{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:F3DYBNQT7NJ6QH4YFTWY7WLF26","short_pith_number":"pith:F3DYBNQT","canonical_record":{"source":{"id":"1401.0817","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2014-01-04T15:07:58Z","cross_cats_sorted":[],"title_canon_sha256":"47887fa37a6fe087472716f35a8179a4b90fb5822de412f6bbe56de337d6bd44","abstract_canon_sha256":"ceaebf9a26cd4c89aff26fa9525fc3f1181380e03bf2c32d6e7b9efacaf3038d"},"schema_version":"1.0"},"canonical_sha256":"2ec780b613fb53e81f982ced8fd965d7b806b045bcf69c697b8ec04054b49b03","source":{"kind":"arxiv","id":"1401.0817","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.0817","created_at":"2026-05-18T02:39:48Z"},{"alias_kind":"arxiv_version","alias_value":"1401.0817v2","created_at":"2026-05-18T02:39:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.0817","created_at":"2026-05-18T02:39:48Z"},{"alias_kind":"pith_short_12","alias_value":"F3DYBNQT7NJ6","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_16","alias_value":"F3DYBNQT7NJ6QH4Y","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_8","alias_value":"F3DYBNQT","created_at":"2026-05-18T12:28:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:F3DYBNQT7NJ6QH4YFTWY7WLF26","target":"record","payload":{"canonical_record":{"source":{"id":"1401.0817","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2014-01-04T15:07:58Z","cross_cats_sorted":[],"title_canon_sha256":"47887fa37a6fe087472716f35a8179a4b90fb5822de412f6bbe56de337d6bd44","abstract_canon_sha256":"ceaebf9a26cd4c89aff26fa9525fc3f1181380e03bf2c32d6e7b9efacaf3038d"},"schema_version":"1.0"},"canonical_sha256":"2ec780b613fb53e81f982ced8fd965d7b806b045bcf69c697b8ec04054b49b03","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:39:48.509074Z","signature_b64":"DU0j/GAxIzKAWJbXRvflPIge/PHu5mqH0IgpsIjMTMD4/8qHAzRiuwottrmBJ6gu2eRowwvOb0cvw2jJhUZoAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2ec780b613fb53e81f982ced8fd965d7b806b045bcf69c697b8ec04054b49b03","last_reissued_at":"2026-05-18T02:39:48.508585Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:39:48.508585Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1401.0817","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:39:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"A79AkihDsJJsfv7sFL0cvr9YEovPbp51VMFkVkdVPVx6QaZrS+BBevk/n1yZzrz3Wborxiwzjk7ToG6MFCFGBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T08:20:33.250927Z"},"content_sha256":"17f666eccbf708d272786bce37ef5461b6d359159aab09504a7855608842d565","schema_version":"1.0","event_id":"sha256:17f666eccbf708d272786bce37ef5461b6d359159aab09504a7855608842d565"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:F3DYBNQT7NJ6QH4YFTWY7WLF26","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Algorithms and dimensionality reductions for continuous multifacility ordered median location problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Justo Puerto, Safae El-Haj Ben-Ali, V\\'ictor Blanco","submitted_at":"2014-01-04T15:07:58Z","abstract_excerpt":"In this paper we propose a general methodology for solving a broad class of continuous, multifacility location problems, in any dimension and with $\\ell_\\tau$-norms proposing two different methodologies: 1) by a new second order cone mixed integer programming formulation and 2) by formulating a sequence of semidefinite programs that converges to the solution of the problem; each of these relaxed problems solvable with SDP solvers in polynomial time. We apply dimensionality reductions of the problems by sparsity and symmetry in order to be able to solve larger problems."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.0817","kind":"arxiv","version":2},"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":"2026-05-18T02:39:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cU1IatqZ7UyhrUwLFKgdg6LCbX0KsozQZRDzMCSxFc84aQqD01lQAB7l3PkZ+sWYlpTOhgbklausTyQmsHU0CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T08:20:33.251279Z"},"content_sha256":"2858f883a5107aeae821a2d7cc3f74eee92390a470b6a4ffb5812637486e0c52","schema_version":"1.0","event_id":"sha256:2858f883a5107aeae821a2d7cc3f74eee92390a470b6a4ffb5812637486e0c52"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/F3DYBNQT7NJ6QH4YFTWY7WLF26/bundle.json","state_url":"https://pith.science/pith/F3DYBNQT7NJ6QH4YFTWY7WLF26/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/F3DYBNQT7NJ6QH4YFTWY7WLF26/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":"2026-06-03T08:20:33Z","links":{"resolver":"https://pith.science/pith/F3DYBNQT7NJ6QH4YFTWY7WLF26","bundle":"https://pith.science/pith/F3DYBNQT7NJ6QH4YFTWY7WLF26/bundle.json","state":"https://pith.science/pith/F3DYBNQT7NJ6QH4YFTWY7WLF26/state.json","well_known_bundle":"https://pith.science/.well-known/pith/F3DYBNQT7NJ6QH4YFTWY7WLF26/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:F3DYBNQT7NJ6QH4YFTWY7WLF26","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":"ceaebf9a26cd4c89aff26fa9525fc3f1181380e03bf2c32d6e7b9efacaf3038d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2014-01-04T15:07:58Z","title_canon_sha256":"47887fa37a6fe087472716f35a8179a4b90fb5822de412f6bbe56de337d6bd44"},"schema_version":"1.0","source":{"id":"1401.0817","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.0817","created_at":"2026-05-18T02:39:48Z"},{"alias_kind":"arxiv_version","alias_value":"1401.0817v2","created_at":"2026-05-18T02:39:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.0817","created_at":"2026-05-18T02:39:48Z"},{"alias_kind":"pith_short_12","alias_value":"F3DYBNQT7NJ6","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_16","alias_value":"F3DYBNQT7NJ6QH4Y","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_8","alias_value":"F3DYBNQT","created_at":"2026-05-18T12:28:28Z"}],"graph_snapshots":[{"event_id":"sha256:2858f883a5107aeae821a2d7cc3f74eee92390a470b6a4ffb5812637486e0c52","target":"graph","created_at":"2026-05-18T02:39:48Z","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":"In this paper we propose a general methodology for solving a broad class of continuous, multifacility location problems, in any dimension and with $\\ell_\\tau$-norms proposing two different methodologies: 1) by a new second order cone mixed integer programming formulation and 2) by formulating a sequence of semidefinite programs that converges to the solution of the problem; each of these relaxed problems solvable with SDP solvers in polynomial time. We apply dimensionality reductions of the problems by sparsity and symmetry in order to be able to solve larger problems.","authors_text":"Justo Puerto, Safae El-Haj Ben-Ali, V\\'ictor Blanco","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2014-01-04T15:07:58Z","title":"Algorithms and dimensionality reductions for continuous multifacility ordered median location problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.0817","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":"sha256:17f666eccbf708d272786bce37ef5461b6d359159aab09504a7855608842d565","target":"record","created_at":"2026-05-18T02:39:48Z","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":"ceaebf9a26cd4c89aff26fa9525fc3f1181380e03bf2c32d6e7b9efacaf3038d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2014-01-04T15:07:58Z","title_canon_sha256":"47887fa37a6fe087472716f35a8179a4b90fb5822de412f6bbe56de337d6bd44"},"schema_version":"1.0","source":{"id":"1401.0817","kind":"arxiv","version":2}},"canonical_sha256":"2ec780b613fb53e81f982ced8fd965d7b806b045bcf69c697b8ec04054b49b03","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2ec780b613fb53e81f982ced8fd965d7b806b045bcf69c697b8ec04054b49b03","first_computed_at":"2026-05-18T02:39:48.508585Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:39:48.508585Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DU0j/GAxIzKAWJbXRvflPIge/PHu5mqH0IgpsIjMTMD4/8qHAzRiuwottrmBJ6gu2eRowwvOb0cvw2jJhUZoAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:39:48.509074Z","signed_message":"canonical_sha256_bytes"},"source_id":"1401.0817","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:17f666eccbf708d272786bce37ef5461b6d359159aab09504a7855608842d565","sha256:2858f883a5107aeae821a2d7cc3f74eee92390a470b6a4ffb5812637486e0c52"],"state_sha256":"ad6db29721033ca685e9471a11d64d93dbd65964b16271f3700f540986c329b2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"q1ZTo4DG9A8U8hXleVQu2u1t5dxrHxv61sEL+XAS7S3Ubdud1T5AJqRN0NqseWjixRJ/sgf8/z0JjgGQXLKLDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T08:20:33.253265Z","bundle_sha256":"285d2174f67bff5080f7175fc4939409aa78a0b2551c229cc77f8555e43e5e16"}}