{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:C4ME62Y5JTXWEW6TUJGAE5EI5I","short_pith_number":"pith:C4ME62Y5","canonical_record":{"source":{"id":"1703.10019","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-03-29T13:13:01Z","cross_cats_sorted":["math.DG","math.OC"],"title_canon_sha256":"0c1952b6d97e9dc708c65025ec969d8ff207a5f2e51d3de53baf00b300d5e287","abstract_canon_sha256":"9703e8e30cb6ea34ef2e1171fe2712ad8214ac27d06f2b1b22c7953c782a63a7"},"schema_version":"1.0"},"canonical_sha256":"17184f6b1d4cef625bd3a24c027488ea186cc8ddc60898848a021c389f51d854","source":{"kind":"arxiv","id":"1703.10019","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.10019","created_at":"2026-05-17T23:59:33Z"},{"alias_kind":"arxiv_version","alias_value":"1703.10019v1","created_at":"2026-05-17T23:59:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.10019","created_at":"2026-05-17T23:59:33Z"},{"alias_kind":"pith_short_12","alias_value":"C4ME62Y5JTXW","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_16","alias_value":"C4ME62Y5JTXWEW6T","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_8","alias_value":"C4ME62Y5","created_at":"2026-05-18T12:31:08Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:C4ME62Y5JTXWEW6TUJGAE5EI5I","target":"record","payload":{"canonical_record":{"source":{"id":"1703.10019","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-03-29T13:13:01Z","cross_cats_sorted":["math.DG","math.OC"],"title_canon_sha256":"0c1952b6d97e9dc708c65025ec969d8ff207a5f2e51d3de53baf00b300d5e287","abstract_canon_sha256":"9703e8e30cb6ea34ef2e1171fe2712ad8214ac27d06f2b1b22c7953c782a63a7"},"schema_version":"1.0"},"canonical_sha256":"17184f6b1d4cef625bd3a24c027488ea186cc8ddc60898848a021c389f51d854","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:59:33.342364Z","signature_b64":"5xPBHPISo9n8fX96qmnGkX3vQEOt+rMP7z5/1eycO8Ig4aVuBBpqriDm1MGQ3E5ZCiP2oidVumLGxo4yyBc/Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"17184f6b1d4cef625bd3a24c027488ea186cc8ddc60898848a021c389f51d854","last_reissued_at":"2026-05-17T23:59:33.341716Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:59:33.341716Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1703.10019","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:59:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fub0e6iMFYOUVudsECMYnMssYcFHjcgRt5a2Fu+rNzD6Rww2+Bp2RRqq9npsgly0ccJlYLCwkoQgXUEuv0fWDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T05:49:43.638452Z"},"content_sha256":"4d944c09bd36b32b21815cdb5f542929b019faa7a14ed62b8fc7e9ed034d1f54","schema_version":"1.0","event_id":"sha256:4d944c09bd36b32b21815cdb5f542929b019faa7a14ed62b8fc7e9ed034d1f54"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:C4ME62Y5JTXWEW6TUJGAE5EI5I","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Riemannian trust-region method for low-rank tensor completion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG","math.OC"],"primary_cat":"math.NA","authors_text":"Gennadij Heidel, Volker Schulz","submitted_at":"2017-03-29T13:13:01Z","abstract_excerpt":"The goal of tensor completion is to fill in missing entries of a partially known tensor (possibly including some noise) under a low-rank constraint. This may be formulated as a least-squares problem. The set of tensors of a given multilinear rank is known to admit a Riemannian manifold structure, thus methods of Riemannian optimization are applicable. In our work, we derive the Riemannian Hessian of an objective function on the low-rank tensor manifolds using the Weingarten map, a concept from differential geometry. We discuss the convergence properties of Riemannian trust-region methods based"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.10019","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:59:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8u2OVS5etKhM/1c0OLwiUIll52lmB8z1vRQNFN/IU3ZfyGEZxmmLtORgQsbeQLC93f0wIhPchMyoE/TQNyYPDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T05:49:43.638984Z"},"content_sha256":"4ea1434977732be89cf7e9db825cbe198d9ba88bd5538bb0bdd8fa7b29f8c191","schema_version":"1.0","event_id":"sha256:4ea1434977732be89cf7e9db825cbe198d9ba88bd5538bb0bdd8fa7b29f8c191"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/C4ME62Y5JTXWEW6TUJGAE5EI5I/bundle.json","state_url":"https://pith.science/pith/C4ME62Y5JTXWEW6TUJGAE5EI5I/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/C4ME62Y5JTXWEW6TUJGAE5EI5I/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":"2026-06-07T05:49:43Z","links":{"resolver":"https://pith.science/pith/C4ME62Y5JTXWEW6TUJGAE5EI5I","bundle":"https://pith.science/pith/C4ME62Y5JTXWEW6TUJGAE5EI5I/bundle.json","state":"https://pith.science/pith/C4ME62Y5JTXWEW6TUJGAE5EI5I/state.json","well_known_bundle":"https://pith.science/.well-known/pith/C4ME62Y5JTXWEW6TUJGAE5EI5I/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:C4ME62Y5JTXWEW6TUJGAE5EI5I","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":"9703e8e30cb6ea34ef2e1171fe2712ad8214ac27d06f2b1b22c7953c782a63a7","cross_cats_sorted":["math.DG","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-03-29T13:13:01Z","title_canon_sha256":"0c1952b6d97e9dc708c65025ec969d8ff207a5f2e51d3de53baf00b300d5e287"},"schema_version":"1.0","source":{"id":"1703.10019","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.10019","created_at":"2026-05-17T23:59:33Z"},{"alias_kind":"arxiv_version","alias_value":"1703.10019v1","created_at":"2026-05-17T23:59:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.10019","created_at":"2026-05-17T23:59:33Z"},{"alias_kind":"pith_short_12","alias_value":"C4ME62Y5JTXW","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_16","alias_value":"C4ME62Y5JTXWEW6T","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_8","alias_value":"C4ME62Y5","created_at":"2026-05-18T12:31:08Z"}],"graph_snapshots":[{"event_id":"sha256:4ea1434977732be89cf7e9db825cbe198d9ba88bd5538bb0bdd8fa7b29f8c191","target":"graph","created_at":"2026-05-17T23:59:33Z","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 goal of tensor completion is to fill in missing entries of a partially known tensor (possibly including some noise) under a low-rank constraint. This may be formulated as a least-squares problem. The set of tensors of a given multilinear rank is known to admit a Riemannian manifold structure, thus methods of Riemannian optimization are applicable. In our work, we derive the Riemannian Hessian of an objective function on the low-rank tensor manifolds using the Weingarten map, a concept from differential geometry. We discuss the convergence properties of Riemannian trust-region methods based","authors_text":"Gennadij Heidel, Volker Schulz","cross_cats":["math.DG","math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-03-29T13:13:01Z","title":"A Riemannian trust-region method for low-rank tensor completion"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.10019","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":"sha256:4d944c09bd36b32b21815cdb5f542929b019faa7a14ed62b8fc7e9ed034d1f54","target":"record","created_at":"2026-05-17T23:59:33Z","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":"9703e8e30cb6ea34ef2e1171fe2712ad8214ac27d06f2b1b22c7953c782a63a7","cross_cats_sorted":["math.DG","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-03-29T13:13:01Z","title_canon_sha256":"0c1952b6d97e9dc708c65025ec969d8ff207a5f2e51d3de53baf00b300d5e287"},"schema_version":"1.0","source":{"id":"1703.10019","kind":"arxiv","version":1}},"canonical_sha256":"17184f6b1d4cef625bd3a24c027488ea186cc8ddc60898848a021c389f51d854","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"17184f6b1d4cef625bd3a24c027488ea186cc8ddc60898848a021c389f51d854","first_computed_at":"2026-05-17T23:59:33.341716Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:59:33.341716Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5xPBHPISo9n8fX96qmnGkX3vQEOt+rMP7z5/1eycO8Ig4aVuBBpqriDm1MGQ3E5ZCiP2oidVumLGxo4yyBc/Dw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:59:33.342364Z","signed_message":"canonical_sha256_bytes"},"source_id":"1703.10019","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4d944c09bd36b32b21815cdb5f542929b019faa7a14ed62b8fc7e9ed034d1f54","sha256:4ea1434977732be89cf7e9db825cbe198d9ba88bd5538bb0bdd8fa7b29f8c191"],"state_sha256":"9d050394376493fd4790ef854e19a61faacdfbedda644905bb7293aa33c35441"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NRKS0/XKotEDD/qwHJOeNK5OjFK7gEYLmq0ak8BmZcZOowLvn7v63jpLhNdRX79Y0NnXigRytS5/BZwT6+qKDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T05:49:43.643323Z","bundle_sha256":"3f97484735a1e563b925065ee090ab5456d30d3123791acff3a366f2c1cd4823"}}