{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:2HR475XB6XMOXQLXCKZOOYZFHH","short_pith_number":"pith:2HR475XB","schema_version":"1.0","canonical_sha256":"d1e3cff6e1f5d8ebc17712b2e7632539c538ea92fbc236c508ea1717870758a0","source":{"kind":"arxiv","id":"1412.0845","version":1},"attestation_state":"computed","paper":{"title":"On the Robustness of the Approximate Price of Anarchy in Generalized Congestion Games","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.GT","authors_text":"Vittorio Bil\\`o","submitted_at":"2014-12-02T10:30:27Z","abstract_excerpt":"One of the main results shown through Roughgarden's notions of smooth games and robust price of anarchy is that, for any sum-bounded utilitarian social function, the worst-case price of anarchy of coarse correlated equilibria coincides with that of pure Nash equilibria in the class of weighted congestion games with non-negative and non-decreasing latency functions and that such a value can always be derived through the, so called, smoothness argument. We significantly extend this result by proving that, for a variety of (even non-sum-bounded) utilitarian and egalitarian social functions and fo"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1412.0845","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2014-12-02T10:30:27Z","cross_cats_sorted":[],"title_canon_sha256":"b071e2339b215e2e21760437df1f635aa02c597845836bcb9770f30ccd860d70","abstract_canon_sha256":"38a9fb32b464c7e7dbb42b63f37218f6c18d8c5c17659f6a0ccb063740098772"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:32:21.042664Z","signature_b64":"29O7GrqLfZcPUseTfM+7mzEGAMhFPWe7ye0cYKdr7QajsY89Sjg5OMoEwDPw37HJVPJSj/Jio53gS7IwiCRLBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d1e3cff6e1f5d8ebc17712b2e7632539c538ea92fbc236c508ea1717870758a0","last_reissued_at":"2026-05-18T02:32:21.042148Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:32:21.042148Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the Robustness of the Approximate Price of Anarchy in Generalized Congestion Games","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.GT","authors_text":"Vittorio Bil\\`o","submitted_at":"2014-12-02T10:30:27Z","abstract_excerpt":"One of the main results shown through Roughgarden's notions of smooth games and robust price of anarchy is that, for any sum-bounded utilitarian social function, the worst-case price of anarchy of coarse correlated equilibria coincides with that of pure Nash equilibria in the class of weighted congestion games with non-negative and non-decreasing latency functions and that such a value can always be derived through the, so called, smoothness argument. We significantly extend this result by proving that, for a variety of (even non-sum-bounded) utilitarian and egalitarian social functions and fo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.0845","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1412.0845","created_at":"2026-05-18T02:32:21.042206+00:00"},{"alias_kind":"arxiv_version","alias_value":"1412.0845v1","created_at":"2026-05-18T02:32:21.042206+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.0845","created_at":"2026-05-18T02:32:21.042206+00:00"},{"alias_kind":"pith_short_12","alias_value":"2HR475XB6XMO","created_at":"2026-05-18T12:28:11.866339+00:00"},{"alias_kind":"pith_short_16","alias_value":"2HR475XB6XMOXQLX","created_at":"2026-05-18T12:28:11.866339+00:00"},{"alias_kind":"pith_short_8","alias_value":"2HR475XB","created_at":"2026-05-18T12:28:11.866339+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/2HR475XB6XMOXQLXCKZOOYZFHH","json":"https://pith.science/pith/2HR475XB6XMOXQLXCKZOOYZFHH.json","graph_json":"https://pith.science/api/pith-number/2HR475XB6XMOXQLXCKZOOYZFHH/graph.json","events_json":"https://pith.science/api/pith-number/2HR475XB6XMOXQLXCKZOOYZFHH/events.json","paper":"https://pith.science/paper/2HR475XB"},"agent_actions":{"view_html":"https://pith.science/pith/2HR475XB6XMOXQLXCKZOOYZFHH","download_json":"https://pith.science/pith/2HR475XB6XMOXQLXCKZOOYZFHH.json","view_paper":"https://pith.science/paper/2HR475XB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1412.0845&json=true","fetch_graph":"https://pith.science/api/pith-number/2HR475XB6XMOXQLXCKZOOYZFHH/graph.json","fetch_events":"https://pith.science/api/pith-number/2HR475XB6XMOXQLXCKZOOYZFHH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2HR475XB6XMOXQLXCKZOOYZFHH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2HR475XB6XMOXQLXCKZOOYZFHH/action/storage_attestation","attest_author":"https://pith.science/pith/2HR475XB6XMOXQLXCKZOOYZFHH/action/author_attestation","sign_citation":"https://pith.science/pith/2HR475XB6XMOXQLXCKZOOYZFHH/action/citation_signature","submit_replication":"https://pith.science/pith/2HR475XB6XMOXQLXCKZOOYZFHH/action/replication_record"}},"created_at":"2026-05-18T02:32:21.042206+00:00","updated_at":"2026-05-18T02:32:21.042206+00:00"}