{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:K6MEYODGFDMEEXAAENFXH2VEZA","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":"c707478ab2fb68d27b1949ae33bcf4388b897ea4ed8a35ae2debbedbc3d042b0","cross_cats_sorted":["math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-07-25T20:23:44Z","title_canon_sha256":"83000b16c37878da539d457c8ead9fe236b80e26c66a6deb03ef9f02c8bbe45d"},"schema_version":"1.0","source":{"id":"1107.5066","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.5066","created_at":"2026-05-18T04:16:53Z"},{"alias_kind":"arxiv_version","alias_value":"1107.5066v1","created_at":"2026-05-18T04:16:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.5066","created_at":"2026-05-18T04:16:53Z"},{"alias_kind":"pith_short_12","alias_value":"K6MEYODGFDME","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_16","alias_value":"K6MEYODGFDMEEXAA","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_8","alias_value":"K6MEYODG","created_at":"2026-05-18T12:26:32Z"}],"graph_snapshots":[{"event_id":"sha256:6d63587124fb3353df8109285f86c80771621f4cbc29ab5d368f7f3b543717cd","target":"graph","created_at":"2026-05-18T04:16:53Z","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":"The Fighter problem with discrete ammunition is studied. An aircraft (fighter) equipped with $n$ anti-aircraft missiles is intercepted by enemy airplanes, the appearance of which follows a homogeneous Poisson process with known intensity. If $j$ of the $n$ missiles are spent at an encounter they destroy an enemy plane with probability $a(j)$, where $a(0) = 0 $ and $\\{a(j)\\}$ is a known, strictly increasing concave sequence, e.g., $a(j) = 1-q^j, \\; \\, 0 < q < 1$. If the enemy is not destroyed, the enemy shoots the fighter down with known probability $1-u$, where $0 \\le u \\le 1$. The goal of the","authors_text":"Ester Samuel-Cahn, Jay Bartroff","cross_cats":["math.ST","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-07-25T20:23:44Z","title":"The Fighter Problem: Optimal Allocation of a Discrete Commodity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.5066","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":"sha256:5edee197a28dfe00e56b3e0e0c3f4be4e639bf8d3ba7edab12bc55bbe91b7663","target":"record","created_at":"2026-05-18T04:16:53Z","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":"c707478ab2fb68d27b1949ae33bcf4388b897ea4ed8a35ae2debbedbc3d042b0","cross_cats_sorted":["math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-07-25T20:23:44Z","title_canon_sha256":"83000b16c37878da539d457c8ead9fe236b80e26c66a6deb03ef9f02c8bbe45d"},"schema_version":"1.0","source":{"id":"1107.5066","kind":"arxiv","version":1}},"canonical_sha256":"57984c386628d8425c00234b73eaa4c80f5bf7b28bd9e820ee66e365d284d635","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"57984c386628d8425c00234b73eaa4c80f5bf7b28bd9e820ee66e365d284d635","first_computed_at":"2026-05-18T04:16:53.113308Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:16:53.113308Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"F1NZO4X1BmJLoVXfcB2MNGySRulr3TD5DrshqfPfkfBCr0C6lNtsEGj+QrwNubhmsQIbjTKSG+CZYwA5IKeICQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:16:53.113882Z","signed_message":"canonical_sha256_bytes"},"source_id":"1107.5066","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5edee197a28dfe00e56b3e0e0c3f4be4e639bf8d3ba7edab12bc55bbe91b7663","sha256:6d63587124fb3353df8109285f86c80771621f4cbc29ab5d368f7f3b543717cd"],"state_sha256":"acee941e94a7be984777da30938fb1207b997e324e38f06a634fc5e840ffa816"}