{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:ALWD74OHLRAOIK37DHLTAIYH25","short_pith_number":"pith:ALWD74OH","canonical_record":{"source":{"id":"1712.02504","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-12-07T06:16:58Z","cross_cats_sorted":[],"title_canon_sha256":"47476a79cbf821aa5739ce70e562732c85429bf9a7b76caa4b254516fb80f625","abstract_canon_sha256":"722917fce5ab72d53f777a775e06668745fa2e7b8650e0c4badb4168f52d6fef"},"schema_version":"1.0"},"canonical_sha256":"02ec3ff1c75c40e42b7f19d7302307d743511342d8b2907e0308ea72b759ecdb","source":{"kind":"arxiv","id":"1712.02504","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.02504","created_at":"2026-05-18T00:28:33Z"},{"alias_kind":"arxiv_version","alias_value":"1712.02504v1","created_at":"2026-05-18T00:28:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.02504","created_at":"2026-05-18T00:28:33Z"},{"alias_kind":"pith_short_12","alias_value":"ALWD74OHLRAO","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_16","alias_value":"ALWD74OHLRAOIK37","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_8","alias_value":"ALWD74OH","created_at":"2026-05-18T12:31:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:ALWD74OHLRAOIK37DHLTAIYH25","target":"record","payload":{"canonical_record":{"source":{"id":"1712.02504","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-12-07T06:16:58Z","cross_cats_sorted":[],"title_canon_sha256":"47476a79cbf821aa5739ce70e562732c85429bf9a7b76caa4b254516fb80f625","abstract_canon_sha256":"722917fce5ab72d53f777a775e06668745fa2e7b8650e0c4badb4168f52d6fef"},"schema_version":"1.0"},"canonical_sha256":"02ec3ff1c75c40e42b7f19d7302307d743511342d8b2907e0308ea72b759ecdb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:28:33.828472Z","signature_b64":"NWonY1w2B5QsQZj3JlChnhX3KaTgydU6Eg3XocVUmZeP/I89Q8osDK/8LIM9EDNN0Oe+c9eHPIOOzHVc0vM6DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"02ec3ff1c75c40e42b7f19d7302307d743511342d8b2907e0308ea72b759ecdb","last_reissued_at":"2026-05-18T00:28:33.827732Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:28:33.827732Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1712.02504","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":"2026-05-18T00:28:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7zSAUh/3exgJV0Yr5gt0afu8RmDYO45ZUrBinuIUkmmqa3rhYh5AZePA5fhiqETtVt9anjth1/pT/k80t9fBCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T22:15:04.560379Z"},"content_sha256":"2a2da70c8eca7d8570bf3dcf6a743144a45d641f909f5de667e5dbcbf7619787","schema_version":"1.0","event_id":"sha256:2a2da70c8eca7d8570bf3dcf6a743144a45d641f909f5de667e5dbcbf7619787"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:ALWD74OHLRAOIK37DHLTAIYH25","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Cooperative Control via Congestion Game Approach","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Daizhan Cheng, Sisi Pan, Yaqi Hao, Yupeng Qiao","submitted_at":"2017-12-07T06:16:58Z","abstract_excerpt":"The optimization of facility-based systems is considered. First, the congestion game is converted into a matrix form, so that the matrix approach is applicable. Then, a facility-based system with a system performance criterion is considered. A necessary and sufficient condition is given to assure that the system is convertible into a congestion game with the given system performance criterion as its potential function by designing proper facility-cost functions. Using this technology, for a dynamic facility-based system the global optimization may be reached when each agent optimizes its payof"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.02504","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":"2026-05-18T00:28:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Q55ftbQzu8eJgA53cr0lKcy6HTwDhTPa7VkCco2KIDfY6fFqWDvIjeNHfriBfBJjGQl265mh+D2yKxq3nDj+DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T22:15:04.561065Z"},"content_sha256":"463d5423f442f315a39c3ef02e4505caa3051a17907df166297aadb2810ee72f","schema_version":"1.0","event_id":"sha256:463d5423f442f315a39c3ef02e4505caa3051a17907df166297aadb2810ee72f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ALWD74OHLRAOIK37DHLTAIYH25/bundle.json","state_url":"https://pith.science/pith/ALWD74OHLRAOIK37DHLTAIYH25/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ALWD74OHLRAOIK37DHLTAIYH25/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":"2026-05-28T22:15:04Z","links":{"resolver":"https://pith.science/pith/ALWD74OHLRAOIK37DHLTAIYH25","bundle":"https://pith.science/pith/ALWD74OHLRAOIK37DHLTAIYH25/bundle.json","state":"https://pith.science/pith/ALWD74OHLRAOIK37DHLTAIYH25/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ALWD74OHLRAOIK37DHLTAIYH25/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:ALWD74OHLRAOIK37DHLTAIYH25","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":"722917fce5ab72d53f777a775e06668745fa2e7b8650e0c4badb4168f52d6fef","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-12-07T06:16:58Z","title_canon_sha256":"47476a79cbf821aa5739ce70e562732c85429bf9a7b76caa4b254516fb80f625"},"schema_version":"1.0","source":{"id":"1712.02504","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.02504","created_at":"2026-05-18T00:28:33Z"},{"alias_kind":"arxiv_version","alias_value":"1712.02504v1","created_at":"2026-05-18T00:28:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.02504","created_at":"2026-05-18T00:28:33Z"},{"alias_kind":"pith_short_12","alias_value":"ALWD74OHLRAO","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_16","alias_value":"ALWD74OHLRAOIK37","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_8","alias_value":"ALWD74OH","created_at":"2026-05-18T12:31:05Z"}],"graph_snapshots":[{"event_id":"sha256:463d5423f442f315a39c3ef02e4505caa3051a17907df166297aadb2810ee72f","target":"graph","created_at":"2026-05-18T00:28:33Z","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 optimization of facility-based systems is considered. First, the congestion game is converted into a matrix form, so that the matrix approach is applicable. Then, a facility-based system with a system performance criterion is considered. A necessary and sufficient condition is given to assure that the system is convertible into a congestion game with the given system performance criterion as its potential function by designing proper facility-cost functions. Using this technology, for a dynamic facility-based system the global optimization may be reached when each agent optimizes its payof","authors_text":"Daizhan Cheng, Sisi Pan, Yaqi Hao, Yupeng Qiao","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-12-07T06:16:58Z","title":"Cooperative Control via Congestion Game Approach"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.02504","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":"sha256:2a2da70c8eca7d8570bf3dcf6a743144a45d641f909f5de667e5dbcbf7619787","target":"record","created_at":"2026-05-18T00:28:33Z","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":"722917fce5ab72d53f777a775e06668745fa2e7b8650e0c4badb4168f52d6fef","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-12-07T06:16:58Z","title_canon_sha256":"47476a79cbf821aa5739ce70e562732c85429bf9a7b76caa4b254516fb80f625"},"schema_version":"1.0","source":{"id":"1712.02504","kind":"arxiv","version":1}},"canonical_sha256":"02ec3ff1c75c40e42b7f19d7302307d743511342d8b2907e0308ea72b759ecdb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"02ec3ff1c75c40e42b7f19d7302307d743511342d8b2907e0308ea72b759ecdb","first_computed_at":"2026-05-18T00:28:33.827732Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:28:33.827732Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NWonY1w2B5QsQZj3JlChnhX3KaTgydU6Eg3XocVUmZeP/I89Q8osDK/8LIM9EDNN0Oe+c9eHPIOOzHVc0vM6DA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:28:33.828472Z","signed_message":"canonical_sha256_bytes"},"source_id":"1712.02504","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2a2da70c8eca7d8570bf3dcf6a743144a45d641f909f5de667e5dbcbf7619787","sha256:463d5423f442f315a39c3ef02e4505caa3051a17907df166297aadb2810ee72f"],"state_sha256":"3c48c9be680f0be111c9c48aa7ca606a459679b8767a73bd69c2638d63da9828"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Iij1ORd2Z4Nq8FhPPQsyHBuAjEEhoc1iyLpwcxakYJzwMQeDN3Jbbd0ybesTxRDstqMNnJrbaGpKTzf1McWyDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T22:15:04.564809Z","bundle_sha256":"24cec32e1df3c18721d9d5c47824c31c6b89f13f238c1bca795a83a3bc203ed7"}}