{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:H6OQWTVILWGSAXIXG6U4GCCVPT","short_pith_number":"pith:H6OQWTVI","canonical_record":{"source":{"id":"1312.1075","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2013-12-04T09:28:51Z","cross_cats_sorted":["cs.SY","math.OC"],"title_canon_sha256":"f0dccffff5cf73b8f2d89079c853486b440700450e34a64ba7db8a9291220601","abstract_canon_sha256":"410aa177e943970ac7fa7e3d94cddde7451d5352a998637541332807613342a3"},"schema_version":"1.0"},"canonical_sha256":"3f9d0b4ea85d8d205d1737a9c308557ced018ec0fd83986047567ee454ff51f5","source":{"kind":"arxiv","id":"1312.1075","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.1075","created_at":"2026-05-18T03:00:25Z"},{"alias_kind":"arxiv_version","alias_value":"1312.1075v2","created_at":"2026-05-18T03:00:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.1075","created_at":"2026-05-18T03:00:25Z"},{"alias_kind":"pith_short_12","alias_value":"H6OQWTVILWGS","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_16","alias_value":"H6OQWTVILWGSAXIX","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_8","alias_value":"H6OQWTVI","created_at":"2026-05-18T12:27:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:H6OQWTVILWGSAXIXG6U4GCCVPT","target":"record","payload":{"canonical_record":{"source":{"id":"1312.1075","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2013-12-04T09:28:51Z","cross_cats_sorted":["cs.SY","math.OC"],"title_canon_sha256":"f0dccffff5cf73b8f2d89079c853486b440700450e34a64ba7db8a9291220601","abstract_canon_sha256":"410aa177e943970ac7fa7e3d94cddde7451d5352a998637541332807613342a3"},"schema_version":"1.0"},"canonical_sha256":"3f9d0b4ea85d8d205d1737a9c308557ced018ec0fd83986047567ee454ff51f5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:00:25.456260Z","signature_b64":"ZoBdGIMYYuGhSa65d6XL2mHHR4tBjZTv97pEsWq0ViluLtve64X2jozZyOAfLV0XpUDh6TbFA9qdWt/CfS6PDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3f9d0b4ea85d8d205d1737a9c308557ced018ec0fd83986047567ee454ff51f5","last_reissued_at":"2026-05-18T03:00:25.455292Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:00:25.455292Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1312.1075","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":"2026-05-18T03:00:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wmLPpIQS/z1FB/dcmydOxSjNAhgh68z6gNJ2vUVW96PpwhLvGv8R80jpSdhXTLeykbPVJmJS+sykwPhpy+bBBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T17:27:32.599675Z"},"content_sha256":"e9ea8154876fbda01201e73537c6dda6664275125f6509e881afbd5ae2b377fa","schema_version":"1.0","event_id":"sha256:e9ea8154876fbda01201e73537c6dda6664275125f6509e881afbd5ae2b377fa"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:H6OQWTVILWGSAXIXG6U4GCCVPT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Necessary and Sufficient Condition for the Existence of Potential Functions for Heterogeneous Routing Games","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SY","math.OC"],"primary_cat":"cs.GT","authors_text":"Alexandre M. Bayen, Farhad Farokhi, Karl H. Johansson, Walid Krichene","submitted_at":"2013-12-04T09:28:51Z","abstract_excerpt":"We study a heterogeneous routing game in which vehicles might belong to more than one type. The type determines the cost of traveling along an edge as a function of the flow of various types of vehicles over that edge. We relax the assumptions needed for the existence of a Nash equilibrium in this heterogeneous routing game. We extend the available results to present necessary and sufficient conditions for the existence of a potential function. We characterize a set of tolls that guarantee the existence of a potential function when only two types of users are participating in the game. We pres"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.1075","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":""},"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":"2026-05-18T03:00:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yG2NaUb4nolkU5PWnwmIOPegOzpyDKNu690m1J5zp5+w3eediqYWD2pnu8Tp6DFljH9fnNyLypYC9osVAI2TBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T17:27:32.600029Z"},"content_sha256":"6ae0564e01603f677889ba530d6f93e0cf678967d089acb30ddb2e24a666f179","schema_version":"1.0","event_id":"sha256:6ae0564e01603f677889ba530d6f93e0cf678967d089acb30ddb2e24a666f179"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/H6OQWTVILWGSAXIXG6U4GCCVPT/bundle.json","state_url":"https://pith.science/pith/H6OQWTVILWGSAXIXG6U4GCCVPT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/H6OQWTVILWGSAXIXG6U4GCCVPT/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":"2026-06-02T17:27:32Z","links":{"resolver":"https://pith.science/pith/H6OQWTVILWGSAXIXG6U4GCCVPT","bundle":"https://pith.science/pith/H6OQWTVILWGSAXIXG6U4GCCVPT/bundle.json","state":"https://pith.science/pith/H6OQWTVILWGSAXIXG6U4GCCVPT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/H6OQWTVILWGSAXIXG6U4GCCVPT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:H6OQWTVILWGSAXIXG6U4GCCVPT","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":"410aa177e943970ac7fa7e3d94cddde7451d5352a998637541332807613342a3","cross_cats_sorted":["cs.SY","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2013-12-04T09:28:51Z","title_canon_sha256":"f0dccffff5cf73b8f2d89079c853486b440700450e34a64ba7db8a9291220601"},"schema_version":"1.0","source":{"id":"1312.1075","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.1075","created_at":"2026-05-18T03:00:25Z"},{"alias_kind":"arxiv_version","alias_value":"1312.1075v2","created_at":"2026-05-18T03:00:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.1075","created_at":"2026-05-18T03:00:25Z"},{"alias_kind":"pith_short_12","alias_value":"H6OQWTVILWGS","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_16","alias_value":"H6OQWTVILWGSAXIX","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_8","alias_value":"H6OQWTVI","created_at":"2026-05-18T12:27:46Z"}],"graph_snapshots":[{"event_id":"sha256:6ae0564e01603f677889ba530d6f93e0cf678967d089acb30ddb2e24a666f179","target":"graph","created_at":"2026-05-18T03:00:25Z","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":"We study a heterogeneous routing game in which vehicles might belong to more than one type. The type determines the cost of traveling along an edge as a function of the flow of various types of vehicles over that edge. We relax the assumptions needed for the existence of a Nash equilibrium in this heterogeneous routing game. We extend the available results to present necessary and sufficient conditions for the existence of a potential function. We characterize a set of tolls that guarantee the existence of a potential function when only two types of users are participating in the game. We pres","authors_text":"Alexandre M. Bayen, Farhad Farokhi, Karl H. Johansson, Walid Krichene","cross_cats":["cs.SY","math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2013-12-04T09:28:51Z","title":"A Necessary and Sufficient Condition for the Existence of Potential Functions for Heterogeneous Routing Games"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.1075","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:e9ea8154876fbda01201e73537c6dda6664275125f6509e881afbd5ae2b377fa","target":"record","created_at":"2026-05-18T03:00:25Z","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":"410aa177e943970ac7fa7e3d94cddde7451d5352a998637541332807613342a3","cross_cats_sorted":["cs.SY","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2013-12-04T09:28:51Z","title_canon_sha256":"f0dccffff5cf73b8f2d89079c853486b440700450e34a64ba7db8a9291220601"},"schema_version":"1.0","source":{"id":"1312.1075","kind":"arxiv","version":2}},"canonical_sha256":"3f9d0b4ea85d8d205d1737a9c308557ced018ec0fd83986047567ee454ff51f5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3f9d0b4ea85d8d205d1737a9c308557ced018ec0fd83986047567ee454ff51f5","first_computed_at":"2026-05-18T03:00:25.455292Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:00:25.455292Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZoBdGIMYYuGhSa65d6XL2mHHR4tBjZTv97pEsWq0ViluLtve64X2jozZyOAfLV0XpUDh6TbFA9qdWt/CfS6PDA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:00:25.456260Z","signed_message":"canonical_sha256_bytes"},"source_id":"1312.1075","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e9ea8154876fbda01201e73537c6dda6664275125f6509e881afbd5ae2b377fa","sha256:6ae0564e01603f677889ba530d6f93e0cf678967d089acb30ddb2e24a666f179"],"state_sha256":"87d7f4fbcccbc2e7efd301ee952d2082e42598cc0f0289994221a925330ac9f9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Tlwz7sqqEZLaw0tLdFBJpVmBTMAz6XujbojlCyAzEQtr3gkEdw0Cn0X+gCaqFJoa4ldA1492hUsPci8p++p/Cw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T17:27:32.602488Z","bundle_sha256":"5eadf1dcc2eeca0afcc0e3295533e0c472992ba555a3cd86315ec4d2d1fc658d"}}