{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:GR7QORL3OEL6PL2BGTIWE45GKM","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":"80c81f1108226c1cfb6eb6a9b85b862b6691ae598ef2f8cd71e70b89dd5e290f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-12-29T17:10:37Z","title_canon_sha256":"1faacc35e19c5448a1a02d1bdf204bce62a4a18ae573c71d57f8c79541d33c88"},"schema_version":"1.0","source":{"id":"1612.09203","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.09203","created_at":"2026-05-18T00:53:46Z"},{"alias_kind":"arxiv_version","alias_value":"1612.09203v1","created_at":"2026-05-18T00:53:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.09203","created_at":"2026-05-18T00:53:46Z"},{"alias_kind":"pith_short_12","alias_value":"GR7QORL3OEL6","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_16","alias_value":"GR7QORL3OEL6PL2B","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_8","alias_value":"GR7QORL3","created_at":"2026-05-18T12:30:19Z"}],"graph_snapshots":[{"event_id":"sha256:8445afecc8fab83c0d8864b75dc529228457bf81e66f1642f6d3f6508d9935b9","target":"graph","created_at":"2026-05-18T00:53:46Z","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":"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","authors_text":"Carola-Bibiane Sch\\\"onlieb, Marie Foged Schmidt, Martin Benning","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-12-29T17:10:37Z","title":"Inverse Scale Space Decomposition"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.09203","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":"sha256:329238196eadc12a9b2f31235496da607ed566878a1dcf63815d3fc2a8c035e8","target":"record","created_at":"2026-05-18T00:53:46Z","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":"80c81f1108226c1cfb6eb6a9b85b862b6691ae598ef2f8cd71e70b89dd5e290f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-12-29T17:10:37Z","title_canon_sha256":"1faacc35e19c5448a1a02d1bdf204bce62a4a18ae573c71d57f8c79541d33c88"},"schema_version":"1.0","source":{"id":"1612.09203","kind":"arxiv","version":1}},"canonical_sha256":"347f07457b7117e7af4134d16273a653298daee8ddad6fa0f05aba44c753973a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"347f07457b7117e7af4134d16273a653298daee8ddad6fa0f05aba44c753973a","first_computed_at":"2026-05-18T00:53:46.256796Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:53:46.256796Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sQA5gS+J56UtytzvUxWP54PpZVTA/f9pYU5OfI6DZ+yDGpqK1DufGMiPagyRYlY7AR5ceBgPgHVj+JpqdcitAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:53:46.257136Z","signed_message":"canonical_sha256_bytes"},"source_id":"1612.09203","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:329238196eadc12a9b2f31235496da607ed566878a1dcf63815d3fc2a8c035e8","sha256:8445afecc8fab83c0d8864b75dc529228457bf81e66f1642f6d3f6508d9935b9"],"state_sha256":"9e8673cbd9018638ad0cf7a5ec19cdf522397275da8169e55915a2bfbb4e702f"}