{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:KQALSGQOHWN5V7UYMYWZCVLTTQ","short_pith_number":"pith:KQALSGQO","canonical_record":{"source":{"id":"1504.05273","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-04-21T01:26:48Z","cross_cats_sorted":[],"title_canon_sha256":"cd971fef67f45849aac657da67a035700e3b1ec4879fb879feea7a0087458c88","abstract_canon_sha256":"24cfd296860ebdd1ede33aec04a29854637148e1b4c7616c31d1fd52042bb06e"},"schema_version":"1.0"},"canonical_sha256":"5400b91a0e3d9bdafe98662d9155739c2dcbdd169391800a6701052b2494d142","source":{"kind":"arxiv","id":"1504.05273","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.05273","created_at":"2026-05-18T01:01:52Z"},{"alias_kind":"arxiv_version","alias_value":"1504.05273v3","created_at":"2026-05-18T01:01:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.05273","created_at":"2026-05-18T01:01:52Z"},{"alias_kind":"pith_short_12","alias_value":"KQALSGQOHWN5","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_16","alias_value":"KQALSGQOHWN5V7UY","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_8","alias_value":"KQALSGQO","created_at":"2026-05-18T12:29:29Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:KQALSGQOHWN5V7UYMYWZCVLTTQ","target":"record","payload":{"canonical_record":{"source":{"id":"1504.05273","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-04-21T01:26:48Z","cross_cats_sorted":[],"title_canon_sha256":"cd971fef67f45849aac657da67a035700e3b1ec4879fb879feea7a0087458c88","abstract_canon_sha256":"24cfd296860ebdd1ede33aec04a29854637148e1b4c7616c31d1fd52042bb06e"},"schema_version":"1.0"},"canonical_sha256":"5400b91a0e3d9bdafe98662d9155739c2dcbdd169391800a6701052b2494d142","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:01:52.360740Z","signature_b64":"KyhOY/CvZ85iA5L7QcThh6S0jqM+2tiIJr4kw54Fqp+mWAjFnLJSJQW3Hx960HTgyPAtu3BuhUsExvGsloiiDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5400b91a0e3d9bdafe98662d9155739c2dcbdd169391800a6701052b2494d142","last_reissued_at":"2026-05-18T01:01:52.360173Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:01:52.360173Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1504.05273","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:01:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"162LUwWywgR52WbUUtrqyYvFZSFf8mPvPTlBUgRtIqfxBE0xGV1YwrfntWyME2SCQV7f25ujgVNIA6vW8+9GAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T04:59:34.645349Z"},"content_sha256":"15b18dd8af22223553a570a935c5c6a035d94decbf745139bc9dd90e5e3f3fd8","schema_version":"1.0","event_id":"sha256:15b18dd8af22223553a570a935c5c6a035d94decbf745139bc9dd90e5e3f3fd8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:KQALSGQOHWN5V7UYMYWZCVLTTQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Low Rank Approximation of Tensors via Sparse Optimization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Carmeliza Navasca, Xiaofei Wang","submitted_at":"2015-04-21T01:26:48Z","abstract_excerpt":"The goal of this paper is to find a low-rank approximation for a given tensor. Specifically, we give a computable strategy on calculating the rank of a given tensor, based on approximating the solution to an NP-hard problem. In this paper, we formulate a sparse optimization problem via an $l_1$-regularization to find a low-rank approximation of tensors. To solve this sparse optimization problem, we propose a rescaling algorithm of the proximal alternating minimization and study the theoretical convergence of this algorithm. Furthermore, we discuss the probabilistic consistency of the sparsity "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.05273","kind":"arxiv","version":3},"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":"2026-05-18T01:01:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nWQBmkhGoJKaM3N7qgofh/PRWXUSjkkSscr45AFkHVhVFOfhCPchlOSxXCt1bClzGo59e2uv3YxVvBEVQhgXAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T04:59:34.645795Z"},"content_sha256":"b3a89cb77f518d1d5ab0960b05668b9f9d5c418c5137e054e359bbba28efa531","schema_version":"1.0","event_id":"sha256:b3a89cb77f518d1d5ab0960b05668b9f9d5c418c5137e054e359bbba28efa531"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KQALSGQOHWN5V7UYMYWZCVLTTQ/bundle.json","state_url":"https://pith.science/pith/KQALSGQOHWN5V7UYMYWZCVLTTQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KQALSGQOHWN5V7UYMYWZCVLTTQ/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":"2026-05-25T04:59:34Z","links":{"resolver":"https://pith.science/pith/KQALSGQOHWN5V7UYMYWZCVLTTQ","bundle":"https://pith.science/pith/KQALSGQOHWN5V7UYMYWZCVLTTQ/bundle.json","state":"https://pith.science/pith/KQALSGQOHWN5V7UYMYWZCVLTTQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KQALSGQOHWN5V7UYMYWZCVLTTQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:KQALSGQOHWN5V7UYMYWZCVLTTQ","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":"24cfd296860ebdd1ede33aec04a29854637148e1b4c7616c31d1fd52042bb06e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-04-21T01:26:48Z","title_canon_sha256":"cd971fef67f45849aac657da67a035700e3b1ec4879fb879feea7a0087458c88"},"schema_version":"1.0","source":{"id":"1504.05273","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.05273","created_at":"2026-05-18T01:01:52Z"},{"alias_kind":"arxiv_version","alias_value":"1504.05273v3","created_at":"2026-05-18T01:01:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.05273","created_at":"2026-05-18T01:01:52Z"},{"alias_kind":"pith_short_12","alias_value":"KQALSGQOHWN5","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_16","alias_value":"KQALSGQOHWN5V7UY","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_8","alias_value":"KQALSGQO","created_at":"2026-05-18T12:29:29Z"}],"graph_snapshots":[{"event_id":"sha256:b3a89cb77f518d1d5ab0960b05668b9f9d5c418c5137e054e359bbba28efa531","target":"graph","created_at":"2026-05-18T01:01:52Z","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 this paper is to find a low-rank approximation for a given tensor. Specifically, we give a computable strategy on calculating the rank of a given tensor, based on approximating the solution to an NP-hard problem. In this paper, we formulate a sparse optimization problem via an $l_1$-regularization to find a low-rank approximation of tensors. To solve this sparse optimization problem, we propose a rescaling algorithm of the proximal alternating minimization and study the theoretical convergence of this algorithm. Furthermore, we discuss the probabilistic consistency of the sparsity ","authors_text":"Carmeliza Navasca, Xiaofei Wang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-04-21T01:26:48Z","title":"Low Rank Approximation of Tensors via Sparse Optimization"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.05273","kind":"arxiv","version":3},"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":"sha256:15b18dd8af22223553a570a935c5c6a035d94decbf745139bc9dd90e5e3f3fd8","target":"record","created_at":"2026-05-18T01:01:52Z","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":"24cfd296860ebdd1ede33aec04a29854637148e1b4c7616c31d1fd52042bb06e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-04-21T01:26:48Z","title_canon_sha256":"cd971fef67f45849aac657da67a035700e3b1ec4879fb879feea7a0087458c88"},"schema_version":"1.0","source":{"id":"1504.05273","kind":"arxiv","version":3}},"canonical_sha256":"5400b91a0e3d9bdafe98662d9155739c2dcbdd169391800a6701052b2494d142","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5400b91a0e3d9bdafe98662d9155739c2dcbdd169391800a6701052b2494d142","first_computed_at":"2026-05-18T01:01:52.360173Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:01:52.360173Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KyhOY/CvZ85iA5L7QcThh6S0jqM+2tiIJr4kw54Fqp+mWAjFnLJSJQW3Hx960HTgyPAtu3BuhUsExvGsloiiDg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:01:52.360740Z","signed_message":"canonical_sha256_bytes"},"source_id":"1504.05273","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:15b18dd8af22223553a570a935c5c6a035d94decbf745139bc9dd90e5e3f3fd8","sha256:b3a89cb77f518d1d5ab0960b05668b9f9d5c418c5137e054e359bbba28efa531"],"state_sha256":"d4f066b8515b9909099f8241e7cc60cb59fcea6095ad4824db9a3f0c23c73e2a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"y1Zq7RSudFOQFxpP7sc3L+1bfjoM3vX1xnh1zIqZnjypor7n/vRQpKU1iQhgARS6eNybdbzZbFgSWMXlFjx+DQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T04:59:34.649325Z","bundle_sha256":"ca42456cdd94c337e88cf94b1c9d33049ba0e087eb1efef702e39fa9fb172b9d"}}