{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2021:4SMCMFHZB7X2K5BZCSERGTUFVO","short_pith_number":"pith:4SMCMFHZ","schema_version":"1.0","canonical_sha256":"e4982614f90fefa574391489134e85abbb0366e84f3dcae65c2af16580a80d9c","source":{"kind":"arxiv","id":"2104.00717","version":2},"attestation_state":"computed","paper":{"title":"Optimal Strategies for Guarding a Compact and Convex Target Set: A Differential Game Approach","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SY"],"primary_cat":"eess.SY","authors_text":"Efstathios Bakolas, Yoonjae Lee","submitted_at":"2021-04-01T18:52:16Z","abstract_excerpt":"We revisit the two-player planar target-defense game initially posed by Isaacs where a pursuer (or defender) attempts to guard a target set from an attack by an evader (or attacker). This paper builds on existing analytical solutions to games of defending a simple shape of target area to develop a generalized and extended solution to the same game with a compact convex target set with smooth boundary. Isaacs' method is applied to address the game of kind and games of degree. A geometric solution approach is used to find the barrier surface that demarcates the winning sets of the players. A val"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2104.00717","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"eess.SY","submitted_at":"2021-04-01T18:52:16Z","cross_cats_sorted":["cs.SY"],"title_canon_sha256":"1a24926111f59cd16dc07c9bc31fc4287649c6636d01cebb8c76fe3eba148072","abstract_canon_sha256":"856b185445191f72d7061a36a746a5c084585b232fe8ecf718157b7cbfaaa4a1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:10:35.286331Z","signature_b64":"zVXWTcrt15UuL2FOnTyUThgH6qq/6DPT37mw8Y2De2MIeZhYlZFgU8NDctn66nHfcOf9Pl2umpPUEyXWio94BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e4982614f90fefa574391489134e85abbb0366e84f3dcae65c2af16580a80d9c","last_reissued_at":"2026-07-05T04:10:35.285843Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:10:35.285843Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Optimal Strategies for Guarding a Compact and Convex Target Set: A Differential Game Approach","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SY"],"primary_cat":"eess.SY","authors_text":"Efstathios Bakolas, Yoonjae Lee","submitted_at":"2021-04-01T18:52:16Z","abstract_excerpt":"We revisit the two-player planar target-defense game initially posed by Isaacs where a pursuer (or defender) attempts to guard a target set from an attack by an evader (or attacker). This paper builds on existing analytical solutions to games of defending a simple shape of target area to develop a generalized and extended solution to the same game with a compact convex target set with smooth boundary. Isaacs' method is applied to address the game of kind and games of degree. A geometric solution approach is used to find the barrier surface that demarcates the winning sets of the players. A val"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2104.00717","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2104.00717/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2104.00717","created_at":"2026-07-05T04:10:35.285902+00:00"},{"alias_kind":"arxiv_version","alias_value":"2104.00717v2","created_at":"2026-07-05T04:10:35.285902+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2104.00717","created_at":"2026-07-05T04:10:35.285902+00:00"},{"alias_kind":"pith_short_12","alias_value":"4SMCMFHZB7X2","created_at":"2026-07-05T04:10:35.285902+00:00"},{"alias_kind":"pith_short_16","alias_value":"4SMCMFHZB7X2K5BZ","created_at":"2026-07-05T04:10:35.285902+00:00"},{"alias_kind":"pith_short_8","alias_value":"4SMCMFHZ","created_at":"2026-07-05T04:10:35.285902+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/4SMCMFHZB7X2K5BZCSERGTUFVO","json":"https://pith.science/pith/4SMCMFHZB7X2K5BZCSERGTUFVO.json","graph_json":"https://pith.science/api/pith-number/4SMCMFHZB7X2K5BZCSERGTUFVO/graph.json","events_json":"https://pith.science/api/pith-number/4SMCMFHZB7X2K5BZCSERGTUFVO/events.json","paper":"https://pith.science/paper/4SMCMFHZ"},"agent_actions":{"view_html":"https://pith.science/pith/4SMCMFHZB7X2K5BZCSERGTUFVO","download_json":"https://pith.science/pith/4SMCMFHZB7X2K5BZCSERGTUFVO.json","view_paper":"https://pith.science/paper/4SMCMFHZ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2104.00717&json=true","fetch_graph":"https://pith.science/api/pith-number/4SMCMFHZB7X2K5BZCSERGTUFVO/graph.json","fetch_events":"https://pith.science/api/pith-number/4SMCMFHZB7X2K5BZCSERGTUFVO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4SMCMFHZB7X2K5BZCSERGTUFVO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4SMCMFHZB7X2K5BZCSERGTUFVO/action/storage_attestation","attest_author":"https://pith.science/pith/4SMCMFHZB7X2K5BZCSERGTUFVO/action/author_attestation","sign_citation":"https://pith.science/pith/4SMCMFHZB7X2K5BZCSERGTUFVO/action/citation_signature","submit_replication":"https://pith.science/pith/4SMCMFHZB7X2K5BZCSERGTUFVO/action/replication_record"}},"created_at":"2026-07-05T04:10:35.285902+00:00","updated_at":"2026-07-05T04:10:35.285902+00:00"}