{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:TCP6D23HDUJDVDAPSTZ25IGJSL","short_pith_number":"pith:TCP6D23H","canonical_record":{"source":{"id":"1906.00144","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2019-06-01T03:36:20Z","cross_cats_sorted":[],"title_canon_sha256":"2f09838275b1c006b25241b6fa08a4e7ae135a18f58506990719603b97ea640f","abstract_canon_sha256":"81abcff229bc57ffb8ff1a2fb9b78fa7bcb301921d30a0134c696ab2a2c534f4"},"schema_version":"1.0"},"canonical_sha256":"989fe1eb671d123a8c0f94f3aea0c992d2ec04c1d439220f30d3107a035aeaf2","source":{"kind":"arxiv","id":"1906.00144","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1906.00144","created_at":"2026-05-17T23:44:28Z"},{"alias_kind":"arxiv_version","alias_value":"1906.00144v1","created_at":"2026-05-17T23:44:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.00144","created_at":"2026-05-17T23:44:28Z"},{"alias_kind":"pith_short_12","alias_value":"TCP6D23HDUJD","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_16","alias_value":"TCP6D23HDUJDVDAP","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_8","alias_value":"TCP6D23H","created_at":"2026-05-18T12:33:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:TCP6D23HDUJDVDAPSTZ25IGJSL","target":"record","payload":{"canonical_record":{"source":{"id":"1906.00144","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2019-06-01T03:36:20Z","cross_cats_sorted":[],"title_canon_sha256":"2f09838275b1c006b25241b6fa08a4e7ae135a18f58506990719603b97ea640f","abstract_canon_sha256":"81abcff229bc57ffb8ff1a2fb9b78fa7bcb301921d30a0134c696ab2a2c534f4"},"schema_version":"1.0"},"canonical_sha256":"989fe1eb671d123a8c0f94f3aea0c992d2ec04c1d439220f30d3107a035aeaf2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:44:28.018293Z","signature_b64":"sNl/2wNRsllNUBNo2rXuW8VDwHyXmlTCr6gcUSSSxrSMP2585oPoLUB3sUTUFP896/zMoYcyL3nqTSbEzpnZDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"989fe1eb671d123a8c0f94f3aea0c992d2ec04c1d439220f30d3107a035aeaf2","last_reissued_at":"2026-05-17T23:44:28.017614Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:44:28.017614Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1906.00144","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":"2026-05-17T23:44:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VqiVEhwm0qWm6yagp+p1yMH/+f4GgN0KEoh4ldkiV/B9WDdR7v7UPpP068ZYWzw2LzMq3ckDRl8hrDVcPRbmCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T21:27:01.484107Z"},"content_sha256":"0f5017a77b71a01cf1bd7ecb908669af24b54f0afea5b44ccf41bb32ca058fa8","schema_version":"1.0","event_id":"sha256:0f5017a77b71a01cf1bd7ecb908669af24b54f0afea5b44ccf41bb32ca058fa8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:TCP6D23HDUJDVDAPSTZ25IGJSL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Theorems of the Alternative for Conic Integer Programming","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Andrew J. Schaefer, Temitayo Ajayi, Varun Suriyanarayana","submitted_at":"2019-06-01T03:36:20Z","abstract_excerpt":"Farkas' Lemma is a foundational result in linear programming, with implications in duality, optimality conditions, and stochastic and bilevel programming. Its generalizations are known as theorems of the alternative. There exist theorems of the alternative for integer programming and conic programming. We present theorems of the alternative for conic integer programming. We provide a nested procedure to construct a function that characterizes feasibility over right-hand sides and can determine which statement in a theorem of the alternative holds."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.00144","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":""},"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":"2026-05-17T23:44:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"x+3qbtYMzqcVTsoEpxQKjjsCppaij8c4nDURRV7xrNff9O69FBpjAv0Zipa81kvQBjCIlaOllhuWTJKKmQhyDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T21:27:01.484452Z"},"content_sha256":"675c7e0e66d1c9961530f743518a1c5d28e2b4c6f5468414432932688f1a05f1","schema_version":"1.0","event_id":"sha256:675c7e0e66d1c9961530f743518a1c5d28e2b4c6f5468414432932688f1a05f1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TCP6D23HDUJDVDAPSTZ25IGJSL/bundle.json","state_url":"https://pith.science/pith/TCP6D23HDUJDVDAPSTZ25IGJSL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TCP6D23HDUJDVDAPSTZ25IGJSL/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":"2026-06-04T21:27:01Z","links":{"resolver":"https://pith.science/pith/TCP6D23HDUJDVDAPSTZ25IGJSL","bundle":"https://pith.science/pith/TCP6D23HDUJDVDAPSTZ25IGJSL/bundle.json","state":"https://pith.science/pith/TCP6D23HDUJDVDAPSTZ25IGJSL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TCP6D23HDUJDVDAPSTZ25IGJSL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:TCP6D23HDUJDVDAPSTZ25IGJSL","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":"81abcff229bc57ffb8ff1a2fb9b78fa7bcb301921d30a0134c696ab2a2c534f4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2019-06-01T03:36:20Z","title_canon_sha256":"2f09838275b1c006b25241b6fa08a4e7ae135a18f58506990719603b97ea640f"},"schema_version":"1.0","source":{"id":"1906.00144","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1906.00144","created_at":"2026-05-17T23:44:28Z"},{"alias_kind":"arxiv_version","alias_value":"1906.00144v1","created_at":"2026-05-17T23:44:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.00144","created_at":"2026-05-17T23:44:28Z"},{"alias_kind":"pith_short_12","alias_value":"TCP6D23HDUJD","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_16","alias_value":"TCP6D23HDUJDVDAP","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_8","alias_value":"TCP6D23H","created_at":"2026-05-18T12:33:27Z"}],"graph_snapshots":[{"event_id":"sha256:675c7e0e66d1c9961530f743518a1c5d28e2b4c6f5468414432932688f1a05f1","target":"graph","created_at":"2026-05-17T23:44:28Z","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":"Farkas' Lemma is a foundational result in linear programming, with implications in duality, optimality conditions, and stochastic and bilevel programming. Its generalizations are known as theorems of the alternative. There exist theorems of the alternative for integer programming and conic programming. We present theorems of the alternative for conic integer programming. We provide a nested procedure to construct a function that characterizes feasibility over right-hand sides and can determine which statement in a theorem of the alternative holds.","authors_text":"Andrew J. Schaefer, Temitayo Ajayi, Varun Suriyanarayana","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2019-06-01T03:36:20Z","title":"Theorems of the Alternative for Conic Integer Programming"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.00144","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":"sha256:0f5017a77b71a01cf1bd7ecb908669af24b54f0afea5b44ccf41bb32ca058fa8","target":"record","created_at":"2026-05-17T23:44:28Z","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":"81abcff229bc57ffb8ff1a2fb9b78fa7bcb301921d30a0134c696ab2a2c534f4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2019-06-01T03:36:20Z","title_canon_sha256":"2f09838275b1c006b25241b6fa08a4e7ae135a18f58506990719603b97ea640f"},"schema_version":"1.0","source":{"id":"1906.00144","kind":"arxiv","version":1}},"canonical_sha256":"989fe1eb671d123a8c0f94f3aea0c992d2ec04c1d439220f30d3107a035aeaf2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"989fe1eb671d123a8c0f94f3aea0c992d2ec04c1d439220f30d3107a035aeaf2","first_computed_at":"2026-05-17T23:44:28.017614Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:44:28.017614Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sNl/2wNRsllNUBNo2rXuW8VDwHyXmlTCr6gcUSSSxrSMP2585oPoLUB3sUTUFP896/zMoYcyL3nqTSbEzpnZDw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:44:28.018293Z","signed_message":"canonical_sha256_bytes"},"source_id":"1906.00144","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0f5017a77b71a01cf1bd7ecb908669af24b54f0afea5b44ccf41bb32ca058fa8","sha256:675c7e0e66d1c9961530f743518a1c5d28e2b4c6f5468414432932688f1a05f1"],"state_sha256":"3c109735e2d5f8617e071f8e9b75c9a11f5398cdf1d0bd7d5f1c4f96ec5e9f1c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ChQidZdVS3MTbtMRQvmNOUSu9/3HG4b7QiMYDaTTqeOJpHlRKtzLdQyqvpBLwu71xVAdIf0qXO2Agh2V+Gb4BA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T21:27:01.486281Z","bundle_sha256":"d53997c4f5e92ef2a95bcb6689e27bd317474f5c783f4d8363e0b200ba4487f0"}}