{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:OD32OQOQALTU6PWFYPBOYYJCYG","short_pith_number":"pith:OD32OQOQ","canonical_record":{"source":{"id":"1912.04007","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-12-09T12:52:14Z","cross_cats_sorted":["cs.NA","math.OC"],"title_canon_sha256":"f3553c3688471595b476ee946e4dc30b74fa189262e3a22ca641b11e037de636","abstract_canon_sha256":"c0f396b0500af8d210a55883627b6afb03578abc746c8029f1cb6c9c14804ba8"},"schema_version":"1.0"},"canonical_sha256":"70f7a741d002e74f3ec5c3c2ec6122c181174fa6732ed8c6acf82554f52f3bf7","source":{"kind":"arxiv","id":"1912.04007","version":5},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1912.04007","created_at":"2026-07-05T10:45:01Z"},{"alias_kind":"arxiv_version","alias_value":"1912.04007v5","created_at":"2026-07-05T10:45:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1912.04007","created_at":"2026-07-05T10:45:01Z"},{"alias_kind":"pith_short_12","alias_value":"OD32OQOQALTU","created_at":"2026-07-05T10:45:01Z"},{"alias_kind":"pith_short_16","alias_value":"OD32OQOQALTU6PWF","created_at":"2026-07-05T10:45:01Z"},{"alias_kind":"pith_short_8","alias_value":"OD32OQOQ","created_at":"2026-07-05T10:45:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:OD32OQOQALTU6PWFYPBOYYJCYG","target":"record","payload":{"canonical_record":{"source":{"id":"1912.04007","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-12-09T12:52:14Z","cross_cats_sorted":["cs.NA","math.OC"],"title_canon_sha256":"f3553c3688471595b476ee946e4dc30b74fa189262e3a22ca641b11e037de636","abstract_canon_sha256":"c0f396b0500af8d210a55883627b6afb03578abc746c8029f1cb6c9c14804ba8"},"schema_version":"1.0"},"canonical_sha256":"70f7a741d002e74f3ec5c3c2ec6122c181174fa6732ed8c6acf82554f52f3bf7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:45:01.247790Z","signature_b64":"FaFro1hl500Cc59ffUWsESb4efP3M0tFp/E0w5lpREf22ry+/1UKTAahUx1bTgfMipT9He3m/pkG0eODBdrCAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"70f7a741d002e74f3ec5c3c2ec6122c181174fa6732ed8c6acf82554f52f3bf7","last_reissued_at":"2026-07-05T10:45:01.247255Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:45:01.247255Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1912.04007","source_version":5,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T10:45:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KhAVg8cZSadO56+bs086QwzN/s2ayJ1ZjmNqYrKJc6bJ5pwPGR9M39F3anuN1sJH5h2EWV2xwiVJfCy2pSQEDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T23:33:17.145294Z"},"content_sha256":"8572ea8b508fab502b6d263c9a5e0877f3cef19babbb5ba530fa00dbea25aaf5","schema_version":"1.0","event_id":"sha256:8572ea8b508fab502b6d263c9a5e0877f3cef19babbb5ba530fa00dbea25aaf5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:OD32OQOQALTU6PWFYPBOYYJCYG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Subspace power method for symmetric tensor decomposition","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math.OC"],"primary_cat":"math.NA","authors_text":"Jo\\~ao M. Pereira, Joe Kileel","submitted_at":"2019-12-09T12:52:14Z","abstract_excerpt":"We introduce the Subspace Power Method (SPM) for calculating the CP decomposition of low-rank real symmetric tensors. This algorithm calculates one new CP component at a time, alternating between applying the shifted symmetric higher-order power method (SS-HOPM) to a certain modified tensor, constructed from a matrix flattening of the original tensor; and using appropriate deflation steps. We obtain rigorous guarantees for SPM regarding convergence and global optima for input tensors of dimension $d$ and order $m$ of CP rank up to $O(d^{\\lfloor m/2\\rfloor})$, via results in classical algebraic"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1912.04007","kind":"arxiv","version":5},"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/1912.04007/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":"2026-07-05T10:45:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qEouVzPV/3OZS5aujKPJfsc3OD7JJf9HWlph7ofE6rkYl4Ff7FzvtRGLtlDzRoddnRy1umggOY7e/RT059OQBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T23:33:17.146286Z"},"content_sha256":"5e92a2ed73ef8cd758cf5e17ac6f5c74fa5bfc851e4f9bbabf0a12132bf5999e","schema_version":"1.0","event_id":"sha256:5e92a2ed73ef8cd758cf5e17ac6f5c74fa5bfc851e4f9bbabf0a12132bf5999e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OD32OQOQALTU6PWFYPBOYYJCYG/bundle.json","state_url":"https://pith.science/pith/OD32OQOQALTU6PWFYPBOYYJCYG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OD32OQOQALTU6PWFYPBOYYJCYG/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":"2026-08-08T23:33:17Z","links":{"resolver":"https://pith.science/pith/OD32OQOQALTU6PWFYPBOYYJCYG","bundle":"https://pith.science/pith/OD32OQOQALTU6PWFYPBOYYJCYG/bundle.json","state":"https://pith.science/pith/OD32OQOQALTU6PWFYPBOYYJCYG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OD32OQOQALTU6PWFYPBOYYJCYG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:OD32OQOQALTU6PWFYPBOYYJCYG","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":"c0f396b0500af8d210a55883627b6afb03578abc746c8029f1cb6c9c14804ba8","cross_cats_sorted":["cs.NA","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-12-09T12:52:14Z","title_canon_sha256":"f3553c3688471595b476ee946e4dc30b74fa189262e3a22ca641b11e037de636"},"schema_version":"1.0","source":{"id":"1912.04007","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1912.04007","created_at":"2026-07-05T10:45:01Z"},{"alias_kind":"arxiv_version","alias_value":"1912.04007v5","created_at":"2026-07-05T10:45:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1912.04007","created_at":"2026-07-05T10:45:01Z"},{"alias_kind":"pith_short_12","alias_value":"OD32OQOQALTU","created_at":"2026-07-05T10:45:01Z"},{"alias_kind":"pith_short_16","alias_value":"OD32OQOQALTU6PWF","created_at":"2026-07-05T10:45:01Z"},{"alias_kind":"pith_short_8","alias_value":"OD32OQOQ","created_at":"2026-07-05T10:45:01Z"}],"graph_snapshots":[{"event_id":"sha256:5e92a2ed73ef8cd758cf5e17ac6f5c74fa5bfc851e4f9bbabf0a12132bf5999e","target":"graph","created_at":"2026-07-05T10:45:01Z","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/1912.04007/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We introduce the Subspace Power Method (SPM) for calculating the CP decomposition of low-rank real symmetric tensors. This algorithm calculates one new CP component at a time, alternating between applying the shifted symmetric higher-order power method (SS-HOPM) to a certain modified tensor, constructed from a matrix flattening of the original tensor; and using appropriate deflation steps. We obtain rigorous guarantees for SPM regarding convergence and global optima for input tensors of dimension $d$ and order $m$ of CP rank up to $O(d^{\\lfloor m/2\\rfloor})$, via results in classical algebraic","authors_text":"Jo\\~ao M. Pereira, Joe Kileel","cross_cats":["cs.NA","math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-12-09T12:52:14Z","title":"Subspace power method for symmetric tensor decomposition"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1912.04007","kind":"arxiv","version":5},"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":"sha256:8572ea8b508fab502b6d263c9a5e0877f3cef19babbb5ba530fa00dbea25aaf5","target":"record","created_at":"2026-07-05T10:45:01Z","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":"c0f396b0500af8d210a55883627b6afb03578abc746c8029f1cb6c9c14804ba8","cross_cats_sorted":["cs.NA","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-12-09T12:52:14Z","title_canon_sha256":"f3553c3688471595b476ee946e4dc30b74fa189262e3a22ca641b11e037de636"},"schema_version":"1.0","source":{"id":"1912.04007","kind":"arxiv","version":5}},"canonical_sha256":"70f7a741d002e74f3ec5c3c2ec6122c181174fa6732ed8c6acf82554f52f3bf7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"70f7a741d002e74f3ec5c3c2ec6122c181174fa6732ed8c6acf82554f52f3bf7","first_computed_at":"2026-07-05T10:45:01.247255Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:45:01.247255Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FaFro1hl500Cc59ffUWsESb4efP3M0tFp/E0w5lpREf22ry+/1UKTAahUx1bTgfMipT9He3m/pkG0eODBdrCAw==","signature_status":"signed_v1","signed_at":"2026-07-05T10:45:01.247790Z","signed_message":"canonical_sha256_bytes"},"source_id":"1912.04007","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8572ea8b508fab502b6d263c9a5e0877f3cef19babbb5ba530fa00dbea25aaf5","sha256:5e92a2ed73ef8cd758cf5e17ac6f5c74fa5bfc851e4f9bbabf0a12132bf5999e"],"state_sha256":"42031569d437c81b2d136955541d4696a6a61a29d5649819573659ec98c00593"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hCM//Piba+Q/sY5hESs5ZKm1OC/LW3Jt2CpSTm6xWtNfSK9IRYUN7g/WKy0WARky3/zWxIkcFTxIKoQKiVzKCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-08T23:33:17.208320Z","bundle_sha256":"db856b49301377e1d95cacd2409540f7652b536e39003bf49a6900f4ea6679e8"}}