented. The main idea behind the method is based on the nested representation and the maximum-volume principle to select submatrices in low-rank matrices. A special iterative approach for the computation of so-called representing sets is established. The main advantage of the method is that it uses only the hierarchical partitioning of the matrix and does not require special \"proxy surfaces\" to be selected in advance.\n  The numerical experiments for the electrostatic problem and for th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.1773","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":"2026-05-18T01:26:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cLDkUZhNS1Ub8cPC1zSawigiCSe6f8nS6jredH53J3/O6hdp1u4WEEN7/0fYiPjMDJNoCLMqNWWi76U1HwVGBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T16:28:55.582681Z"},"content_sha256":"1b533ef5cd4fca36927f67dd6cbb15cfe4e95e493e1252f07c92e15e9485b47e","schema_version":"1.0","event_id":"sha256:1b533ef5cd4fca36927f67dd6cbb15cfe4e95e493e1252f07c92e15e9485b47e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KLFVBWFYUEDR67LDXFHPCBWLHM/bundle.json","state_url":"https://pith.science/pith/KLFVBWFYUEDR67LDXFHPCBWLHM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KLFVBWFYUEDR67LDXFHPCBWLHM/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":"2026-06-27T16:28:55Z","links":{"resolver":"https://pith.science/pith/KLFVBWFYUEDR67LDXFHPCBWLHM","bundle":"https://pith.science/pith/KLFVBWFYUEDR67LDXFHPCBWLHM/bundle.json","state":"https://pith.science/pith/KLFVBWFYUEDR67LDXFHPCBWLHM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KLFVBWFYUEDR67LDXFHPCBWLHM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:KLFVBWFYUEDR67LDXFHPCBWLHM","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":"54dac60555a02cdfa95d026d360a819dce7e944da7de7ac79ba0c6d15d626948","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-09-06T20:32:20Z","title_canon_sha256":"9aa5279886cd1ef9667be0cb88dfe3fd59ff56abfc077fca2dd6e95f65720434"},"schema_version":"1.0","source":{"id":"1309.1773","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.1773","created_at":"2026-05-18T01:26:58Z"},{"alias_kind":"arxiv_version","alias_value":"1309.1773v3","created_at":"2026-05-18T01:26:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.1773","created_at":"2026-05-18T01:26:58Z"},{"alias_kind":"pith_short_12","alias_value":"KLFVBWFYUEDR","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_16","alias_value":"KLFVBWFYUEDR67LD","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_8","alias_value":"KLFVBWFY","created_at":"2026-05-18T12:27:51Z"}],"graph_snapshots":[{"event_id":"sha256:1b533ef5cd4fca36927f67dd6cbb15cfe4e95e493e1252f07c92e15e9485b47e","target":"graph","created_at":"2026-05-18T01:26:58Z","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":"A new fast algebraic method for obtaining an $\\mathcal{H}^2$-approximation of a matrix from its entries is presented. The main idea behind the method is based on the nested representation and the maximum-volume principle to select submatrices in low-rank matrices. A special iterative approach for the computation of so-called representing sets is established. The main advantage of the method is that it uses only the hierarchical partitioning of the matrix and does not require special \"proxy surfaces\" to be selected in advance.\n  The numerical experiments for the electrostatic problem and for th","authors_text":"A. Yu Mikhalev, I. V. Oseledets","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-09-06T20:32:20Z","title":"Iterative representing set selection for nested cross approximation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.1773","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:ae9341fc832114e06ba4ab18c150c7cbf01fe82fb5bbc85578c049d3ee6a1b12","target":"record","created_at":"2026-05-18T01:26:58Z","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":"54dac60555a02cdfa95d026d360a819dce7e944da7de7ac79ba0c6d15d626948","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-09-06T20:32:20Z","title_canon_sha256":"9aa5279886cd1ef9667be0cb88dfe3fd59ff56abfc077fca2dd6e95f65720434"},"schema_version":"1.0","source":{"id":"1309.1773","kind":"arxiv","version":3}},"canonical_sha256":"52cb50d8b8a1071f7d63b94ef106cb3b21db35e50c01fb6b17a4189145e32065","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"52cb50d8b8a1071f7d63b94ef106cb3b21db35e50c01fb6b17a4189145e32065","first_computed_at":"2026-05-18T01:26:58.559450Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:26:58.559450Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rx9uM7a92iIJUmYBfYuRt8JQF428od/X91O0/E8AM+9r6j9TwXjWJzDZmTvxMln8GhayIazw+pzT57SEktLGCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:26:58.560038Z","signed_message":"canonical_sha256_bytes"},"source_id":"1309.1773","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ae9341fc832114e06ba4ab18c150c7cbf01fe82fb5bbc85578c049d3ee6a1b12","sha256:1b533ef5cd4fca36927f67dd6cbb15cfe4e95e493e1252f07c92e15e9485b47e"],"state_sha256":"2108e166d71e7053e710e82e6eb5167ba81405340fbf91f141739a619210263a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Hhvd0dRc32rIDAcbNlTbCTKSpYNPA/FpiQFVTq8v29wW4B1QMBqlqWzJcQOg2CzwPnW/YIYu3UIc64XKCZmFAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T16:28:55.584644Z","bundle_sha256":"6acecab3ff67b0cf57870717aa1b31eed5b9363f11be94d673838a5aed35b4ae"}}