{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:RT66TM7DNVKXMW6CPQR564SHDM","short_pith_number":"pith:RT66TM7D","schema_version":"1.0","canonical_sha256":"8cfde9b3e36d55765bc27c23df72471b2094349a5de7bdda4ea28c8327e567ae","source":{"kind":"arxiv","id":"1811.03813","version":1},"attestation_state":"computed","paper":{"title":"The trouble with tensor ring decompositions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.NA","authors_text":"Kim Batselier","submitted_at":"2018-11-09T08:20:43Z","abstract_excerpt":"The tensor train decomposition decomposes a tensor into a \"train\" of 3-way tensors that are interconnected through the summation of auxiliary indices. The decomposition is stable, has a well-defined notion of rank and enables the user to perform various linear algebra operations on vectors and matrices of exponential size in a computationally efficient manner. The tensor ring decomposition replaces the train by a ring through the introduction of one additional auxiliary variable. This article discusses a major issue with the tensor ring decomposition: its inability to compute an exact minimal-"},"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":"1811.03813","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NA","submitted_at":"2018-11-09T08:20:43Z","cross_cats_sorted":[],"title_canon_sha256":"029df93dd0aa9d97cf52df178ae0e3eb8827c00a2fee168fa725642cae9a8d66","abstract_canon_sha256":"206239bc6a4da756b1517eb0fe94fb4721454d8dc9486665c614e9e937871155"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:01:11.940153Z","signature_b64":"VhzypmC5tkvxMsj1VHmIx2ZMO3T9PPdstDdpYic2GooE2RiKd1FwvS4NHCqoS8bzffCInEiMavB7RjFAEUDVDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8cfde9b3e36d55765bc27c23df72471b2094349a5de7bdda4ea28c8327e567ae","last_reissued_at":"2026-05-18T00:01:11.939518Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:01:11.939518Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The trouble with tensor ring decompositions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.NA","authors_text":"Kim Batselier","submitted_at":"2018-11-09T08:20:43Z","abstract_excerpt":"The tensor train decomposition decomposes a tensor into a \"train\" of 3-way tensors that are interconnected through the summation of auxiliary indices. The decomposition is stable, has a well-defined notion of rank and enables the user to perform various linear algebra operations on vectors and matrices of exponential size in a computationally efficient manner. The tensor ring decomposition replaces the train by a ring through the introduction of one additional auxiliary variable. This article discusses a major issue with the tensor ring decomposition: its inability to compute an exact minimal-"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.03813","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"1811.03813","created_at":"2026-05-18T00:01:11.939618+00:00"},{"alias_kind":"arxiv_version","alias_value":"1811.03813v1","created_at":"2026-05-18T00:01:11.939618+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.03813","created_at":"2026-05-18T00:01:11.939618+00:00"},{"alias_kind":"pith_short_12","alias_value":"RT66TM7DNVKX","created_at":"2026-05-18T12:32:50.500415+00:00"},{"alias_kind":"pith_short_16","alias_value":"RT66TM7DNVKXMW6C","created_at":"2026-05-18T12:32:50.500415+00:00"},{"alias_kind":"pith_short_8","alias_value":"RT66TM7D","created_at":"2026-05-18T12:32:50.500415+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2605.16610","citing_title":"Tensor Cookbook: Mastering Tensors through Diagrams","ref_index":43,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/RT66TM7DNVKXMW6CPQR564SHDM","json":"https://pith.science/pith/RT66TM7DNVKXMW6CPQR564SHDM.json","graph_json":"https://pith.science/api/pith-number/RT66TM7DNVKXMW6CPQR564SHDM/graph.json","events_json":"https://pith.science/api/pith-number/RT66TM7DNVKXMW6CPQR564SHDM/events.json","paper":"https://pith.science/paper/RT66TM7D"},"agent_actions":{"view_html":"https://pith.science/pith/RT66TM7DNVKXMW6CPQR564SHDM","download_json":"https://pith.science/pith/RT66TM7DNVKXMW6CPQR564SHDM.json","view_paper":"https://pith.science/paper/RT66TM7D","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1811.03813&json=true","fetch_graph":"https://pith.science/api/pith-number/RT66TM7DNVKXMW6CPQR564SHDM/graph.json","fetch_events":"https://pith.science/api/pith-number/RT66TM7DNVKXMW6CPQR564SHDM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/RT66TM7DNVKXMW6CPQR564SHDM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/RT66TM7DNVKXMW6CPQR564SHDM/action/storage_attestation","attest_author":"https://pith.science/pith/RT66TM7DNVKXMW6CPQR564SHDM/action/author_attestation","sign_citation":"https://pith.science/pith/RT66TM7DNVKXMW6CPQR564SHDM/action/citation_signature","submit_replication":"https://pith.science/pith/RT66TM7DNVKXMW6CPQR564SHDM/action/replication_record"}},"created_at":"2026-05-18T00:01:11.939618+00:00","updated_at":"2026-05-18T00:01:11.939618+00:00"}