{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:YY5PPP3FFLQRENRMPFXMYVOQYX","short_pith_number":"pith:YY5PPP3F","canonical_record":{"source":{"id":"2402.07027","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"cs.DS","submitted_at":"2024-02-10T19:21:29Z","cross_cats_sorted":["cs.ET","cs.LG","math.QA","quant-ph"],"title_canon_sha256":"d8fe8d36b96b014a9819506ae5ee82cc59e0f6b7e3152ff9a103e81e4c99c4d3","abstract_canon_sha256":"dfece1291bc77cae6d46f542bbb53e17486998f634059c7a57ddbf9599eee984"},"schema_version":"1.0"},"canonical_sha256":"c63af7bf652ae112362c796ecc55d0c5c91f6eac8681fbd4706b4acbfdbb44bc","source":{"kind":"arxiv","id":"2402.07027","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2402.07027","created_at":"2026-07-05T07:44:46Z"},{"alias_kind":"arxiv_version","alias_value":"2402.07027v1","created_at":"2026-07-05T07:44:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2402.07027","created_at":"2026-07-05T07:44:46Z"},{"alias_kind":"pith_short_12","alias_value":"YY5PPP3FFLQR","created_at":"2026-07-05T07:44:46Z"},{"alias_kind":"pith_short_16","alias_value":"YY5PPP3FFLQRENRM","created_at":"2026-07-05T07:44:46Z"},{"alias_kind":"pith_short_8","alias_value":"YY5PPP3F","created_at":"2026-07-05T07:44:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:YY5PPP3FFLQRENRMPFXMYVOQYX","target":"record","payload":{"canonical_record":{"source":{"id":"2402.07027","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"cs.DS","submitted_at":"2024-02-10T19:21:29Z","cross_cats_sorted":["cs.ET","cs.LG","math.QA","quant-ph"],"title_canon_sha256":"d8fe8d36b96b014a9819506ae5ee82cc59e0f6b7e3152ff9a103e81e4c99c4d3","abstract_canon_sha256":"dfece1291bc77cae6d46f542bbb53e17486998f634059c7a57ddbf9599eee984"},"schema_version":"1.0"},"canonical_sha256":"c63af7bf652ae112362c796ecc55d0c5c91f6eac8681fbd4706b4acbfdbb44bc","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:44:46.736750Z","signature_b64":"DWoP2cqPENwv0kLq0m5W52ypWLI7nJyWod0HZpIX4N83ttcwaMpE/EaZi6ZvIkyY3AwTanvyhd/XZ+UctnIrAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c63af7bf652ae112362c796ecc55d0c5c91f6eac8681fbd4706b4acbfdbb44bc","last_reissued_at":"2026-07-05T07:44:46.736210Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:44:46.736210Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2402.07027","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":"2026-07-05T07:44:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EFtIJoFflwZHrIfCYYefskP8DY6zDgld5FXAbwxXdxY+qZzLWW/FlNeAlO3Zx0dIbsbxVfBycE9daC9kVrjkDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T04:07:51.959305Z"},"content_sha256":"1b270cbef4f5739767be755654106800b8cb83a51d8bf6a3b72a5998d5f46bcc","schema_version":"1.0","event_id":"sha256:1b270cbef4f5739767be755654106800b8cb83a51d8bf6a3b72a5998d5f46bcc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:YY5PPP3FFLQRENRMPFXMYVOQYX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Quantum Speedup for Spectral Approximation of Kronecker Products","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":["cs.ET","cs.LG","math.QA","quant-ph"],"primary_cat":"cs.DS","authors_text":"Ruizhe Zhang, Yeqi Gao, Zhao Song","submitted_at":"2024-02-10T19:21:29Z","abstract_excerpt":"Given its widespread application in machine learning and optimization, the Kronecker product emerges as a pivotal linear algebra operator. However, its computational demands render it an expensive operation, leading to heightened costs in spectral approximation of it through traditional computation algorithms. Existing classical methods for spectral approximation exhibit a linear dependency on the matrix dimension denoted by $n$, considering matrices of size $A_1 \\in \\mathbb{R}^{n \\times d}$ and $A_2 \\in \\mathbb{R}^{n \\times d}$. Our work introduces an innovative approach to efficiently addres"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2402.07027","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/2402.07027/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":"2026-07-05T07:44:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zGfJdWC2xMRVa5jAXFCSSGdZ6/10XytgIh9mU1iVWJ63+LKVn4/X2mWg9mROWfB0ZpxvMe7mQcQaiYXbW7O3Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T04:07:51.959814Z"},"content_sha256":"f0799004613182280386408f5eb5c63963d23d08a040fc4ce11c16ab15caa4ed","schema_version":"1.0","event_id":"sha256:f0799004613182280386408f5eb5c63963d23d08a040fc4ce11c16ab15caa4ed"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YY5PPP3FFLQRENRMPFXMYVOQYX/bundle.json","state_url":"https://pith.science/pith/YY5PPP3FFLQRENRMPFXMYVOQYX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YY5PPP3FFLQRENRMPFXMYVOQYX/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":"2026-08-08T04:07:51Z","links":{"resolver":"https://pith.science/pith/YY5PPP3FFLQRENRMPFXMYVOQYX","bundle":"https://pith.science/pith/YY5PPP3FFLQRENRMPFXMYVOQYX/bundle.json","state":"https://pith.science/pith/YY5PPP3FFLQRENRMPFXMYVOQYX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YY5PPP3FFLQRENRMPFXMYVOQYX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:YY5PPP3FFLQRENRMPFXMYVOQYX","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":"dfece1291bc77cae6d46f542bbb53e17486998f634059c7a57ddbf9599eee984","cross_cats_sorted":["cs.ET","cs.LG","math.QA","quant-ph"],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"cs.DS","submitted_at":"2024-02-10T19:21:29Z","title_canon_sha256":"d8fe8d36b96b014a9819506ae5ee82cc59e0f6b7e3152ff9a103e81e4c99c4d3"},"schema_version":"1.0","source":{"id":"2402.07027","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2402.07027","created_at":"2026-07-05T07:44:46Z"},{"alias_kind":"arxiv_version","alias_value":"2402.07027v1","created_at":"2026-07-05T07:44:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2402.07027","created_at":"2026-07-05T07:44:46Z"},{"alias_kind":"pith_short_12","alias_value":"YY5PPP3FFLQR","created_at":"2026-07-05T07:44:46Z"},{"alias_kind":"pith_short_16","alias_value":"YY5PPP3FFLQRENRM","created_at":"2026-07-05T07:44:46Z"},{"alias_kind":"pith_short_8","alias_value":"YY5PPP3F","created_at":"2026-07-05T07:44:46Z"}],"graph_snapshots":[{"event_id":"sha256:f0799004613182280386408f5eb5c63963d23d08a040fc4ce11c16ab15caa4ed","target":"graph","created_at":"2026-07-05T07:44:46Z","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/2402.07027/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Given its widespread application in machine learning and optimization, the Kronecker product emerges as a pivotal linear algebra operator. However, its computational demands render it an expensive operation, leading to heightened costs in spectral approximation of it through traditional computation algorithms. Existing classical methods for spectral approximation exhibit a linear dependency on the matrix dimension denoted by $n$, considering matrices of size $A_1 \\in \\mathbb{R}^{n \\times d}$ and $A_2 \\in \\mathbb{R}^{n \\times d}$. Our work introduces an innovative approach to efficiently addres","authors_text":"Ruizhe Zhang, Yeqi Gao, Zhao Song","cross_cats":["cs.ET","cs.LG","math.QA","quant-ph"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"cs.DS","submitted_at":"2024-02-10T19:21:29Z","title":"Quantum Speedup for Spectral Approximation of Kronecker Products"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2402.07027","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":"sha256:1b270cbef4f5739767be755654106800b8cb83a51d8bf6a3b72a5998d5f46bcc","target":"record","created_at":"2026-07-05T07:44:46Z","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":"dfece1291bc77cae6d46f542bbb53e17486998f634059c7a57ddbf9599eee984","cross_cats_sorted":["cs.ET","cs.LG","math.QA","quant-ph"],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"cs.DS","submitted_at":"2024-02-10T19:21:29Z","title_canon_sha256":"d8fe8d36b96b014a9819506ae5ee82cc59e0f6b7e3152ff9a103e81e4c99c4d3"},"schema_version":"1.0","source":{"id":"2402.07027","kind":"arxiv","version":1}},"canonical_sha256":"c63af7bf652ae112362c796ecc55d0c5c91f6eac8681fbd4706b4acbfdbb44bc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c63af7bf652ae112362c796ecc55d0c5c91f6eac8681fbd4706b4acbfdbb44bc","first_computed_at":"2026-07-05T07:44:46.736210Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T07:44:46.736210Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DWoP2cqPENwv0kLq0m5W52ypWLI7nJyWod0HZpIX4N83ttcwaMpE/EaZi6ZvIkyY3AwTanvyhd/XZ+UctnIrAg==","signature_status":"signed_v1","signed_at":"2026-07-05T07:44:46.736750Z","signed_message":"canonical_sha256_bytes"},"source_id":"2402.07027","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1b270cbef4f5739767be755654106800b8cb83a51d8bf6a3b72a5998d5f46bcc","sha256:f0799004613182280386408f5eb5c63963d23d08a040fc4ce11c16ab15caa4ed"],"state_sha256":"c75a09631c8fb4aafc9831c61b23722dca867b3c6712847c26de36eac2f80c0d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5RxuPmZUxpMZgWogEJYDN6Lgrb/dEefosjgA7RN/k0OL7p89cbRFGkskKtbyCU3q1KMctSw7eiMWrCLL/zvXDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-08T04:07:51.963396Z","bundle_sha256":"600a2125ee5cb0fde29ebbc021830267bb33f5aedc14890315fe8a954619ff86"}}