{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:EOLQM7PWQ2SE3JX4DAXMFF7TBU","short_pith_number":"pith:EOLQM7PW","schema_version":"1.0","canonical_sha256":"2397067df686a44da6fc182ec297f30d10cc1ac6da359c777a0ab7e6c9239102","source":{"kind":"arxiv","id":"2510.18627","version":2},"attestation_state":"computed","paper":{"title":"Multi-subspace power method for decomposing partially symmetric tensors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Anna Seigal, Jo\\~ao M. Pereira, Joe Kileel, Kexin Wang","submitted_at":"2025-10-21T13:31:02Z","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 "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2510.18627","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2025-10-21T13:31:02Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"b5135a345298206db3db9b61bd76ebba250970699da0939b323fcc55e8e6fdf8","abstract_canon_sha256":"7bd59016e2b1913c1a0156e90313f0d7caa3851f961af0909fedf161a9759f8e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-22T01:03:15.835607Z","signature_b64":"VJu9gx51DbaGMSztqsopskYsp+FdZzubJEunidezclOqMLPH1JkPh7uA7zMRatxO0QKaya/OO4oi/kqOFKMNCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2397067df686a44da6fc182ec297f30d10cc1ac6da359c777a0ab7e6c9239102","last_reissued_at":"2026-05-22T01:03:15.834775Z","signature_status":"signed_v1","first_computed_at":"2026-05-22T01:03:15.834775Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Multi-subspace power method for decomposing partially symmetric tensors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Anna Seigal, Jo\\~ao M. Pereira, Joe Kileel, Kexin Wang","submitted_at":"2025-10-21T13:31:02Z","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 "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2510.18627","kind":"arxiv","version":2},"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/2510.18627/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2510.18627","created_at":"2026-05-22T01:03:15.834883+00:00"},{"alias_kind":"arxiv_version","alias_value":"2510.18627v2","created_at":"2026-05-22T01:03:15.834883+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2510.18627","created_at":"2026-05-22T01:03:15.834883+00:00"},{"alias_kind":"pith_short_12","alias_value":"EOLQM7PWQ2SE","created_at":"2026-05-22T01:03:15.834883+00:00"},{"alias_kind":"pith_short_16","alias_value":"EOLQM7PWQ2SE3JX4","created_at":"2026-05-22T01:03:15.834883+00:00"},{"alias_kind":"pith_short_8","alias_value":"EOLQM7PW","created_at":"2026-05-22T01:03:15.834883+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2605.06854","citing_title":"Simplicial Regularizability of the Pseudo-Moment Cone and Carath\\'eodory-Type Atomic Decomposition of Moment Matrices","ref_index":34,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/EOLQM7PWQ2SE3JX4DAXMFF7TBU","json":"https://pith.science/pith/EOLQM7PWQ2SE3JX4DAXMFF7TBU.json","graph_json":"https://pith.science/api/pith-number/EOLQM7PWQ2SE3JX4DAXMFF7TBU/graph.json","events_json":"https://pith.science/api/pith-number/EOLQM7PWQ2SE3JX4DAXMFF7TBU/events.json","paper":"https://pith.science/paper/EOLQM7PW"},"agent_actions":{"view_html":"https://pith.science/pith/EOLQM7PWQ2SE3JX4DAXMFF7TBU","download_json":"https://pith.science/pith/EOLQM7PWQ2SE3JX4DAXMFF7TBU.json","view_paper":"https://pith.science/paper/EOLQM7PW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2510.18627&json=true","fetch_graph":"https://pith.science/api/pith-number/EOLQM7PWQ2SE3JX4DAXMFF7TBU/graph.json","fetch_events":"https://pith.science/api/pith-number/EOLQM7PWQ2SE3JX4DAXMFF7TBU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/EOLQM7PWQ2SE3JX4DAXMFF7TBU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/EOLQM7PWQ2SE3JX4DAXMFF7TBU/action/storage_attestation","attest_author":"https://pith.science/pith/EOLQM7PWQ2SE3JX4DAXMFF7TBU/action/author_attestation","sign_citation":"https://pith.science/pith/EOLQM7PWQ2SE3JX4DAXMFF7TBU/action/citation_signature","submit_replication":"https://pith.science/pith/EOLQM7PWQ2SE3JX4DAXMFF7TBU/action/replication_record"}},"created_at":"2026-05-22T01:03:15.834883+00:00","updated_at":"2026-05-22T01:03:15.834883+00:00"}