{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:WHZBPOHDQIET4NSGQ4CEQG3IKH","short_pith_number":"pith:WHZBPOHD","canonical_record":{"source":{"id":"1008.2804","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2010-08-17T02:04:28Z","cross_cats_sorted":[],"title_canon_sha256":"535e26d8e5fed4514af774eafac53dce4be3778ca5790a08278b1509fca7f1e4","abstract_canon_sha256":"1247349d46a0e59d6efd5debd6abfaa856fc0b4380504c286559aafe37753297"},"schema_version":"1.0"},"canonical_sha256":"b1f217b8e382093e36468704481b6851fef9c802fda22377633402f4fdcb5513","source":{"kind":"arxiv","id":"1008.2804","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1008.2804","created_at":"2026-05-18T04:31:51Z"},{"alias_kind":"arxiv_version","alias_value":"1008.2804v2","created_at":"2026-05-18T04:31:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1008.2804","created_at":"2026-05-18T04:31:51Z"},{"alias_kind":"pith_short_12","alias_value":"WHZBPOHDQIET","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_16","alias_value":"WHZBPOHDQIET4NSG","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_8","alias_value":"WHZBPOHD","created_at":"2026-05-18T12:26:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:WHZBPOHDQIET4NSGQ4CEQG3IKH","target":"record","payload":{"canonical_record":{"source":{"id":"1008.2804","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2010-08-17T02:04:28Z","cross_cats_sorted":[],"title_canon_sha256":"535e26d8e5fed4514af774eafac53dce4be3778ca5790a08278b1509fca7f1e4","abstract_canon_sha256":"1247349d46a0e59d6efd5debd6abfaa856fc0b4380504c286559aafe37753297"},"schema_version":"1.0"},"canonical_sha256":"b1f217b8e382093e36468704481b6851fef9c802fda22377633402f4fdcb5513","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:31:51.453267Z","signature_b64":"g3zur6lUHa194xynkPA7N1ZAfhGKJaSg07SHxOygMcmAcG02Bi/1te3F1cV+Rgkk2RNVH9l/UJw6FgFYUVgsCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b1f217b8e382093e36468704481b6851fef9c802fda22377633402f4fdcb5513","last_reissued_at":"2026-05-18T04:31:51.452562Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:31:51.452562Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1008.2804","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":"2026-05-18T04:31:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"O1UcUvnMdlOwocie0eF5VBfC2oXc3d6CRLfu/iS7MA51QbQg3wDJajqhGAS31s4/MqVpqJTZ4X54AKQ7JVlEAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T10:36:28.744436Z"},"content_sha256":"a1f53eea04530ced03510019d91282dfc7e7113317c78a708c243cb65fac83d8","schema_version":"1.0","event_id":"sha256:a1f53eea04530ced03510019d91282dfc7e7113317c78a708c243cb65fac83d8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:WHZBPOHDQIET4NSGQ4CEQG3IKH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Dimension Reduction Scheme for the Computation of Optimal Unions of Subspaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Akram Aldroubi, Carlos Cabrelli, Magal\\'i Anastasio, Ursula Molter","submitted_at":"2010-08-17T02:04:28Z","abstract_excerpt":"Given a set of points \\F in a high dimensional space, the problem of finding a union of subspaces \\cup_i V_i\\subset \\R^N that best explains the data \\F increases dramatically with the dimension of \\R^N. In this article, we study a class of transformations that map the problem into another one in lower dimension. We use the best model in the low dimensional space to approximate the best solution in the original high dimensional space. We then estimate the error produced between this solution and the optimal solution in the high dimensional space."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.2804","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":"2026-05-18T04:31:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aghsbE31QtCaMBQl/GXYw9hosrh0rISjCEPZm79k4eEzUOCdhDMCs8xHAFMLA/9H7mEHAVIAeIU/gqifQRbVBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T10:36:28.745042Z"},"content_sha256":"d2c780bfcfb9741349f786e536d0df2050248bc8dcdc4e042a7890f08f35d556","schema_version":"1.0","event_id":"sha256:d2c780bfcfb9741349f786e536d0df2050248bc8dcdc4e042a7890f08f35d556"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WHZBPOHDQIET4NSGQ4CEQG3IKH/bundle.json","state_url":"https://pith.science/pith/WHZBPOHDQIET4NSGQ4CEQG3IKH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WHZBPOHDQIET4NSGQ4CEQG3IKH/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":"2026-05-27T10:36:28Z","links":{"resolver":"https://pith.science/pith/WHZBPOHDQIET4NSGQ4CEQG3IKH","bundle":"https://pith.science/pith/WHZBPOHDQIET4NSGQ4CEQG3IKH/bundle.json","state":"https://pith.science/pith/WHZBPOHDQIET4NSGQ4CEQG3IKH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WHZBPOHDQIET4NSGQ4CEQG3IKH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:WHZBPOHDQIET4NSGQ4CEQG3IKH","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":"1247349d46a0e59d6efd5debd6abfaa856fc0b4380504c286559aafe37753297","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2010-08-17T02:04:28Z","title_canon_sha256":"535e26d8e5fed4514af774eafac53dce4be3778ca5790a08278b1509fca7f1e4"},"schema_version":"1.0","source":{"id":"1008.2804","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1008.2804","created_at":"2026-05-18T04:31:51Z"},{"alias_kind":"arxiv_version","alias_value":"1008.2804v2","created_at":"2026-05-18T04:31:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1008.2804","created_at":"2026-05-18T04:31:51Z"},{"alias_kind":"pith_short_12","alias_value":"WHZBPOHDQIET","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_16","alias_value":"WHZBPOHDQIET4NSG","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_8","alias_value":"WHZBPOHD","created_at":"2026-05-18T12:26:15Z"}],"graph_snapshots":[{"event_id":"sha256:d2c780bfcfb9741349f786e536d0df2050248bc8dcdc4e042a7890f08f35d556","target":"graph","created_at":"2026-05-18T04:31:51Z","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":"Given a set of points \\F in a high dimensional space, the problem of finding a union of subspaces \\cup_i V_i\\subset \\R^N that best explains the data \\F increases dramatically with the dimension of \\R^N. In this article, we study a class of transformations that map the problem into another one in lower dimension. We use the best model in the low dimensional space to approximate the best solution in the original high dimensional space. We then estimate the error produced between this solution and the optimal solution in the high dimensional space.","authors_text":"Akram Aldroubi, Carlos Cabrelli, Magal\\'i Anastasio, Ursula Molter","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2010-08-17T02:04:28Z","title":"A Dimension Reduction Scheme for the Computation of Optimal Unions of Subspaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.2804","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:a1f53eea04530ced03510019d91282dfc7e7113317c78a708c243cb65fac83d8","target":"record","created_at":"2026-05-18T04:31:51Z","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":"1247349d46a0e59d6efd5debd6abfaa856fc0b4380504c286559aafe37753297","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2010-08-17T02:04:28Z","title_canon_sha256":"535e26d8e5fed4514af774eafac53dce4be3778ca5790a08278b1509fca7f1e4"},"schema_version":"1.0","source":{"id":"1008.2804","kind":"arxiv","version":2}},"canonical_sha256":"b1f217b8e382093e36468704481b6851fef9c802fda22377633402f4fdcb5513","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b1f217b8e382093e36468704481b6851fef9c802fda22377633402f4fdcb5513","first_computed_at":"2026-05-18T04:31:51.452562Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:31:51.452562Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"g3zur6lUHa194xynkPA7N1ZAfhGKJaSg07SHxOygMcmAcG02Bi/1te3F1cV+Rgkk2RNVH9l/UJw6FgFYUVgsCg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:31:51.453267Z","signed_message":"canonical_sha256_bytes"},"source_id":"1008.2804","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a1f53eea04530ced03510019d91282dfc7e7113317c78a708c243cb65fac83d8","sha256:d2c780bfcfb9741349f786e536d0df2050248bc8dcdc4e042a7890f08f35d556"],"state_sha256":"fc81df22427d8c4f68d7850539b084b1d86433a1dfa632d456cd67d2ba57b9be"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lpIkTIF3JrhNwu3CsC4T9O2bko0DfhlX3/A7MZg6e4uSP7MjkIlueh+QlDx0vOKd9J/dZwAHX2q6AeFs5hyoDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T10:36:28.748574Z","bundle_sha256":"8947145df2d8860d61e32d38c43a63f9049af576460f9e9c4d92fa68c4547cde"}}