{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:ULEUJLXIDIPWYXT376XUCWWA2G","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":"449bf172f0916d3880ac13c192dcaaffe4eebbf82b00e41fbffeda471a9eaf3e","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CV","submitted_at":"2016-02-23T08:01:58Z","title_canon_sha256":"6cf2d10da07233aee2e3036b30b385dbf0bcc68d4165ee06c553ed7ccd43d4a9"},"schema_version":"1.0","source":{"id":"1602.07613","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.07613","created_at":"2026-05-18T01:11:35Z"},{"alias_kind":"arxiv_version","alias_value":"1602.07613v2","created_at":"2026-05-18T01:11:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.07613","created_at":"2026-05-18T01:11:35Z"},{"alias_kind":"pith_short_12","alias_value":"ULEUJLXIDIPW","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_16","alias_value":"ULEUJLXIDIPWYXT3","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_8","alias_value":"ULEUJLXI","created_at":"2026-05-18T12:30:46Z"}],"graph_snapshots":[{"event_id":"sha256:b7b84782b671120805a1c9ac295879dadc57dc33760917d8f73a28b1d9900cfc","target":"graph","created_at":"2026-05-18T01:11:35Z","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 present a mathematical and algorithmic scheme for learning the principal geometric elements in an image or 3D object. We build on recent work that convexifies the basic problem of finding a combination of a small number shapes that overlap and occlude one another in such a way that they \"match\" a given scene as closely as possible. This paper derives general sufficient conditions under which this convex shape composition identifies a target composition. From a computational standpoint, we present two different methods for solving the associated optimization programs. The first method simply","authors_text":"Alireza Aghasi, Justin Romberg","cross_cats":["math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CV","submitted_at":"2016-02-23T08:01:58Z","title":"Learning Shapes by Convex Composition"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.07613","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":"sha256:075015d25b017d2edc475ea33ad92a46b780a64397f0c41fcb9241ed1b8d0e1e","target":"record","created_at":"2026-05-18T01:11:35Z","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":"449bf172f0916d3880ac13c192dcaaffe4eebbf82b00e41fbffeda471a9eaf3e","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CV","submitted_at":"2016-02-23T08:01:58Z","title_canon_sha256":"6cf2d10da07233aee2e3036b30b385dbf0bcc68d4165ee06c553ed7ccd43d4a9"},"schema_version":"1.0","source":{"id":"1602.07613","kind":"arxiv","version":2}},"canonical_sha256":"a2c944aee81a1f6c5e7bffaf415ac0d199c97583d98e29529393e14797e2dedc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a2c944aee81a1f6c5e7bffaf415ac0d199c97583d98e29529393e14797e2dedc","first_computed_at":"2026-05-18T01:11:35.047466Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:11:35.047466Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"iArDR2zZLdzneN9tyg2RRWyxiqroeakVutuh3FomFwLVt/zD558hrSGJnKgG4FVTgaROszmt38VDukvsvMSjDw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:11:35.047900Z","signed_message":"canonical_sha256_bytes"},"source_id":"1602.07613","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:075015d25b017d2edc475ea33ad92a46b780a64397f0c41fcb9241ed1b8d0e1e","sha256:b7b84782b671120805a1c9ac295879dadc57dc33760917d8f73a28b1d9900cfc"],"state_sha256":"f0b81514121de0381b45305d0eeecaace4ae21daae8aa01cea38d3b38327f300"}