{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:MVFROVPXVOW4FKDHMFBPHOBC5F","short_pith_number":"pith:MVFROVPX","canonical_record":{"source":{"id":"1601.01469","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-01-07T10:34:23Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"59c4a0852eae612330c82b2d91a6b80d84d371a11476c614dfa97c85d376c31e","abstract_canon_sha256":"e8d6412f3a1ee214255f01cd7a47c6d8fd2bbbe0df2fe0cbddc835ea59600314"},"schema_version":"1.0"},"canonical_sha256":"654b1755f7abadc2a8676142f3b822e94b5569477eea2cb7b792eb81d24956a8","source":{"kind":"arxiv","id":"1601.01469","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.01469","created_at":"2026-05-18T01:00:09Z"},{"alias_kind":"arxiv_version","alias_value":"1601.01469v2","created_at":"2026-05-18T01:00:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.01469","created_at":"2026-05-18T01:00:09Z"},{"alias_kind":"pith_short_12","alias_value":"MVFROVPXVOW4","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_16","alias_value":"MVFROVPXVOW4FKDH","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_8","alias_value":"MVFROVPX","created_at":"2026-05-18T12:30:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:MVFROVPXVOW4FKDHMFBPHOBC5F","target":"record","payload":{"canonical_record":{"source":{"id":"1601.01469","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-01-07T10:34:23Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"59c4a0852eae612330c82b2d91a6b80d84d371a11476c614dfa97c85d376c31e","abstract_canon_sha256":"e8d6412f3a1ee214255f01cd7a47c6d8fd2bbbe0df2fe0cbddc835ea59600314"},"schema_version":"1.0"},"canonical_sha256":"654b1755f7abadc2a8676142f3b822e94b5569477eea2cb7b792eb81d24956a8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:00:09.811022Z","signature_b64":"OvKrpxyr7OiLgHx9z9z+MD6GCLkuBS5KFVhD+ODgt4GSNN9k7uhHVNw37zuVtTrGjxKA/GKQSle2DXVXwtORAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"654b1755f7abadc2a8676142f3b822e94b5569477eea2cb7b792eb81d24956a8","last_reissued_at":"2026-05-18T01:00:09.810536Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:00:09.810536Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1601.01469","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:00:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VnYp9bCHsa9LnagoBTfB+4Rqfb4ikWWSjzRaG8VhHUjzkkFjF8YKBpZFJhAyfesVKU5928zwSPrS12pwDRDBBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T04:54:50.268236Z"},"content_sha256":"a64a294455ff99384b8dd8260f57c63a55192b21924113e0c379c6c1cf5cbf07","schema_version":"1.0","event_id":"sha256:a64a294455ff99384b8dd8260f57c63a55192b21924113e0c379c6c1cf5cbf07"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:MVFROVPXVOW4FKDHMFBPHOBC5F","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Tensor and Its Tucker Core: the Invariance Relationships","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.OC","authors_text":"Bo Jiang, Fan Yang, Shuzhong Zhang","submitted_at":"2016-01-07T10:34:23Z","abstract_excerpt":"In [13], Hillar and Lim famously demonstrated that \"multilinear (tensor) analogues of many efficiently computable problems in numerical linear algebra are NP-hard\". Despite many recent advancements, the state-of-the-art methods for computing such `tensor analogues' still suffer severely from the curse of dimensionality. In this paper we show that the Tucker core of a tensor however, retains many properties of the original tensor, including the CP rank, the border rank, the tensor Schatten quasi norms, and the Z-eigenvalues. When the core tensor is smaller than the original tensor, this propert"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.01469","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":""},"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":"2026-05-18T01:00:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tc0KRVEfQyCxNWnqDIVwlyuVIYZj0B5P2v7RUDQQ0HSoJUPJj9NcqzN+htfmG/pl57eEPqo3noh2D4UzarSfCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T04:54:50.268887Z"},"content_sha256":"c6de28c7f343acdaa63bc68c75d64a36b77402e92d6fcab6dfd2085f4a9561d6","schema_version":"1.0","event_id":"sha256:c6de28c7f343acdaa63bc68c75d64a36b77402e92d6fcab6dfd2085f4a9561d6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MVFROVPXVOW4FKDHMFBPHOBC5F/bundle.json","state_url":"https://pith.science/pith/MVFROVPXVOW4FKDHMFBPHOBC5F/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MVFROVPXVOW4FKDHMFBPHOBC5F/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":"2026-06-02T04:54:50Z","links":{"resolver":"https://pith.science/pith/MVFROVPXVOW4FKDHMFBPHOBC5F","bundle":"https://pith.science/pith/MVFROVPXVOW4FKDHMFBPHOBC5F/bundle.json","state":"https://pith.science/pith/MVFROVPXVOW4FKDHMFBPHOBC5F/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MVFROVPXVOW4FKDHMFBPHOBC5F/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:MVFROVPXVOW4FKDHMFBPHOBC5F","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":"e8d6412f3a1ee214255f01cd7a47c6d8fd2bbbe0df2fe0cbddc835ea59600314","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-01-07T10:34:23Z","title_canon_sha256":"59c4a0852eae612330c82b2d91a6b80d84d371a11476c614dfa97c85d376c31e"},"schema_version":"1.0","source":{"id":"1601.01469","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.01469","created_at":"2026-05-18T01:00:09Z"},{"alias_kind":"arxiv_version","alias_value":"1601.01469v2","created_at":"2026-05-18T01:00:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.01469","created_at":"2026-05-18T01:00:09Z"},{"alias_kind":"pith_short_12","alias_value":"MVFROVPXVOW4","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_16","alias_value":"MVFROVPXVOW4FKDH","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_8","alias_value":"MVFROVPX","created_at":"2026-05-18T12:30:32Z"}],"graph_snapshots":[{"event_id":"sha256:c6de28c7f343acdaa63bc68c75d64a36b77402e92d6fcab6dfd2085f4a9561d6","target":"graph","created_at":"2026-05-18T01:00:09Z","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":"In [13], Hillar and Lim famously demonstrated that \"multilinear (tensor) analogues of many efficiently computable problems in numerical linear algebra are NP-hard\". Despite many recent advancements, the state-of-the-art methods for computing such `tensor analogues' still suffer severely from the curse of dimensionality. In this paper we show that the Tucker core of a tensor however, retains many properties of the original tensor, including the CP rank, the border rank, the tensor Schatten quasi norms, and the Z-eigenvalues. When the core tensor is smaller than the original tensor, this propert","authors_text":"Bo Jiang, Fan Yang, Shuzhong Zhang","cross_cats":["cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-01-07T10:34:23Z","title":"Tensor and Its Tucker Core: the Invariance Relationships"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.01469","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:a64a294455ff99384b8dd8260f57c63a55192b21924113e0c379c6c1cf5cbf07","target":"record","created_at":"2026-05-18T01:00:09Z","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":"e8d6412f3a1ee214255f01cd7a47c6d8fd2bbbe0df2fe0cbddc835ea59600314","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-01-07T10:34:23Z","title_canon_sha256":"59c4a0852eae612330c82b2d91a6b80d84d371a11476c614dfa97c85d376c31e"},"schema_version":"1.0","source":{"id":"1601.01469","kind":"arxiv","version":2}},"canonical_sha256":"654b1755f7abadc2a8676142f3b822e94b5569477eea2cb7b792eb81d24956a8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"654b1755f7abadc2a8676142f3b822e94b5569477eea2cb7b792eb81d24956a8","first_computed_at":"2026-05-18T01:00:09.810536Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:00:09.810536Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OvKrpxyr7OiLgHx9z9z+MD6GCLkuBS5KFVhD+ODgt4GSNN9k7uhHVNw37zuVtTrGjxKA/GKQSle2DXVXwtORAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:00:09.811022Z","signed_message":"canonical_sha256_bytes"},"source_id":"1601.01469","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a64a294455ff99384b8dd8260f57c63a55192b21924113e0c379c6c1cf5cbf07","sha256:c6de28c7f343acdaa63bc68c75d64a36b77402e92d6fcab6dfd2085f4a9561d6"],"state_sha256":"d525b3da9bb19fc7035dd123529ef649956ac4114b3fc8598b5454d3053b3269"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vMn/4cCoiN2cPKc/s642FHQePhqVx+KZHlcAQg/P9Qpjw0JIlxTbzAvQH+zUip9JoN+3d5U5PgCkTjTkpdEKAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T04:54:50.271858Z","bundle_sha256":"4b26e4ccedd6745482cb5f00f07f333a4863750a593f6aedba09c39ca5501fd4"}}