{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:RNB6JIWMMUNTRQEN4BPEIAIPIB","short_pith_number":"pith:RNB6JIWM","canonical_record":{"source":{"id":"1908.02019","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2019-08-06T08:43:53Z","cross_cats_sorted":[],"title_canon_sha256":"c6bca2c11835685947cc2d5ca812ba8f6d5e2a7c55aa69b006773f4834652bcd","abstract_canon_sha256":"98d2f358f9a5992d9ff725cda125e8b074dae132d2eba75b8ceb282da2b8b2e6"},"schema_version":"1.0"},"canonical_sha256":"8b43e4a2cc651b38c08de05e44010f40555f8a9c02dc9f9880e42cc3349b22f5","source":{"kind":"arxiv","id":"1908.02019","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.02019","created_at":"2026-07-05T00:16:04Z"},{"alias_kind":"arxiv_version","alias_value":"1908.02019v2","created_at":"2026-07-05T00:16:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.02019","created_at":"2026-07-05T00:16:04Z"},{"alias_kind":"pith_short_12","alias_value":"RNB6JIWMMUNT","created_at":"2026-07-05T00:16:04Z"},{"alias_kind":"pith_short_16","alias_value":"RNB6JIWMMUNTRQEN","created_at":"2026-07-05T00:16:04Z"},{"alias_kind":"pith_short_8","alias_value":"RNB6JIWM","created_at":"2026-07-05T00:16:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:RNB6JIWMMUNTRQEN4BPEIAIPIB","target":"record","payload":{"canonical_record":{"source":{"id":"1908.02019","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2019-08-06T08:43:53Z","cross_cats_sorted":[],"title_canon_sha256":"c6bca2c11835685947cc2d5ca812ba8f6d5e2a7c55aa69b006773f4834652bcd","abstract_canon_sha256":"98d2f358f9a5992d9ff725cda125e8b074dae132d2eba75b8ceb282da2b8b2e6"},"schema_version":"1.0"},"canonical_sha256":"8b43e4a2cc651b38c08de05e44010f40555f8a9c02dc9f9880e42cc3349b22f5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:16:04.898979Z","signature_b64":"bvejBXXRpFi1AxT4Orz+/0wMZUpylrr/au26H8nzgf/DD7/qrjgIJdvvbcU1GzqYufuXyGZlX/hvN/xSo0JwAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8b43e4a2cc651b38c08de05e44010f40555f8a9c02dc9f9880e42cc3349b22f5","last_reissued_at":"2026-07-05T00:16:04.898564Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:16:04.898564Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1908.02019","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T00:16:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"clp7+w3+a/86GLDL8CmWfUnTbtFdf6Qqcd75J+mV7puBitrh0E8vvjsObP7CLQU8uftcRwN2svL3DYs48B9zBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T13:34:48.156277Z"},"content_sha256":"ac7235d691449cf11109a6d44a1fe93fb56f5a5c660421f96ace969b0f7ea6ea","schema_version":"1.0","event_id":"sha256:ac7235d691449cf11109a6d44a1fe93fb56f5a5c660421f96ace969b0f7ea6ea"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:RNB6JIWMMUNTRQEN4BPEIAIPIB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Finite-Horizon Optimal Control of Boolean Control Networks: A Unified Graph-Theoretical Approach","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Changkai Sun, Cheng Xiang, Kairong Qin, Shuhua Gao, Tong Heng Lee","submitted_at":"2019-08-06T08:43:53Z","abstract_excerpt":"This paper investigates the finite-horizon optimal control (FHOC) problem of Boolean control networks (BCNs) from a graph theory perspective. We first formulate two general problems to unify various special cases studied in the literature: (i) the horizon length is $\\textit{a priori}$ fixed; (ii) the horizon length is unspecified but finite for given destination states. Notably, both problems can incorporate time-variant costs, which are rarely considered in existing work, and a variety of constraints. The existence of an optimal control sequence is analyzed under mild assumptions. Motivated b"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.02019","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/1908.02019/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":"2026-07-05T00:16:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"X62IkLU25kld7wKiGPSBvopX6eDmqny6WO2WNX10vrcPXe+vmP5+zOP0hqaw7nz5whe2UBAs+/z3INRqnmt5Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T13:34:48.156790Z"},"content_sha256":"f47a967c2d80702552414012bc3ddd13d906182130272e28a20320c3f2a8f132","schema_version":"1.0","event_id":"sha256:f47a967c2d80702552414012bc3ddd13d906182130272e28a20320c3f2a8f132"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RNB6JIWMMUNTRQEN4BPEIAIPIB/bundle.json","state_url":"https://pith.science/pith/RNB6JIWMMUNTRQEN4BPEIAIPIB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RNB6JIWMMUNTRQEN4BPEIAIPIB/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":"2026-08-16T13:34:48Z","links":{"resolver":"https://pith.science/pith/RNB6JIWMMUNTRQEN4BPEIAIPIB","bundle":"https://pith.science/pith/RNB6JIWMMUNTRQEN4BPEIAIPIB/bundle.json","state":"https://pith.science/pith/RNB6JIWMMUNTRQEN4BPEIAIPIB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RNB6JIWMMUNTRQEN4BPEIAIPIB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:RNB6JIWMMUNTRQEN4BPEIAIPIB","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":"98d2f358f9a5992d9ff725cda125e8b074dae132d2eba75b8ceb282da2b8b2e6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2019-08-06T08:43:53Z","title_canon_sha256":"c6bca2c11835685947cc2d5ca812ba8f6d5e2a7c55aa69b006773f4834652bcd"},"schema_version":"1.0","source":{"id":"1908.02019","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.02019","created_at":"2026-07-05T00:16:04Z"},{"alias_kind":"arxiv_version","alias_value":"1908.02019v2","created_at":"2026-07-05T00:16:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.02019","created_at":"2026-07-05T00:16:04Z"},{"alias_kind":"pith_short_12","alias_value":"RNB6JIWMMUNT","created_at":"2026-07-05T00:16:04Z"},{"alias_kind":"pith_short_16","alias_value":"RNB6JIWMMUNTRQEN","created_at":"2026-07-05T00:16:04Z"},{"alias_kind":"pith_short_8","alias_value":"RNB6JIWM","created_at":"2026-07-05T00:16:04Z"}],"graph_snapshots":[{"event_id":"sha256:f47a967c2d80702552414012bc3ddd13d906182130272e28a20320c3f2a8f132","target":"graph","created_at":"2026-07-05T00:16:04Z","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/1908.02019/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This paper investigates the finite-horizon optimal control (FHOC) problem of Boolean control networks (BCNs) from a graph theory perspective. We first formulate two general problems to unify various special cases studied in the literature: (i) the horizon length is $\\textit{a priori}$ fixed; (ii) the horizon length is unspecified but finite for given destination states. Notably, both problems can incorporate time-variant costs, which are rarely considered in existing work, and a variety of constraints. The existence of an optimal control sequence is analyzed under mild assumptions. Motivated b","authors_text":"Changkai Sun, Cheng Xiang, Kairong Qin, Shuhua Gao, Tong Heng Lee","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2019-08-06T08:43:53Z","title":"Finite-Horizon Optimal Control of Boolean Control Networks: A Unified Graph-Theoretical Approach"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.02019","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:ac7235d691449cf11109a6d44a1fe93fb56f5a5c660421f96ace969b0f7ea6ea","target":"record","created_at":"2026-07-05T00:16:04Z","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":"98d2f358f9a5992d9ff725cda125e8b074dae132d2eba75b8ceb282da2b8b2e6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2019-08-06T08:43:53Z","title_canon_sha256":"c6bca2c11835685947cc2d5ca812ba8f6d5e2a7c55aa69b006773f4834652bcd"},"schema_version":"1.0","source":{"id":"1908.02019","kind":"arxiv","version":2}},"canonical_sha256":"8b43e4a2cc651b38c08de05e44010f40555f8a9c02dc9f9880e42cc3349b22f5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8b43e4a2cc651b38c08de05e44010f40555f8a9c02dc9f9880e42cc3349b22f5","first_computed_at":"2026-07-05T00:16:04.898564Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:16:04.898564Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bvejBXXRpFi1AxT4Orz+/0wMZUpylrr/au26H8nzgf/DD7/qrjgIJdvvbcU1GzqYufuXyGZlX/hvN/xSo0JwAA==","signature_status":"signed_v1","signed_at":"2026-07-05T00:16:04.898979Z","signed_message":"canonical_sha256_bytes"},"source_id":"1908.02019","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ac7235d691449cf11109a6d44a1fe93fb56f5a5c660421f96ace969b0f7ea6ea","sha256:f47a967c2d80702552414012bc3ddd13d906182130272e28a20320c3f2a8f132"],"state_sha256":"795f8de5e514b76bf2e4a6cc791974f4787a28c25f60f043280b88202801dfa1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aJWRd9RBeKmIzazCrFoCzHdyCmSIIQYaPzW5YBzZsPsLZLtAbGPUE0MlQ9V55dFMgR8+cBpmo7q7N7EzEynPCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-16T13:34:48.160732Z","bundle_sha256":"ab123009e0eca4ddacf4e7d9d17cf2c403aff56614caf5f9232a6fa09a371dac"}}