{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:R3QF7MBXRVATRFNBIOYKIAX4VW","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":"47c14f59664fdca7cc7aec45985c00947213411d2a278b835cd64d782af29cd1","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2026-07-30T20:21:49Z","title_canon_sha256":"2f2c74df5f84776d28970590703c1f3534b7d34e3fd5d40a2028b1d764c2f7d6"},"schema_version":"1.0","source":{"id":"2607.28819","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.28819","created_at":"2026-08-03T00:13:08Z"},{"alias_kind":"arxiv_version","alias_value":"2607.28819v1","created_at":"2026-08-03T00:13:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.28819","created_at":"2026-08-03T00:13:08Z"},{"alias_kind":"pith_short_12","alias_value":"R3QF7MBXRVAT","created_at":"2026-08-03T00:13:08Z"},{"alias_kind":"pith_short_16","alias_value":"R3QF7MBXRVATRFNB","created_at":"2026-08-03T00:13:08Z"},{"alias_kind":"pith_short_8","alias_value":"R3QF7MBX","created_at":"2026-08-03T00:13:08Z"}],"graph_snapshots":[{"event_id":"sha256:09b30270d67f3f504c8a5c78dca34a04986c91fa256ee10b6db89e104e794de6","target":"graph","created_at":"2026-08-03T00:13:08Z","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/2607.28819/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We define the $M$-point query problem in data streams. Given a fixed matrix $M$, the goal is to maintain a vector $x$ under turnstile updates and answer each query $u$ with an estimate $\\widehat{y}_u$ satisfying $|y_u-\\widehat{y}_u| \\leq \\varepsilon \\|x\\|_1$, where $y=Mx$. We show that if $M$ admits a factorization $M=AB$, where $A$ and $B$ have space-efficient representations, then there is a streaming algorithm using $O(\\varepsilon^{-1}\\|A\\|_{2\\rightarrow\\infty}\\|B\\|_{1\\rightarrow 1}+(\\varepsilon^{-1}\\|A\\|_{\\infty\\rightarrow\\infty}\\|B\\|_{1\\rightarrow 1})^{2/3})$ words of memory.\n  An importa","authors_text":"Jan Bulanek, Jelani Nelson, Raghu Meka, Ravi Kumar, Tamas Sarlos","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2026-07-30T20:21:49Z","title":"A Matrix Factorization Approach in Turnstile Streaming"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.28819","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:aa78eaa784527724677b2e47d66e64b61b6760d6c945cd7b346647f83e5ed803","target":"record","created_at":"2026-08-03T00:13:08Z","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":"47c14f59664fdca7cc7aec45985c00947213411d2a278b835cd64d782af29cd1","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2026-07-30T20:21:49Z","title_canon_sha256":"2f2c74df5f84776d28970590703c1f3534b7d34e3fd5d40a2028b1d764c2f7d6"},"schema_version":"1.0","source":{"id":"2607.28819","kind":"arxiv","version":1}},"canonical_sha256":"8ee05fb0378d413895a143b0a402fcada487ff99675bbad20823d6359cf122f9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8ee05fb0378d413895a143b0a402fcada487ff99675bbad20823d6359cf122f9","first_computed_at":"2026-08-03T00:13:08.032608Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-08-03T00:13:08.032608Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9t3zxSbSrlcsFHwlftNMZXhwipeYLxB7ZCHEl6QHweO4vdOEQFWDoL83jyWbYQpEmCVSbxrAYCV6LUOfTJSLCA==","signature_status":"signed_v1","signed_at":"2026-08-03T00:13:08.034978Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.28819","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:aa78eaa784527724677b2e47d66e64b61b6760d6c945cd7b346647f83e5ed803","sha256:09b30270d67f3f504c8a5c78dca34a04986c91fa256ee10b6db89e104e794de6"],"state_sha256":"e0bbd78dcd79cd069c715891e9c2f56a59403c543a3e1651366bddf6ac6a2659"}