{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:E6AD4QXM3SAHSEF3JFZDECLC6I","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":"269d0603cad7251136c8b4bda5d9a34c47ca8902a80f3921357aed3bf54fe0dc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2013-11-26T10:49:36Z","title_canon_sha256":"d8fbf158228e8c3122797f72b82b20b2dbb2f3ea27ac6224fbf48f18a94b9573"},"schema_version":"1.0","source":{"id":"1311.6615","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1311.6615","created_at":"2026-05-18T02:59:20Z"},{"alias_kind":"arxiv_version","alias_value":"1311.6615v2","created_at":"2026-05-18T02:59:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.6615","created_at":"2026-05-18T02:59:20Z"},{"alias_kind":"pith_short_12","alias_value":"E6AD4QXM3SAH","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_16","alias_value":"E6AD4QXM3SAHSEF3","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_8","alias_value":"E6AD4QXM","created_at":"2026-05-18T12:27:43Z"}],"graph_snapshots":[{"event_id":"sha256:caa135f7ce2be08a51adcf3cf18f13c6322913ed9413c05913c45f62f19baa14","target":"graph","created_at":"2026-05-18T02:59:20Z","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 consider the Fault-Tolerant Facility Placement problem ($FTFP$), which is a generalization of the classical Uncapacitated Facility Location problem ($UFL$). In the $FTFP$ problem we have a set of clients $C$ and a set of facilities $F$. Each facility $i \\in F$ can be opened many times. For each opening of facility $i$ we pay $f_i \\geq 0$. Our goal is to connect each client $j \\in C$ with $r_j \\geq 1$ open facilities in a way that minimizes the total cost of open facilities and established connections.\n  In a series of recent papers $FTFP$ was essentially reduced to $FTFL$ and then to $UFL$ ","authors_text":"Bartosz Rybicki, Jaroslaw Byrka","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2013-11-26T10:49:36Z","title":"Improved approximation algorithm for Fault-Tolerant Facility Placement"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.6615","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":"sha256:1a6107d95c6c355cf4e72ad83263cf56a9267f400d5f1a85c593e4b871a6b088","target":"record","created_at":"2026-05-18T02:59:20Z","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":"269d0603cad7251136c8b4bda5d9a34c47ca8902a80f3921357aed3bf54fe0dc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2013-11-26T10:49:36Z","title_canon_sha256":"d8fbf158228e8c3122797f72b82b20b2dbb2f3ea27ac6224fbf48f18a94b9573"},"schema_version":"1.0","source":{"id":"1311.6615","kind":"arxiv","version":2}},"canonical_sha256":"27803e42ecdc807910bb4972320962f206e8e909f8d516f3ddbb5cabcad77d56","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"27803e42ecdc807910bb4972320962f206e8e909f8d516f3ddbb5cabcad77d56","first_computed_at":"2026-05-18T02:59:20.460124Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:59:20.460124Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"98h/QATQLe1JrpC0OFl9guhCzQ8ctzUfwwmGLYPkU+E3jk4JAxa1f9jxh+AmPREUduDLjDQIPLdlhg6g35fuDg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:59:20.461020Z","signed_message":"canonical_sha256_bytes"},"source_id":"1311.6615","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1a6107d95c6c355cf4e72ad83263cf56a9267f400d5f1a85c593e4b871a6b088","sha256:caa135f7ce2be08a51adcf3cf18f13c6322913ed9413c05913c45f62f19baa14"],"state_sha256":"82247bff39e68dcbae3d821be668299c2c257a494b6653bbaaa17131c222bf9d"}