{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:RT66TM7DNVKXMW6CPQR564SHDM","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":"206239bc6a4da756b1517eb0fe94fb4721454d8dc9486665c614e9e937871155","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NA","submitted_at":"2018-11-09T08:20:43Z","title_canon_sha256":"029df93dd0aa9d97cf52df178ae0e3eb8827c00a2fee168fa725642cae9a8d66"},"schema_version":"1.0","source":{"id":"1811.03813","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.03813","created_at":"2026-05-18T00:01:11Z"},{"alias_kind":"arxiv_version","alias_value":"1811.03813v1","created_at":"2026-05-18T00:01:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.03813","created_at":"2026-05-18T00:01:11Z"},{"alias_kind":"pith_short_12","alias_value":"RT66TM7DNVKX","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_16","alias_value":"RT66TM7DNVKXMW6C","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_8","alias_value":"RT66TM7D","created_at":"2026-05-18T12:32:50Z"}],"graph_snapshots":[{"event_id":"sha256:2c47bb5ad2269af0b819896bcb9f339596fbdd617c1bc281a85b299ebbc6e535","target":"graph","created_at":"2026-05-18T00:01:11Z","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"},"paper":{"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-","authors_text":"Kim Batselier","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NA","submitted_at":"2018-11-09T08:20:43Z","title":"The trouble with tensor ring decompositions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.03813","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":"sha256:23867db780d9e2af536395c608cc937942edcece8187d2d210214e3045547885","target":"record","created_at":"2026-05-18T00:01:11Z","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":"206239bc6a4da756b1517eb0fe94fb4721454d8dc9486665c614e9e937871155","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NA","submitted_at":"2018-11-09T08:20:43Z","title_canon_sha256":"029df93dd0aa9d97cf52df178ae0e3eb8827c00a2fee168fa725642cae9a8d66"},"schema_version":"1.0","source":{"id":"1811.03813","kind":"arxiv","version":1}},"canonical_sha256":"8cfde9b3e36d55765bc27c23df72471b2094349a5de7bdda4ea28c8327e567ae","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8cfde9b3e36d55765bc27c23df72471b2094349a5de7bdda4ea28c8327e567ae","first_computed_at":"2026-05-18T00:01:11.939518Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:01:11.939518Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VhzypmC5tkvxMsj1VHmIx2ZMO3T9PPdstDdpYic2GooE2RiKd1FwvS4NHCqoS8bzffCInEiMavB7RjFAEUDVDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:01:11.940153Z","signed_message":"canonical_sha256_bytes"},"source_id":"1811.03813","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:23867db780d9e2af536395c608cc937942edcece8187d2d210214e3045547885","sha256:2c47bb5ad2269af0b819896bcb9f339596fbdd617c1bc281a85b299ebbc6e535"],"state_sha256":"e822ea4ca93b701306c16a71a7bd3e1f862571ea86db9826c0aa8790353ab33c"}