{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:IUXUKNLIL52RRVJQRUZGAK2MKI","short_pith_number":"pith:IUXUKNLI","canonical_record":{"source":{"id":"1810.08754","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-10-20T05:57:38Z","cross_cats_sorted":["cs.LG","eess.SP"],"title_canon_sha256":"7b3f7ca580054bc37a9aedf8c95a875f260cb23e85b858b10fd7e6fba1569ff6","abstract_canon_sha256":"713b6611035be1b320615cc0f76f1ec7fc173cc588652aa2cf665e1b630f196e"},"schema_version":"1.0"},"canonical_sha256":"452f4535685f7518d5308d32602b4c520f8e6e2dc2698b44a213e61eaa152c4b","source":{"kind":"arxiv","id":"1810.08754","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.08754","created_at":"2026-05-17T23:50:23Z"},{"alias_kind":"arxiv_version","alias_value":"1810.08754v1","created_at":"2026-05-17T23:50:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.08754","created_at":"2026-05-17T23:50:23Z"},{"alias_kind":"pith_short_12","alias_value":"IUXUKNLIL52R","created_at":"2026-05-18T12:32:31Z"},{"alias_kind":"pith_short_16","alias_value":"IUXUKNLIL52RRVJQ","created_at":"2026-05-18T12:32:31Z"},{"alias_kind":"pith_short_8","alias_value":"IUXUKNLI","created_at":"2026-05-18T12:32:31Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:IUXUKNLIL52RRVJQRUZGAK2MKI","target":"record","payload":{"canonical_record":{"source":{"id":"1810.08754","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-10-20T05:57:38Z","cross_cats_sorted":["cs.LG","eess.SP"],"title_canon_sha256":"7b3f7ca580054bc37a9aedf8c95a875f260cb23e85b858b10fd7e6fba1569ff6","abstract_canon_sha256":"713b6611035be1b320615cc0f76f1ec7fc173cc588652aa2cf665e1b630f196e"},"schema_version":"1.0"},"canonical_sha256":"452f4535685f7518d5308d32602b4c520f8e6e2dc2698b44a213e61eaa152c4b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:50:23.322388Z","signature_b64":"rH5Qa6NQ/TOhvN2bLSdbefP2Mw4L7qBVZV2z/TMAzO040t6JPZHrzIhMO9m58isr8b1dWdDv4nwQsdMxwcAPCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"452f4535685f7518d5308d32602b4c520f8e6e2dc2698b44a213e61eaa152c4b","last_reissued_at":"2026-05-17T23:50:23.321967Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:50:23.321967Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1810.08754","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":"2026-05-17T23:50:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"T2Wx+eaO1+mksQKC9uJHb3rIAR9fOnkFoHDQQJhbRqn1NycgVKC7IJ7RTywISXI1zxQkKjdD0kq/1b4vCmJxDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T02:30:34.612458Z"},"content_sha256":"5c64138615693ab0de4ffc7f7a6d989eb0103d2d75e2205a8011a488d589c99d","schema_version":"1.0","event_id":"sha256:5c64138615693ab0de4ffc7f7a6d989eb0103d2d75e2205a8011a488d589c99d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:IUXUKNLIL52RRVJQRUZGAK2MKI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"BCR-Net: a neural network based on the nonstandard wavelet form","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","eess.SP"],"primary_cat":"math.NA","authors_text":"Cindy Orozco Bohorquez, Lexing Ying, Yuwei Fan","submitted_at":"2018-10-20T05:57:38Z","abstract_excerpt":"This paper proposes a novel neural network architecture inspired by the nonstandard form proposed by Beylkin, Coifman, and Rokhlin in [Communications on Pure and Applied Mathematics, 44(2), 141-183]. The nonstandard form is a highly effective wavelet-based compression scheme for linear integral operators. In this work, we first represent the matrix-vector product algorithm of the nonstandard form as a linear neural network where every scale of the multiresolution computation is carried out by a locally connected linear sub-network. In order to address nonlinear problems, we propose an extensio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.08754","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":"2026-05-17T23:50:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4FvBbWzbQQta+xJn6bfqjjXVlLj4AFKn5dMbhBTK0G46TpHDRRYNCRy2gn5syeUSCJoD6OBJ8bhQt0bmrKzmDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T02:30:34.613001Z"},"content_sha256":"12eddfccddf6ad3783cd6f46063146277dd9e7aa5bba71395210172514b06b6c","schema_version":"1.0","event_id":"sha256:12eddfccddf6ad3783cd6f46063146277dd9e7aa5bba71395210172514b06b6c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IUXUKNLIL52RRVJQRUZGAK2MKI/bundle.json","state_url":"https://pith.science/pith/IUXUKNLIL52RRVJQRUZGAK2MKI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IUXUKNLIL52RRVJQRUZGAK2MKI/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":"2026-08-14T02:30:34Z","links":{"resolver":"https://pith.science/pith/IUXUKNLIL52RRVJQRUZGAK2MKI","bundle":"https://pith.science/pith/IUXUKNLIL52RRVJQRUZGAK2MKI/bundle.json","state":"https://pith.science/pith/IUXUKNLIL52RRVJQRUZGAK2MKI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IUXUKNLIL52RRVJQRUZGAK2MKI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:IUXUKNLIL52RRVJQRUZGAK2MKI","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":"713b6611035be1b320615cc0f76f1ec7fc173cc588652aa2cf665e1b630f196e","cross_cats_sorted":["cs.LG","eess.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-10-20T05:57:38Z","title_canon_sha256":"7b3f7ca580054bc37a9aedf8c95a875f260cb23e85b858b10fd7e6fba1569ff6"},"schema_version":"1.0","source":{"id":"1810.08754","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.08754","created_at":"2026-05-17T23:50:23Z"},{"alias_kind":"arxiv_version","alias_value":"1810.08754v1","created_at":"2026-05-17T23:50:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.08754","created_at":"2026-05-17T23:50:23Z"},{"alias_kind":"pith_short_12","alias_value":"IUXUKNLIL52R","created_at":"2026-05-18T12:32:31Z"},{"alias_kind":"pith_short_16","alias_value":"IUXUKNLIL52RRVJQ","created_at":"2026-05-18T12:32:31Z"},{"alias_kind":"pith_short_8","alias_value":"IUXUKNLI","created_at":"2026-05-18T12:32:31Z"}],"graph_snapshots":[{"event_id":"sha256:12eddfccddf6ad3783cd6f46063146277dd9e7aa5bba71395210172514b06b6c","target":"graph","created_at":"2026-05-17T23:50:23Z","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":"This paper proposes a novel neural network architecture inspired by the nonstandard form proposed by Beylkin, Coifman, and Rokhlin in [Communications on Pure and Applied Mathematics, 44(2), 141-183]. The nonstandard form is a highly effective wavelet-based compression scheme for linear integral operators. In this work, we first represent the matrix-vector product algorithm of the nonstandard form as a linear neural network where every scale of the multiresolution computation is carried out by a locally connected linear sub-network. In order to address nonlinear problems, we propose an extensio","authors_text":"Cindy Orozco Bohorquez, Lexing Ying, Yuwei Fan","cross_cats":["cs.LG","eess.SP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-10-20T05:57:38Z","title":"BCR-Net: a neural network based on the nonstandard wavelet form"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.08754","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":"sha256:5c64138615693ab0de4ffc7f7a6d989eb0103d2d75e2205a8011a488d589c99d","target":"record","created_at":"2026-05-17T23:50:23Z","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":"713b6611035be1b320615cc0f76f1ec7fc173cc588652aa2cf665e1b630f196e","cross_cats_sorted":["cs.LG","eess.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-10-20T05:57:38Z","title_canon_sha256":"7b3f7ca580054bc37a9aedf8c95a875f260cb23e85b858b10fd7e6fba1569ff6"},"schema_version":"1.0","source":{"id":"1810.08754","kind":"arxiv","version":1}},"canonical_sha256":"452f4535685f7518d5308d32602b4c520f8e6e2dc2698b44a213e61eaa152c4b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"452f4535685f7518d5308d32602b4c520f8e6e2dc2698b44a213e61eaa152c4b","first_computed_at":"2026-05-17T23:50:23.321967Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:50:23.321967Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rH5Qa6NQ/TOhvN2bLSdbefP2Mw4L7qBVZV2z/TMAzO040t6JPZHrzIhMO9m58isr8b1dWdDv4nwQsdMxwcAPCA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:50:23.322388Z","signed_message":"canonical_sha256_bytes"},"source_id":"1810.08754","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5c64138615693ab0de4ffc7f7a6d989eb0103d2d75e2205a8011a488d589c99d","sha256:12eddfccddf6ad3783cd6f46063146277dd9e7aa5bba71395210172514b06b6c"],"state_sha256":"4c96f11c11d2633ced0b2dda610d5827ea987230f1e22e32f22e179e88495408"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xE2ZdFn8GQKPBtr3TbWPfAWn6GsR8jpcohWbqHvRojNUJ5FYI2VKqDL+52u3hji7sNwEdlc8yrkAiIMhmUjXBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-14T02:30:34.618344Z","bundle_sha256":"f34e07987f95844f70a6367c8ee9d03e4c79830982ed6f80989382ebe12b1307"}}