{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:ZIILJD7WZV45YTE7GDOBNPBOJJ","short_pith_number":"pith:ZIILJD7W","canonical_record":{"source":{"id":"1908.00702","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2019-08-02T04:37:06Z","cross_cats_sorted":["cs.SY","eess.SY","math.OC"],"title_canon_sha256":"72527a10973edd0eaf9b2fe68f7b12de3fafc9249de8fc9012e157ba7315c032","abstract_canon_sha256":"bd02ab1dec88388b06ac6725957c264dbfa6632afdb4ccbb5929db551c6b624f"},"schema_version":"1.0"},"canonical_sha256":"ca10b48ff6cd79dc4c9f30dc16bc2e4a7ba3c68ef456702f7f0b7543a7f67c4f","source":{"kind":"arxiv","id":"1908.00702","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.00702","created_at":"2026-07-04T23:51:08Z"},{"alias_kind":"arxiv_version","alias_value":"1908.00702v1","created_at":"2026-07-04T23:51:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.00702","created_at":"2026-07-04T23:51:08Z"},{"alias_kind":"pith_short_12","alias_value":"ZIILJD7WZV45","created_at":"2026-07-04T23:51:08Z"},{"alias_kind":"pith_short_16","alias_value":"ZIILJD7WZV45YTE7","created_at":"2026-07-04T23:51:08Z"},{"alias_kind":"pith_short_8","alias_value":"ZIILJD7W","created_at":"2026-07-04T23:51:08Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:ZIILJD7WZV45YTE7GDOBNPBOJJ","target":"record","payload":{"canonical_record":{"source":{"id":"1908.00702","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2019-08-02T04:37:06Z","cross_cats_sorted":["cs.SY","eess.SY","math.OC"],"title_canon_sha256":"72527a10973edd0eaf9b2fe68f7b12de3fafc9249de8fc9012e157ba7315c032","abstract_canon_sha256":"bd02ab1dec88388b06ac6725957c264dbfa6632afdb4ccbb5929db551c6b624f"},"schema_version":"1.0"},"canonical_sha256":"ca10b48ff6cd79dc4c9f30dc16bc2e4a7ba3c68ef456702f7f0b7543a7f67c4f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T23:51:08.713274Z","signature_b64":"N7qn1PRifPVoZjvejPEgn14QZl4yrWUs5RhFKpCBtgdnIFJR4R6UteKQmHEAzuLNxUVQAXFaoL2Sb7GXcwk9Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ca10b48ff6cd79dc4c9f30dc16bc2e4a7ba3c68ef456702f7f0b7543a7f67c4f","last_reissued_at":"2026-07-04T23:51:08.712791Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T23:51:08.712791Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1908.00702","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":"2026-07-04T23:51:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SrtFSyTwdkGV8YOQdo4uKVJkjZ6krufL9Kj951saGUG2KT9uGbSn4YeNJmWBp4qgkbaYtt0zAmwBrNLbFcCkAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T06:07:16.530286Z"},"content_sha256":"574932e057f04a32bdcbfad47faac35d09492cb2f74be60d1cbdade9b189eebf","schema_version":"1.0","event_id":"sha256:574932e057f04a32bdcbfad47faac35d09492cb2f74be60d1cbdade9b189eebf"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:ZIILJD7WZV45YTE7GDOBNPBOJJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Efficiency of Generalized Nash and Variational Equilibria","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SY","eess.SY","math.OC"],"primary_cat":"cs.GT","authors_text":"Ankur A. Kulkarni","submitted_at":"2019-08-02T04:37:06Z","abstract_excerpt":"Shared-constraint games are noncooperative $N$-player games where players are coupled through a common coupling constraint. It is known that such games admit two kinds of equilibria -- generalized Nash equilibria (GNE) and variational equilibria (VE) -- with two different economic interpretations. We consider such games in the context of resource allocation, where players move simultaneously to decide portions of the resource they can consume under a coupling constraint that the sum of the portions they demand be no more than the capacity of the resource. We clarify the worst case and best cas"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.00702","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1908.00702/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":"2026-07-04T23:51:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3ke9Vi6kqd1lYkR/DYI9FrH79z9UaJjY/gOD3lpTG4TKyx1yPknxvkFeXDpFg2cPlbnsEZZxMqY70tUc9kdsAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T06:07:16.530955Z"},"content_sha256":"51f837a309a85e04a1a9633a2309a657adc3c6dc74535a61b70358945c9d4870","schema_version":"1.0","event_id":"sha256:51f837a309a85e04a1a9633a2309a657adc3c6dc74535a61b70358945c9d4870"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZIILJD7WZV45YTE7GDOBNPBOJJ/bundle.json","state_url":"https://pith.science/pith/ZIILJD7WZV45YTE7GDOBNPBOJJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZIILJD7WZV45YTE7GDOBNPBOJJ/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":"2026-08-16T06:07:16Z","links":{"resolver":"https://pith.science/pith/ZIILJD7WZV45YTE7GDOBNPBOJJ","bundle":"https://pith.science/pith/ZIILJD7WZV45YTE7GDOBNPBOJJ/bundle.json","state":"https://pith.science/pith/ZIILJD7WZV45YTE7GDOBNPBOJJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZIILJD7WZV45YTE7GDOBNPBOJJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:ZIILJD7WZV45YTE7GDOBNPBOJJ","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":"bd02ab1dec88388b06ac6725957c264dbfa6632afdb4ccbb5929db551c6b624f","cross_cats_sorted":["cs.SY","eess.SY","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2019-08-02T04:37:06Z","title_canon_sha256":"72527a10973edd0eaf9b2fe68f7b12de3fafc9249de8fc9012e157ba7315c032"},"schema_version":"1.0","source":{"id":"1908.00702","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.00702","created_at":"2026-07-04T23:51:08Z"},{"alias_kind":"arxiv_version","alias_value":"1908.00702v1","created_at":"2026-07-04T23:51:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.00702","created_at":"2026-07-04T23:51:08Z"},{"alias_kind":"pith_short_12","alias_value":"ZIILJD7WZV45","created_at":"2026-07-04T23:51:08Z"},{"alias_kind":"pith_short_16","alias_value":"ZIILJD7WZV45YTE7","created_at":"2026-07-04T23:51:08Z"},{"alias_kind":"pith_short_8","alias_value":"ZIILJD7W","created_at":"2026-07-04T23:51:08Z"}],"graph_snapshots":[{"event_id":"sha256:51f837a309a85e04a1a9633a2309a657adc3c6dc74535a61b70358945c9d4870","target":"graph","created_at":"2026-07-04T23:51:08Z","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/1908.00702/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Shared-constraint games are noncooperative $N$-player games where players are coupled through a common coupling constraint. It is known that such games admit two kinds of equilibria -- generalized Nash equilibria (GNE) and variational equilibria (VE) -- with two different economic interpretations. We consider such games in the context of resource allocation, where players move simultaneously to decide portions of the resource they can consume under a coupling constraint that the sum of the portions they demand be no more than the capacity of the resource. We clarify the worst case and best cas","authors_text":"Ankur A. Kulkarni","cross_cats":["cs.SY","eess.SY","math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2019-08-02T04:37:06Z","title":"The Efficiency of Generalized Nash and Variational Equilibria"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.00702","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":"sha256:574932e057f04a32bdcbfad47faac35d09492cb2f74be60d1cbdade9b189eebf","target":"record","created_at":"2026-07-04T23:51:08Z","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":"bd02ab1dec88388b06ac6725957c264dbfa6632afdb4ccbb5929db551c6b624f","cross_cats_sorted":["cs.SY","eess.SY","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2019-08-02T04:37:06Z","title_canon_sha256":"72527a10973edd0eaf9b2fe68f7b12de3fafc9249de8fc9012e157ba7315c032"},"schema_version":"1.0","source":{"id":"1908.00702","kind":"arxiv","version":1}},"canonical_sha256":"ca10b48ff6cd79dc4c9f30dc16bc2e4a7ba3c68ef456702f7f0b7543a7f67c4f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ca10b48ff6cd79dc4c9f30dc16bc2e4a7ba3c68ef456702f7f0b7543a7f67c4f","first_computed_at":"2026-07-04T23:51:08.712791Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T23:51:08.712791Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"N7qn1PRifPVoZjvejPEgn14QZl4yrWUs5RhFKpCBtgdnIFJR4R6UteKQmHEAzuLNxUVQAXFaoL2Sb7GXcwk9Dg==","signature_status":"signed_v1","signed_at":"2026-07-04T23:51:08.713274Z","signed_message":"canonical_sha256_bytes"},"source_id":"1908.00702","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:574932e057f04a32bdcbfad47faac35d09492cb2f74be60d1cbdade9b189eebf","sha256:51f837a309a85e04a1a9633a2309a657adc3c6dc74535a61b70358945c9d4870"],"state_sha256":"115fe2857d43384c81ed43c472eae9419a76e63d82f905be99cfe46b3c5e4c58"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0pCHnW27kmA9FDMJ75NKbyyxMbsXxTKe/czywktpWMIwn0N4TXMe/Fnds5tGoRe5tMxGpPLEs20JAwY8UDfLBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-16T06:07:16.539129Z","bundle_sha256":"158b02567805ff99773fad7855b25b43aac745a01f0b204258bc40450a18aaf0"}}