{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:EOLQM7PWQ2SE3JX4DAXMFF7TBU","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":"7bd59016e2b1913c1a0156e90313f0d7caa3851f961af0909fedf161a9759f8e","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2025-10-21T13:31:02Z","title_canon_sha256":"b5135a345298206db3db9b61bd76ebba250970699da0939b323fcc55e8e6fdf8"},"schema_version":"1.0","source":{"id":"2510.18627","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2510.18627","created_at":"2026-05-22T01:03:15Z"},{"alias_kind":"arxiv_version","alias_value":"2510.18627v2","created_at":"2026-05-22T01:03:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2510.18627","created_at":"2026-05-22T01:03:15Z"},{"alias_kind":"pith_short_12","alias_value":"EOLQM7PWQ2SE","created_at":"2026-05-22T01:03:15Z"},{"alias_kind":"pith_short_16","alias_value":"EOLQM7PWQ2SE3JX4","created_at":"2026-05-22T01:03:15Z"},{"alias_kind":"pith_short_8","alias_value":"EOLQM7PW","created_at":"2026-05-22T01:03:15Z"}],"graph_snapshots":[{"event_id":"sha256:a33af10c4a286a3dda78ff32c6fed4856ac5fccdb1530dd462daad1b7191466a","target":"graph","created_at":"2026-05-22T01:03:15Z","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/2510.18627/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We present an algorithm for low rank decomposition of tensors of any symmetry type, from fully asymmetric to fully symmetric. It recovers the decomposition one summand at a time via the higher-order power method. This approach is known to fail in general: there need not be a relationship between the summands of a decomposition and the (partially symmetric) singular vector tuples (pSVTs) of the tensor. Our approach overcomes this problem by transforming the input to a tensor with orthonormal slices, via orthogonalization of a flattening. The summands of the decomposition of the original tensor ","authors_text":"Anna Seigal, Jo\\~ao M. Pereira, Joe Kileel, Kexin Wang","cross_cats":["cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2025-10-21T13:31:02Z","title":"Multi-subspace power method for decomposing partially symmetric tensors"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2510.18627","kind":"arxiv","version":2},"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":"sha256:1dc0d1e6bc2205c274bbbfa7ec1a52413daa6e4256a6377e952291b41b741a4e","target":"record","created_at":"2026-05-22T01:03:15Z","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":"7bd59016e2b1913c1a0156e90313f0d7caa3851f961af0909fedf161a9759f8e","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2025-10-21T13:31:02Z","title_canon_sha256":"b5135a345298206db3db9b61bd76ebba250970699da0939b323fcc55e8e6fdf8"},"schema_version":"1.0","source":{"id":"2510.18627","kind":"arxiv","version":2}},"canonical_sha256":"2397067df686a44da6fc182ec297f30d10cc1ac6da359c777a0ab7e6c9239102","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2397067df686a44da6fc182ec297f30d10cc1ac6da359c777a0ab7e6c9239102","first_computed_at":"2026-05-22T01:03:15.834775Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-22T01:03:15.834775Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VJu9gx51DbaGMSztqsopskYsp+FdZzubJEunidezclOqMLPH1JkPh7uA7zMRatxO0QKaya/OO4oi/kqOFKMNCA==","signature_status":"signed_v1","signed_at":"2026-05-22T01:03:15.835607Z","signed_message":"canonical_sha256_bytes"},"source_id":"2510.18627","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1dc0d1e6bc2205c274bbbfa7ec1a52413daa6e4256a6377e952291b41b741a4e","sha256:a33af10c4a286a3dda78ff32c6fed4856ac5fccdb1530dd462daad1b7191466a"],"state_sha256":"28db2186387a8712ec98bc0d073407610e5eb62069d61d62296f64d3fa8ec8f5"}