{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:P5MXZ2JUDNMIJRQZXDA7MHV77R","merge_version":"pith-open-graph-merge-v1","event_count":4,"valid_event_count":4,"invalid_event_count":0,"equivocation_count":1,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"e3d951d2cf98142bf9794e7758dc6be4c910a9a45805db6f4771e66bcb31ee56","cross_cats_sorted":["cs.DS","math.FA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CR","submitted_at":"2026-07-30T14:41:34Z","title_canon_sha256":"dae76e1f60ed7bfa0dfe1b2cd2fbf5ab9b6853b6edd9e626b8bfc2ae660b94ff"},"schema_version":"1.0","source":{"id":"2607.28703","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.28703","created_at":"2026-08-03T00:12:13Z"},{"alias_kind":"arxiv_version","alias_value":"2607.28703v1","created_at":"2026-08-03T00:12:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.28703","created_at":"2026-08-03T00:12:13Z"},{"alias_kind":"pith_short_12","alias_value":"P5MXZ2JUDNMI","created_at":"2026-08-03T00:12:13Z"},{"alias_kind":"pith_short_16","alias_value":"P5MXZ2JUDNMIJRQZ","created_at":"2026-08-03T00:12:13Z"},{"alias_kind":"pith_short_8","alias_value":"P5MXZ2JU","created_at":"2026-08-03T00:12:13Z"}],"graph_snapshots":[{"event_id":"sha256:8854c7d77b842fcb8a951d8ea53e8c93962aafc7245e795812b020bb5e476646","target":"graph","created_at":"2026-08-03T00:12:13Z","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/2607.28703/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let \\(T_n\\) be the lower-triangular prefix-sum matrix and let \\(\\cfrob(T_n)\\) and \\(\\ctwo(T_n)\\) be the factorization costs that govern mean and maximum per-coordinate squared error of the Laplace matrix mechanism under pure \\(\\eps\\)-differential privacy, for \\(\\eps>0\\). We prove \\(\\cfrob(T_n),\\ctwo(T_n)=\\Theta\\bigl((\\log(n+1))^{3/2}\\bigr)\\) with no sign, sparsity, or squareness restriction and with arbitrary finite inner dimension. Consequently, within the pure-\\(\\eps\\)-DP matrix-mechanism class the optimized maximum and mean squared errors are both \\(\\Theta(\\eps^{-2}\\log^{3}(n+1))\\). Under t","authors_text":"Awnon Bhowmik, Mahmudul Hasan","cross_cats":["cs.DS","math.FA"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CR","submitted_at":"2026-07-30T14:41:34Z","title":"Costs of Arbitrary Real Matrix Factorizations for Pure-DP Continual Counting"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.28703","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":"sha256:76ccf61a226e8d360797c65d53cf01c75a5659739df1253b973b4a53a555cbe9","target":"record","created_at":"2026-08-03T00:12:13Z","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":"e3d951d2cf98142bf9794e7758dc6be4c910a9a45805db6f4771e66bcb31ee56","cross_cats_sorted":["cs.DS","math.FA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CR","submitted_at":"2026-07-30T14:41:34Z","title_canon_sha256":"dae76e1f60ed7bfa0dfe1b2cd2fbf5ab9b6853b6edd9e626b8bfc2ae660b94ff"},"schema_version":"1.0","source":{"id":"2607.28703","kind":"arxiv","version":1}},"canonical_sha256":"7f597ce9341b5884c619b8c1f61ebffc6578a2ee4905fb6f6568e60d31a26cd8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7f597ce9341b5884c619b8c1f61ebffc6578a2ee4905fb6f6568e60d31a26cd8","first_computed_at":"2026-08-03T00:12:13.350003Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-08-03T00:12:13.350003Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZN4CSwY8tFad5JGXnXvGGmjP56bK6+IY+VgaTJ0GkKrUkXeTRjwWYQqsnEXbuHGckR8ToJDwTYaBpBTvC8qGBw==","signature_status":"signed_v1","signed_at":"2026-08-03T00:12:13.352249Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.28703","source_kind":"arxiv","source_version":1}}},"equivocations":[{"signer_id":"pith.science","event_type":"integrity_finding","target":"integrity","event_ids":["sha256:9b4b97cc8633afab3878fa79e708dd284e2a2b9bacdb829650107c70f7270d86","sha256:a342616caa877a5fc1f12ef3c8fceb7d0e29c01670ce241d9952f201cf29bba8"]}],"invalid_events":[],"applied_event_ids":["sha256:76ccf61a226e8d360797c65d53cf01c75a5659739df1253b973b4a53a555cbe9","sha256:8854c7d77b842fcb8a951d8ea53e8c93962aafc7245e795812b020bb5e476646"],"state_sha256":"13b3f3a92872f5e7c5a9ee0ea2182d5687eaf03c191a20f28e45c4dc08d08166"}