{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:32HIGL63VQ3XMAKZCANJ2TKO3O","short_pith_number":"pith:32HIGL63","canonical_record":{"source":{"id":"1203.6675","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2012-03-29T21:38:20Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"0052024a8e0217dfaf9a86dce3c856feda9c8cf438ae7bff9f1e46e3fdf7ed49","abstract_canon_sha256":"2aa9cabf96af70ad8e353ad2665a7d1b171436a483f5df038e209f53ebd638c9"},"schema_version":"1.0"},"canonical_sha256":"de8e832fdbac37760159101a9d4d4edb834754c69a81cfc6c9d4d380fcb83eac","source":{"kind":"arxiv","id":"1203.6675","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1203.6675","created_at":"2026-05-18T03:52:27Z"},{"alias_kind":"arxiv_version","alias_value":"1203.6675v1","created_at":"2026-05-18T03:52:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.6675","created_at":"2026-05-18T03:52:27Z"},{"alias_kind":"pith_short_12","alias_value":"32HIGL63VQ3X","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_16","alias_value":"32HIGL63VQ3XMAKZ","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_8","alias_value":"32HIGL63","created_at":"2026-05-18T12:26:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:32HIGL63VQ3XMAKZCANJ2TKO3O","target":"record","payload":{"canonical_record":{"source":{"id":"1203.6675","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2012-03-29T21:38:20Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"0052024a8e0217dfaf9a86dce3c856feda9c8cf438ae7bff9f1e46e3fdf7ed49","abstract_canon_sha256":"2aa9cabf96af70ad8e353ad2665a7d1b171436a483f5df038e209f53ebd638c9"},"schema_version":"1.0"},"canonical_sha256":"de8e832fdbac37760159101a9d4d4edb834754c69a81cfc6c9d4d380fcb83eac","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:52:27.951295Z","signature_b64":"yXH/kpa6kVPEvxjwUdtdmOE+8mzk/+87sCuRYlDRYaA92NNedDAFDFnNjGBSwPru/krbn/gKj13K4C1noekBDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"de8e832fdbac37760159101a9d4d4edb834754c69a81cfc6c9d4d380fcb83eac","last_reissued_at":"2026-05-18T03:52:27.950612Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:52:27.950612Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1203.6675","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":"2026-05-18T03:52:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xuwwi08qcPa6ISIhraQVSarO2z7a9WxCq7bz7Q6TygjWa3kFk8jCOsmKkIcNL1j8RcqvCoqVOqod5LJojJ4EDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T14:47:03.227020Z"},"content_sha256":"4d746180b1b534e0a54f8c5c740b4f4e0cffc7d826447dd1791cf229b8b040c4","schema_version":"1.0","event_id":"sha256:4d746180b1b534e0a54f8c5c740b4f4e0cffc7d826447dd1791cf229b8b040c4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:32HIGL63VQ3XMAKZCANJ2TKO3O","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Efficiency Loss in a Cournot Oligopoly with Convex Market Demand","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.OC","authors_text":"John N. Tsitsiklis, Yunjian Xu","submitted_at":"2012-03-29T21:38:20Z","abstract_excerpt":"We consider a Cournot oligopoly model where multiple suppliers (oligopolists) compete by choosing quantities. We compare the social welfare achieved at a Cournot equilibrium to the maximum possible, for the case where the inverse market demand function is convex. We establish a lower bound on the efficiency of Cournot equilibria in terms of a scalar parameter derived from the inverse demand function, namely, the ratio of the slope of the inverse demand function at the Cournot equilibrium to the average slope of the inverse demand function between the Cournot equilibrium and a social optimum. A"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.6675","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":"2026-05-18T03:52:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XTvFu8IPZKHhWMq1QaoUvtZ+2a8u7i3QWNRsgPb5rHnoc/WREdXfQRwtNQvOzs8pYq8agTIhW0WLaRJBIYLGAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T14:47:03.227376Z"},"content_sha256":"587e3d4f46580c5479be67595a001f93169f16d7122ff60503ab30138cafaba5","schema_version":"1.0","event_id":"sha256:587e3d4f46580c5479be67595a001f93169f16d7122ff60503ab30138cafaba5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/32HIGL63VQ3XMAKZCANJ2TKO3O/bundle.json","state_url":"https://pith.science/pith/32HIGL63VQ3XMAKZCANJ2TKO3O/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/32HIGL63VQ3XMAKZCANJ2TKO3O/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":"2026-06-03T14:47:03Z","links":{"resolver":"https://pith.science/pith/32HIGL63VQ3XMAKZCANJ2TKO3O","bundle":"https://pith.science/pith/32HIGL63VQ3XMAKZCANJ2TKO3O/bundle.json","state":"https://pith.science/pith/32HIGL63VQ3XMAKZCANJ2TKO3O/state.json","well_known_bundle":"https://pith.science/.well-known/pith/32HIGL63VQ3XMAKZCANJ2TKO3O/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:32HIGL63VQ3XMAKZCANJ2TKO3O","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":"2aa9cabf96af70ad8e353ad2665a7d1b171436a483f5df038e209f53ebd638c9","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2012-03-29T21:38:20Z","title_canon_sha256":"0052024a8e0217dfaf9a86dce3c856feda9c8cf438ae7bff9f1e46e3fdf7ed49"},"schema_version":"1.0","source":{"id":"1203.6675","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1203.6675","created_at":"2026-05-18T03:52:27Z"},{"alias_kind":"arxiv_version","alias_value":"1203.6675v1","created_at":"2026-05-18T03:52:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.6675","created_at":"2026-05-18T03:52:27Z"},{"alias_kind":"pith_short_12","alias_value":"32HIGL63VQ3X","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_16","alias_value":"32HIGL63VQ3XMAKZ","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_8","alias_value":"32HIGL63","created_at":"2026-05-18T12:26:50Z"}],"graph_snapshots":[{"event_id":"sha256:587e3d4f46580c5479be67595a001f93169f16d7122ff60503ab30138cafaba5","target":"graph","created_at":"2026-05-18T03:52:27Z","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 consider a Cournot oligopoly model where multiple suppliers (oligopolists) compete by choosing quantities. We compare the social welfare achieved at a Cournot equilibrium to the maximum possible, for the case where the inverse market demand function is convex. We establish a lower bound on the efficiency of Cournot equilibria in terms of a scalar parameter derived from the inverse demand function, namely, the ratio of the slope of the inverse demand function at the Cournot equilibrium to the average slope of the inverse demand function between the Cournot equilibrium and a social optimum. A","authors_text":"John N. Tsitsiklis, Yunjian Xu","cross_cats":["math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2012-03-29T21:38:20Z","title":"Efficiency Loss in a Cournot Oligopoly with Convex Market Demand"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.6675","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":"sha256:4d746180b1b534e0a54f8c5c740b4f4e0cffc7d826447dd1791cf229b8b040c4","target":"record","created_at":"2026-05-18T03:52:27Z","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":"2aa9cabf96af70ad8e353ad2665a7d1b171436a483f5df038e209f53ebd638c9","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2012-03-29T21:38:20Z","title_canon_sha256":"0052024a8e0217dfaf9a86dce3c856feda9c8cf438ae7bff9f1e46e3fdf7ed49"},"schema_version":"1.0","source":{"id":"1203.6675","kind":"arxiv","version":1}},"canonical_sha256":"de8e832fdbac37760159101a9d4d4edb834754c69a81cfc6c9d4d380fcb83eac","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"de8e832fdbac37760159101a9d4d4edb834754c69a81cfc6c9d4d380fcb83eac","first_computed_at":"2026-05-18T03:52:27.950612Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:52:27.950612Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yXH/kpa6kVPEvxjwUdtdmOE+8mzk/+87sCuRYlDRYaA92NNedDAFDFnNjGBSwPru/krbn/gKj13K4C1noekBDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:52:27.951295Z","signed_message":"canonical_sha256_bytes"},"source_id":"1203.6675","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4d746180b1b534e0a54f8c5c740b4f4e0cffc7d826447dd1791cf229b8b040c4","sha256:587e3d4f46580c5479be67595a001f93169f16d7122ff60503ab30138cafaba5"],"state_sha256":"57194cfe7bf535bfa1398d14b33699fdc545cb9939c6a7d8503773dcac731ab7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GJryEOP0reExxuYFPUXeC/qeIVgvpLpTv+Df/WBKYDSx9fZUAlLchKw1LhmlFAhQhop1RedJM/gUwnYb27VPBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T14:47:03.229286Z","bundle_sha256":"2876b35d3275464aef2edbdec9e599cc7b6365166f5b14e087d6c76735a16686"}}