{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:GR7QORL3OEL6PL2BGTIWE45GKM","short_pith_number":"pith:GR7QORL3","schema_version":"1.0","canonical_sha256":"347f07457b7117e7af4134d16273a653298daee8ddad6fa0f05aba44c753973a","source":{"kind":"arxiv","id":"1612.09203","version":1},"attestation_state":"computed","paper":{"title":"Inverse Scale Space Decomposition","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Carola-Bibiane Sch\\\"onlieb, Marie Foged Schmidt, Martin Benning","submitted_at":"2016-12-29T17:10:37Z","abstract_excerpt":"We investigate the inverse scale space flow as a decomposition method for decomposing data into generalised singular vectors. We show that the inverse scale space flow, based on convex and absolutely one-homogeneous regularisation functionals, can decompose data represented by the application of a forward operator to a linear combination of generalised singular vectors into its individual singular vectors. We verify that for this decomposition to hold true, two additional conditions on the singular vectors are sufficient: orthogonality in the data space and inclusion of partial sums of the sub"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1612.09203","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-12-29T17:10:37Z","cross_cats_sorted":[],"title_canon_sha256":"1faacc35e19c5448a1a02d1bdf204bce62a4a18ae573c71d57f8c79541d33c88","abstract_canon_sha256":"80c81f1108226c1cfb6eb6a9b85b862b6691ae598ef2f8cd71e70b89dd5e290f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:53:46.257136Z","signature_b64":"sQA5gS+J56UtytzvUxWP54PpZVTA/f9pYU5OfI6DZ+yDGpqK1DufGMiPagyRYlY7AR5ceBgPgHVj+JpqdcitAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"347f07457b7117e7af4134d16273a653298daee8ddad6fa0f05aba44c753973a","last_reissued_at":"2026-05-18T00:53:46.256796Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:53:46.256796Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Inverse Scale Space Decomposition","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Carola-Bibiane Sch\\\"onlieb, Marie Foged Schmidt, Martin Benning","submitted_at":"2016-12-29T17:10:37Z","abstract_excerpt":"We investigate the inverse scale space flow as a decomposition method for decomposing data into generalised singular vectors. We show that the inverse scale space flow, based on convex and absolutely one-homogeneous regularisation functionals, can decompose data represented by the application of a forward operator to a linear combination of generalised singular vectors into its individual singular vectors. We verify that for this decomposition to hold true, two additional conditions on the singular vectors are sufficient: orthogonality in the data space and inclusion of partial sums of the sub"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.09203","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1612.09203","created_at":"2026-05-18T00:53:46.256851+00:00"},{"alias_kind":"arxiv_version","alias_value":"1612.09203v1","created_at":"2026-05-18T00:53:46.256851+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.09203","created_at":"2026-05-18T00:53:46.256851+00:00"},{"alias_kind":"pith_short_12","alias_value":"GR7QORL3OEL6","created_at":"2026-05-18T12:30:19.053100+00:00"},{"alias_kind":"pith_short_16","alias_value":"GR7QORL3OEL6PL2B","created_at":"2026-05-18T12:30:19.053100+00:00"},{"alias_kind":"pith_short_8","alias_value":"GR7QORL3","created_at":"2026-05-18T12:30:19.053100+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/GR7QORL3OEL6PL2BGTIWE45GKM","json":"https://pith.science/pith/GR7QORL3OEL6PL2BGTIWE45GKM.json","graph_json":"https://pith.science/api/pith-number/GR7QORL3OEL6PL2BGTIWE45GKM/graph.json","events_json":"https://pith.science/api/pith-number/GR7QORL3OEL6PL2BGTIWE45GKM/events.json","paper":"https://pith.science/paper/GR7QORL3"},"agent_actions":{"view_html":"https://pith.science/pith/GR7QORL3OEL6PL2BGTIWE45GKM","download_json":"https://pith.science/pith/GR7QORL3OEL6PL2BGTIWE45GKM.json","view_paper":"https://pith.science/paper/GR7QORL3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1612.09203&json=true","fetch_graph":"https://pith.science/api/pith-number/GR7QORL3OEL6PL2BGTIWE45GKM/graph.json","fetch_events":"https://pith.science/api/pith-number/GR7QORL3OEL6PL2BGTIWE45GKM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GR7QORL3OEL6PL2BGTIWE45GKM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GR7QORL3OEL6PL2BGTIWE45GKM/action/storage_attestation","attest_author":"https://pith.science/pith/GR7QORL3OEL6PL2BGTIWE45GKM/action/author_attestation","sign_citation":"https://pith.science/pith/GR7QORL3OEL6PL2BGTIWE45GKM/action/citation_signature","submit_replication":"https://pith.science/pith/GR7QORL3OEL6PL2BGTIWE45GKM/action/replication_record"}},"created_at":"2026-05-18T00:53:46.256851+00:00","updated_at":"2026-05-18T00:53:46.256851+00:00"}