{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:FVJNZEW4ZELAP7SCXA5SAU7M3U","short_pith_number":"pith:FVJNZEW4","canonical_record":{"source":{"id":"2004.03288","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2020-04-07T11:48:45Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"ab84d8a14aeef4225c84f72a0cb786671e36ef86f9e0b04e3d2fe7b9578dcdf6","abstract_canon_sha256":"a02d8792346bf7e72d08adbcff960391071e9bc68e8b581ad6a01e29534bdf63"},"schema_version":"1.0"},"canonical_sha256":"2d52dc92dcc91607fe42b83b2053ecdd35e7d82e27668e60e1af80acf928144d","source":{"kind":"arxiv","id":"2004.03288","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2004.03288","created_at":"2026-07-05T00:53:24Z"},{"alias_kind":"arxiv_version","alias_value":"2004.03288v1","created_at":"2026-07-05T00:53:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2004.03288","created_at":"2026-07-05T00:53:24Z"},{"alias_kind":"pith_short_12","alias_value":"FVJNZEW4ZELA","created_at":"2026-07-05T00:53:24Z"},{"alias_kind":"pith_short_16","alias_value":"FVJNZEW4ZELAP7SC","created_at":"2026-07-05T00:53:24Z"},{"alias_kind":"pith_short_8","alias_value":"FVJNZEW4","created_at":"2026-07-05T00:53:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:FVJNZEW4ZELAP7SCXA5SAU7M3U","target":"record","payload":{"canonical_record":{"source":{"id":"2004.03288","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2020-04-07T11:48:45Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"ab84d8a14aeef4225c84f72a0cb786671e36ef86f9e0b04e3d2fe7b9578dcdf6","abstract_canon_sha256":"a02d8792346bf7e72d08adbcff960391071e9bc68e8b581ad6a01e29534bdf63"},"schema_version":"1.0"},"canonical_sha256":"2d52dc92dcc91607fe42b83b2053ecdd35e7d82e27668e60e1af80acf928144d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:53:24.642914Z","signature_b64":"Hk8TDbIQeGzD1GuLUPkaINTi0dfnSafPpGjBtdttW6Nmdd1zJU6bRwIVkVAEDeP1RCjSm9PfSd29XLaB7K++BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2d52dc92dcc91607fe42b83b2053ecdd35e7d82e27668e60e1af80acf928144d","last_reissued_at":"2026-07-05T00:53:24.642448Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:53:24.642448Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2004.03288","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":"2026-07-05T00:53:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Pdcd1nBK7EM+npV3bHHsVBkY/rzl6PHDNXJO5FQZ7jBmTmzy2znN2oLwpjaPghYL/Zc4A4bhAKq8MUI53w1eBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-05T10:28:00.776805Z"},"content_sha256":"a200af036caf58e4a57b64e52c59965eacd47337ad5d1c6bf593aa7ab8862373","schema_version":"1.0","event_id":"sha256:a200af036caf58e4a57b64e52c59965eacd47337ad5d1c6bf593aa7ab8862373"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:FVJNZEW4ZELAP7SCXA5SAU7M3U","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Nearly optimal scaling in the SR decomposition","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Heike Fassbender, Miroslav Rozloznik, Sanja Singer","submitted_at":"2020-04-07T11:48:45Z","abstract_excerpt":"In this paper we analyze the nearly optimal block diagonal scalings of the rows of one factor and the columns of the other factor in the triangular form of the SR decomposition. The result is a block generalization of the result of the van der Sluis about the almost optimal diagonal scalings of the general rectangular matrices."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2004.03288","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/2004.03288/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":"2026-07-05T00:53:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xsc2fGgabW4h/Yaxi3H25rLqoN12pSiONZne5IVybNOtMdecP/YPxF1b3APJw8GGyYOTyQwqBWiU/5Aco5Q8CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-05T10:28:00.777445Z"},"content_sha256":"d3e38e00dc71bdd9de01b2adef8f8492268d212c0b1eeed6839be3a41a8d0e49","schema_version":"1.0","event_id":"sha256:d3e38e00dc71bdd9de01b2adef8f8492268d212c0b1eeed6839be3a41a8d0e49"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FVJNZEW4ZELAP7SCXA5SAU7M3U/bundle.json","state_url":"https://pith.science/pith/FVJNZEW4ZELAP7SCXA5SAU7M3U/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FVJNZEW4ZELAP7SCXA5SAU7M3U/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":"2026-07-05T10:28:00Z","links":{"resolver":"https://pith.science/pith/FVJNZEW4ZELAP7SCXA5SAU7M3U","bundle":"https://pith.science/pith/FVJNZEW4ZELAP7SCXA5SAU7M3U/bundle.json","state":"https://pith.science/pith/FVJNZEW4ZELAP7SCXA5SAU7M3U/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FVJNZEW4ZELAP7SCXA5SAU7M3U/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:FVJNZEW4ZELAP7SCXA5SAU7M3U","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":"a02d8792346bf7e72d08adbcff960391071e9bc68e8b581ad6a01e29534bdf63","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2020-04-07T11:48:45Z","title_canon_sha256":"ab84d8a14aeef4225c84f72a0cb786671e36ef86f9e0b04e3d2fe7b9578dcdf6"},"schema_version":"1.0","source":{"id":"2004.03288","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2004.03288","created_at":"2026-07-05T00:53:24Z"},{"alias_kind":"arxiv_version","alias_value":"2004.03288v1","created_at":"2026-07-05T00:53:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2004.03288","created_at":"2026-07-05T00:53:24Z"},{"alias_kind":"pith_short_12","alias_value":"FVJNZEW4ZELA","created_at":"2026-07-05T00:53:24Z"},{"alias_kind":"pith_short_16","alias_value":"FVJNZEW4ZELAP7SC","created_at":"2026-07-05T00:53:24Z"},{"alias_kind":"pith_short_8","alias_value":"FVJNZEW4","created_at":"2026-07-05T00:53:24Z"}],"graph_snapshots":[{"event_id":"sha256:d3e38e00dc71bdd9de01b2adef8f8492268d212c0b1eeed6839be3a41a8d0e49","target":"graph","created_at":"2026-07-05T00:53:24Z","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/2004.03288/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper we analyze the nearly optimal block diagonal scalings of the rows of one factor and the columns of the other factor in the triangular form of the SR decomposition. The result is a block generalization of the result of the van der Sluis about the almost optimal diagonal scalings of the general rectangular matrices.","authors_text":"Heike Fassbender, Miroslav Rozloznik, Sanja Singer","cross_cats":["cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2020-04-07T11:48:45Z","title":"Nearly optimal scaling in the SR decomposition"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2004.03288","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:a200af036caf58e4a57b64e52c59965eacd47337ad5d1c6bf593aa7ab8862373","target":"record","created_at":"2026-07-05T00:53:24Z","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":"a02d8792346bf7e72d08adbcff960391071e9bc68e8b581ad6a01e29534bdf63","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2020-04-07T11:48:45Z","title_canon_sha256":"ab84d8a14aeef4225c84f72a0cb786671e36ef86f9e0b04e3d2fe7b9578dcdf6"},"schema_version":"1.0","source":{"id":"2004.03288","kind":"arxiv","version":1}},"canonical_sha256":"2d52dc92dcc91607fe42b83b2053ecdd35e7d82e27668e60e1af80acf928144d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2d52dc92dcc91607fe42b83b2053ecdd35e7d82e27668e60e1af80acf928144d","first_computed_at":"2026-07-05T00:53:24.642448Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:53:24.642448Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Hk8TDbIQeGzD1GuLUPkaINTi0dfnSafPpGjBtdttW6Nmdd1zJU6bRwIVkVAEDeP1RCjSm9PfSd29XLaB7K++BA==","signature_status":"signed_v1","signed_at":"2026-07-05T00:53:24.642914Z","signed_message":"canonical_sha256_bytes"},"source_id":"2004.03288","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a200af036caf58e4a57b64e52c59965eacd47337ad5d1c6bf593aa7ab8862373","sha256:d3e38e00dc71bdd9de01b2adef8f8492268d212c0b1eeed6839be3a41a8d0e49"],"state_sha256":"183e593f9cd2427d75208b13e8af93388865a2c3c18c8f1bde5fd6d18dcb318a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"u/bbqEYiZJbcEXf4t78dtnzWaki5bn4GGemITqTlb493mxs+Jd2FtyuwNC+wlN9Fsf1v4TaP1La903viTOTNCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-05T10:28:00.780893Z","bundle_sha256":"6807bf892dc72c2be7704649f006bc22653265c3b45ded295e38faa68ab1195a"}}