{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:UXCSZRGXXMB5UTN6VLTXM62YIN","short_pith_number":"pith:UXCSZRGX","canonical_record":{"source":{"id":"1912.12151","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2019-12-27T15:20:56Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"a042e391d5e0a07ff5f9347d7d0c231e3c56181d6a412665570b8c28c51abb80","abstract_canon_sha256":"265c97bc0007b35483760e80ea4cf4e3ffa65b4e2da0512dd8a0b8013f908219"},"schema_version":"1.0"},"canonical_sha256":"a5c52cc4d7bb03da4dbeaae7767b584347561040ae9c7595daca8cfb24448fc8","source":{"kind":"arxiv","id":"1912.12151","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1912.12151","created_at":"2026-07-05T00:28:40Z"},{"alias_kind":"arxiv_version","alias_value":"1912.12151v1","created_at":"2026-07-05T00:28:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1912.12151","created_at":"2026-07-05T00:28:40Z"},{"alias_kind":"pith_short_12","alias_value":"UXCSZRGXXMB5","created_at":"2026-07-05T00:28:40Z"},{"alias_kind":"pith_short_16","alias_value":"UXCSZRGXXMB5UTN6","created_at":"2026-07-05T00:28:40Z"},{"alias_kind":"pith_short_8","alias_value":"UXCSZRGX","created_at":"2026-07-05T00:28:40Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:UXCSZRGXXMB5UTN6VLTXM62YIN","target":"record","payload":{"canonical_record":{"source":{"id":"1912.12151","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2019-12-27T15:20:56Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"a042e391d5e0a07ff5f9347d7d0c231e3c56181d6a412665570b8c28c51abb80","abstract_canon_sha256":"265c97bc0007b35483760e80ea4cf4e3ffa65b4e2da0512dd8a0b8013f908219"},"schema_version":"1.0"},"canonical_sha256":"a5c52cc4d7bb03da4dbeaae7767b584347561040ae9c7595daca8cfb24448fc8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:28:40.723092Z","signature_b64":"MCPT8D0h150yHoc8F26csP4PG3tHr6yKme1kS/pp5d1MMoTpafKInwNyNPwKoFlItB3c3c/jQn6PykfQYPr9Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a5c52cc4d7bb03da4dbeaae7767b584347561040ae9c7595daca8cfb24448fc8","last_reissued_at":"2026-07-05T00:28:40.722651Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:28:40.722651Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1912.12151","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":"2026-07-05T00:28:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hwWf/cGJoS+QtvJGdyDPC/TJGDtq1RxMTwACp3TgQon5wTne7b/4PJUDFjOfZY/k0iRShvYwjfsTFYlLzj7gCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-11T19:17:21.075130Z"},"content_sha256":"cea2aa0314711c3e95a24130a733651e0fa61b8b8e9f651eba7fdf992ecfa061","schema_version":"1.0","event_id":"sha256:cea2aa0314711c3e95a24130a733651e0fa61b8b8e9f651eba7fdf992ecfa061"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:UXCSZRGXXMB5UTN6VLTXM62YIN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Water-Filling Primal-Dual Algorithm for Approximating Non-Linear Covering Problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"cs.DS","authors_text":"Andr\\'es Fielbaum, Ignacio Morales, Jos\\'e Verschae","submitted_at":"2019-12-27T15:20:56Z","abstract_excerpt":"Obtaining strong linear relaxations of capacitated covering problems constitute a major technical challenge even for simple settings. For one of the most basic cases, the Knapsack-Cover (Min-Knapsack) problem, the relaxation based on knapsack-cover inequalities achieves an integrality gap of 2. These inequalities have been exploited in more general environments, many of which admit primal-dual approximation algorithms.\n  Inspired by problems from power and transport systems, we introduce a new general setting in which items can be taken fractionally to cover a given demand. The cost incurred b"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1912.12151","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1912.12151/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T00:28:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bNC9i97OqQV0gDa+7Qc89m4MSO8nr50q9yLewKI6QLJDOzMr8JgG+BsLJIg3s6T7KKUepcVwB3akjoo/g3DsBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-11T19:17:21.075525Z"},"content_sha256":"b5a85d418bad2b96d75a84a6c7b8c7fc0d8aaa169c531102f9ce3a676ed869d2","schema_version":"1.0","event_id":"sha256:b5a85d418bad2b96d75a84a6c7b8c7fc0d8aaa169c531102f9ce3a676ed869d2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UXCSZRGXXMB5UTN6VLTXM62YIN/bundle.json","state_url":"https://pith.science/pith/UXCSZRGXXMB5UTN6VLTXM62YIN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UXCSZRGXXMB5UTN6VLTXM62YIN/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":"2026-07-11T19:17:21Z","links":{"resolver":"https://pith.science/pith/UXCSZRGXXMB5UTN6VLTXM62YIN","bundle":"https://pith.science/pith/UXCSZRGXXMB5UTN6VLTXM62YIN/bundle.json","state":"https://pith.science/pith/UXCSZRGXXMB5UTN6VLTXM62YIN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UXCSZRGXXMB5UTN6VLTXM62YIN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:UXCSZRGXXMB5UTN6VLTXM62YIN","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":"265c97bc0007b35483760e80ea4cf4e3ffa65b4e2da0512dd8a0b8013f908219","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2019-12-27T15:20:56Z","title_canon_sha256":"a042e391d5e0a07ff5f9347d7d0c231e3c56181d6a412665570b8c28c51abb80"},"schema_version":"1.0","source":{"id":"1912.12151","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1912.12151","created_at":"2026-07-05T00:28:40Z"},{"alias_kind":"arxiv_version","alias_value":"1912.12151v1","created_at":"2026-07-05T00:28:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1912.12151","created_at":"2026-07-05T00:28:40Z"},{"alias_kind":"pith_short_12","alias_value":"UXCSZRGXXMB5","created_at":"2026-07-05T00:28:40Z"},{"alias_kind":"pith_short_16","alias_value":"UXCSZRGXXMB5UTN6","created_at":"2026-07-05T00:28:40Z"},{"alias_kind":"pith_short_8","alias_value":"UXCSZRGX","created_at":"2026-07-05T00:28:40Z"}],"graph_snapshots":[{"event_id":"sha256:b5a85d418bad2b96d75a84a6c7b8c7fc0d8aaa169c531102f9ce3a676ed869d2","target":"graph","created_at":"2026-07-05T00:28:40Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1912.12151/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Obtaining strong linear relaxations of capacitated covering problems constitute a major technical challenge even for simple settings. For one of the most basic cases, the Knapsack-Cover (Min-Knapsack) problem, the relaxation based on knapsack-cover inequalities achieves an integrality gap of 2. These inequalities have been exploited in more general environments, many of which admit primal-dual approximation algorithms.\n  Inspired by problems from power and transport systems, we introduce a new general setting in which items can be taken fractionally to cover a given demand. The cost incurred b","authors_text":"Andr\\'es Fielbaum, Ignacio Morales, Jos\\'e Verschae","cross_cats":["math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2019-12-27T15:20:56Z","title":"A Water-Filling Primal-Dual Algorithm for Approximating Non-Linear Covering Problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1912.12151","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:cea2aa0314711c3e95a24130a733651e0fa61b8b8e9f651eba7fdf992ecfa061","target":"record","created_at":"2026-07-05T00:28:40Z","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":"265c97bc0007b35483760e80ea4cf4e3ffa65b4e2da0512dd8a0b8013f908219","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2019-12-27T15:20:56Z","title_canon_sha256":"a042e391d5e0a07ff5f9347d7d0c231e3c56181d6a412665570b8c28c51abb80"},"schema_version":"1.0","source":{"id":"1912.12151","kind":"arxiv","version":1}},"canonical_sha256":"a5c52cc4d7bb03da4dbeaae7767b584347561040ae9c7595daca8cfb24448fc8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a5c52cc4d7bb03da4dbeaae7767b584347561040ae9c7595daca8cfb24448fc8","first_computed_at":"2026-07-05T00:28:40.722651Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:28:40.722651Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MCPT8D0h150yHoc8F26csP4PG3tHr6yKme1kS/pp5d1MMoTpafKInwNyNPwKoFlItB3c3c/jQn6PykfQYPr9Bw==","signature_status":"signed_v1","signed_at":"2026-07-05T00:28:40.723092Z","signed_message":"canonical_sha256_bytes"},"source_id":"1912.12151","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cea2aa0314711c3e95a24130a733651e0fa61b8b8e9f651eba7fdf992ecfa061","sha256:b5a85d418bad2b96d75a84a6c7b8c7fc0d8aaa169c531102f9ce3a676ed869d2"],"state_sha256":"d3425cf9112850c4653a342fa5b834e6637bf6d7d9610fb97ae5e5603e87b52e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sG1pDFapEn/8gMG9o+q5RDnNNKXtMjRK1tAXVM/m94F6MheclLYZaGnm4seaLSiUGaXlSumncaEQdWckMOdoDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-11T19:17:21.077701Z","bundle_sha256":"4b8aec29fec88dca5456ffaf2c96775f1368c8077361f33c5bb17d0793e16bb6"}}