{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:QVOSIJNCXXM76HLBWOCQ6PLZES","short_pith_number":"pith:QVOSIJNC","canonical_record":{"source":{"id":"1804.05284","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-04-14T22:33:55Z","cross_cats_sorted":[],"title_canon_sha256":"e3c62424b86f3f2794f7b9121b782b42a09dee03b9784221703d4bfd041f27e4","abstract_canon_sha256":"259b66d32301a9755498162bd8131221a11d90f2828f4b07db48aba7d31f99ab"},"schema_version":"1.0"},"canonical_sha256":"855d2425a2bdd9ff1d61b3850f3d7924b6fecec5629f031785257476aa430d39","source":{"kind":"arxiv","id":"1804.05284","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.05284","created_at":"2026-05-18T00:18:28Z"},{"alias_kind":"arxiv_version","alias_value":"1804.05284v1","created_at":"2026-05-18T00:18:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.05284","created_at":"2026-05-18T00:18:28Z"},{"alias_kind":"pith_short_12","alias_value":"QVOSIJNCXXM7","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_16","alias_value":"QVOSIJNCXXM76HLB","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_8","alias_value":"QVOSIJNC","created_at":"2026-05-18T12:32:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:QVOSIJNCXXM76HLBWOCQ6PLZES","target":"record","payload":{"canonical_record":{"source":{"id":"1804.05284","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-04-14T22:33:55Z","cross_cats_sorted":[],"title_canon_sha256":"e3c62424b86f3f2794f7b9121b782b42a09dee03b9784221703d4bfd041f27e4","abstract_canon_sha256":"259b66d32301a9755498162bd8131221a11d90f2828f4b07db48aba7d31f99ab"},"schema_version":"1.0"},"canonical_sha256":"855d2425a2bdd9ff1d61b3850f3d7924b6fecec5629f031785257476aa430d39","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:18:28.419452Z","signature_b64":"qdPdpQkA0p+VxQR1JRmLHlwo2DdsftpQ80HPqrPUszyI1Q18G/nxNHWpf19q2M7io2csuvDzUQWIkG5gKqVADQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"855d2425a2bdd9ff1d61b3850f3d7924b6fecec5629f031785257476aa430d39","last_reissued_at":"2026-05-18T00:18:28.418988Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:18:28.418988Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1804.05284","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":"2026-05-18T00:18:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QLZX/uIA5uIpkQ5/3kId/8We2/wJxppP78dAkod7tp0r4G+u4GaCojxRSBqbK/HzNHGr29PvUbp3Umd7HmbaDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T11:03:21.761466Z"},"content_sha256":"b88e0a04a0146c7be8aee86a2599c52e36d9765cc492808388ada9337aba14d3","schema_version":"1.0","event_id":"sha256:b88e0a04a0146c7be8aee86a2599c52e36d9765cc492808388ada9337aba14d3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:QVOSIJNCXXM76HLBWOCQ6PLZES","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Strong Formulations for Quadratic Optimization with M-matrices and Indicator Variables","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Alper Atamturk, Andres Gomez","submitted_at":"2018-04-14T22:33:55Z","abstract_excerpt":"We study quadratic optimization with indicator variables and an M-matrix, i.e., a PSD matrix with non-positive off-diagonal entries, which arises directly in image segmentation and portfolio optimization with transaction costs, as well as a substructure of general quadratic optimization problems. We prove, under mild assumptions, that the minimization problem is solvable in polynomial time by showing its equivalence to a submodular minimization problem. To strengthen the formulation, we decompose the quadratic function into a sum of simple quadratic functions with at most two indicator variabl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.05284","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":"2026-05-18T00:18:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"o+OWsZIyZjU1A2wfsQ3RzVQqoWivdLABnayvShP5C3XyWcO6aJTShs1VTRH5h/VUQOz5CsdSKsh4F940Qz9mBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T11:03:21.762180Z"},"content_sha256":"ccf12da6affb4d94e529709a69f284a502fab79c700f25136256d036c01f5ff3","schema_version":"1.0","event_id":"sha256:ccf12da6affb4d94e529709a69f284a502fab79c700f25136256d036c01f5ff3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QVOSIJNCXXM76HLBWOCQ6PLZES/bundle.json","state_url":"https://pith.science/pith/QVOSIJNCXXM76HLBWOCQ6PLZES/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QVOSIJNCXXM76HLBWOCQ6PLZES/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":"2026-05-31T11:03:21Z","links":{"resolver":"https://pith.science/pith/QVOSIJNCXXM76HLBWOCQ6PLZES","bundle":"https://pith.science/pith/QVOSIJNCXXM76HLBWOCQ6PLZES/bundle.json","state":"https://pith.science/pith/QVOSIJNCXXM76HLBWOCQ6PLZES/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QVOSIJNCXXM76HLBWOCQ6PLZES/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:QVOSIJNCXXM76HLBWOCQ6PLZES","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":"259b66d32301a9755498162bd8131221a11d90f2828f4b07db48aba7d31f99ab","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-04-14T22:33:55Z","title_canon_sha256":"e3c62424b86f3f2794f7b9121b782b42a09dee03b9784221703d4bfd041f27e4"},"schema_version":"1.0","source":{"id":"1804.05284","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.05284","created_at":"2026-05-18T00:18:28Z"},{"alias_kind":"arxiv_version","alias_value":"1804.05284v1","created_at":"2026-05-18T00:18:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.05284","created_at":"2026-05-18T00:18:28Z"},{"alias_kind":"pith_short_12","alias_value":"QVOSIJNCXXM7","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_16","alias_value":"QVOSIJNCXXM76HLB","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_8","alias_value":"QVOSIJNC","created_at":"2026-05-18T12:32:46Z"}],"graph_snapshots":[{"event_id":"sha256:ccf12da6affb4d94e529709a69f284a502fab79c700f25136256d036c01f5ff3","target":"graph","created_at":"2026-05-18T00:18:28Z","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 study quadratic optimization with indicator variables and an M-matrix, i.e., a PSD matrix with non-positive off-diagonal entries, which arises directly in image segmentation and portfolio optimization with transaction costs, as well as a substructure of general quadratic optimization problems. We prove, under mild assumptions, that the minimization problem is solvable in polynomial time by showing its equivalence to a submodular minimization problem. To strengthen the formulation, we decompose the quadratic function into a sum of simple quadratic functions with at most two indicator variabl","authors_text":"Alper Atamturk, Andres Gomez","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-04-14T22:33:55Z","title":"Strong Formulations for Quadratic Optimization with M-matrices and Indicator Variables"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.05284","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:b88e0a04a0146c7be8aee86a2599c52e36d9765cc492808388ada9337aba14d3","target":"record","created_at":"2026-05-18T00:18:28Z","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":"259b66d32301a9755498162bd8131221a11d90f2828f4b07db48aba7d31f99ab","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-04-14T22:33:55Z","title_canon_sha256":"e3c62424b86f3f2794f7b9121b782b42a09dee03b9784221703d4bfd041f27e4"},"schema_version":"1.0","source":{"id":"1804.05284","kind":"arxiv","version":1}},"canonical_sha256":"855d2425a2bdd9ff1d61b3850f3d7924b6fecec5629f031785257476aa430d39","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"855d2425a2bdd9ff1d61b3850f3d7924b6fecec5629f031785257476aa430d39","first_computed_at":"2026-05-18T00:18:28.418988Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:18:28.418988Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qdPdpQkA0p+VxQR1JRmLHlwo2DdsftpQ80HPqrPUszyI1Q18G/nxNHWpf19q2M7io2csuvDzUQWIkG5gKqVADQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:18:28.419452Z","signed_message":"canonical_sha256_bytes"},"source_id":"1804.05284","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b88e0a04a0146c7be8aee86a2599c52e36d9765cc492808388ada9337aba14d3","sha256:ccf12da6affb4d94e529709a69f284a502fab79c700f25136256d036c01f5ff3"],"state_sha256":"c25b2f7de0e94afa853c8f838bf4094829ff9f29a457a0f1824ca0d75075d96e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WTrmodIOmzE+AKNAu1gDl1VdNeV+wEMFhtWExZ7Pl4Ts1+ZHdhZLEA8FyQs6BMexn/APO3Qiug7vpYYn97DRBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T11:03:21.766537Z","bundle_sha256":"d327129d61b8b57207cc57a317ab7ed777c66a907bb2c95e235d33f5aef88a6f"}}