{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:C6FNBBBSLAHB35TDZC6W5QUBRM","short_pith_number":"pith:C6FNBBBS","canonical_record":{"source":{"id":"1905.03773","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2019-05-09T17:55:46Z","cross_cats_sorted":[],"title_canon_sha256":"efbae16cd489dcb78030acf38ce0529a44a224dcfdafcc993ca9e7d3ca72c45e","abstract_canon_sha256":"1fca36f8398bbac764d87b893d5eec06a9caaf057af67b8a9c6920c7589fbeff"},"schema_version":"1.0"},"canonical_sha256":"178ad08432580e1df663c8bd6ec2818b0c1405e48cec7f03652e056a2de4113d","source":{"kind":"arxiv","id":"1905.03773","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1905.03773","created_at":"2026-05-17T23:46:36Z"},{"alias_kind":"arxiv_version","alias_value":"1905.03773v1","created_at":"2026-05-17T23:46:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.03773","created_at":"2026-05-17T23:46:36Z"},{"alias_kind":"pith_short_12","alias_value":"C6FNBBBSLAHB","created_at":"2026-05-18T12:33:12Z"},{"alias_kind":"pith_short_16","alias_value":"C6FNBBBSLAHB35TD","created_at":"2026-05-18T12:33:12Z"},{"alias_kind":"pith_short_8","alias_value":"C6FNBBBS","created_at":"2026-05-18T12:33:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:C6FNBBBSLAHB35TDZC6W5QUBRM","target":"record","payload":{"canonical_record":{"source":{"id":"1905.03773","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2019-05-09T17:55:46Z","cross_cats_sorted":[],"title_canon_sha256":"efbae16cd489dcb78030acf38ce0529a44a224dcfdafcc993ca9e7d3ca72c45e","abstract_canon_sha256":"1fca36f8398bbac764d87b893d5eec06a9caaf057af67b8a9c6920c7589fbeff"},"schema_version":"1.0"},"canonical_sha256":"178ad08432580e1df663c8bd6ec2818b0c1405e48cec7f03652e056a2de4113d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:46:36.747142Z","signature_b64":"Sj42b8FAuDKw/onDfIAq/LdJ13yEQs03BSU0k5Y2IRlYBT2Lp4AO1Mz6pZrRlH+gLEyyZM8kPa19lqBZixjkAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"178ad08432580e1df663c8bd6ec2818b0c1405e48cec7f03652e056a2de4113d","last_reissued_at":"2026-05-17T23:46:36.746524Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:46:36.746524Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1905.03773","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":"2026-05-17T23:46:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+byjww2ipG3hLIe+KH3SnA9pZoHt12FZiv72igjK/+w58SvewkuPj8LvZlzq7WViWgqVxFwGQzXdJAXjQKBQAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T07:11:34.961639Z"},"content_sha256":"3e3e0d733ca6ca64ea05c7c8958321e63d138a76b559ba4a716aed452ea7cbc7","schema_version":"1.0","event_id":"sha256:3e3e0d733ca6ca64ea05c7c8958321e63d138a76b559ba4a716aed452ea7cbc7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:C6FNBBBSLAHB35TDZC6W5QUBRM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Vickrey Auction with a Single Duplicate Bidder Approximates the Optimal Revenue","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.GT","authors_text":"Christopher Liaw, Hu Fu, Sikander Randhawa","submitted_at":"2019-05-09T17:55:46Z","abstract_excerpt":"Bulow and Klemperer's well-known result states that, in a single-item auction where the $n$ bidders' values are independently and identically drawn from a regular distribution, the Vickrey auction with one additional bidder (a duplicate) extracts at least as much revenue as the optimal auction without the duplicate. Hartline and Roughgarden, in their influential 2009 paper, removed the requirement that the distributions be identical, at the cost of allowing the Vickrey auction to recruit $n$ duplicates, one from each distribution, and relaxing its revenue advantage to a $2$-approximation.\n  In"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.03773","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":"2026-05-17T23:46:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iS27Rc1v1IyW2es7wpNY8KaVtBjxnBn2LFZA6EFr9Tf1ccgn6FcCB5xz8xc1bzd05K+Y7gXNJrSSDUNjDjTZBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T07:11:34.962225Z"},"content_sha256":"9121be905948f66f96cbfaf23aa77abb942c7c24c3ec5286af6671341e714840","schema_version":"1.0","event_id":"sha256:9121be905948f66f96cbfaf23aa77abb942c7c24c3ec5286af6671341e714840"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/C6FNBBBSLAHB35TDZC6W5QUBRM/bundle.json","state_url":"https://pith.science/pith/C6FNBBBSLAHB35TDZC6W5QUBRM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/C6FNBBBSLAHB35TDZC6W5QUBRM/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":"2026-06-07T07:11:34Z","links":{"resolver":"https://pith.science/pith/C6FNBBBSLAHB35TDZC6W5QUBRM","bundle":"https://pith.science/pith/C6FNBBBSLAHB35TDZC6W5QUBRM/bundle.json","state":"https://pith.science/pith/C6FNBBBSLAHB35TDZC6W5QUBRM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/C6FNBBBSLAHB35TDZC6W5QUBRM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:C6FNBBBSLAHB35TDZC6W5QUBRM","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":"1fca36f8398bbac764d87b893d5eec06a9caaf057af67b8a9c6920c7589fbeff","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2019-05-09T17:55:46Z","title_canon_sha256":"efbae16cd489dcb78030acf38ce0529a44a224dcfdafcc993ca9e7d3ca72c45e"},"schema_version":"1.0","source":{"id":"1905.03773","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1905.03773","created_at":"2026-05-17T23:46:36Z"},{"alias_kind":"arxiv_version","alias_value":"1905.03773v1","created_at":"2026-05-17T23:46:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.03773","created_at":"2026-05-17T23:46:36Z"},{"alias_kind":"pith_short_12","alias_value":"C6FNBBBSLAHB","created_at":"2026-05-18T12:33:12Z"},{"alias_kind":"pith_short_16","alias_value":"C6FNBBBSLAHB35TD","created_at":"2026-05-18T12:33:12Z"},{"alias_kind":"pith_short_8","alias_value":"C6FNBBBS","created_at":"2026-05-18T12:33:12Z"}],"graph_snapshots":[{"event_id":"sha256:9121be905948f66f96cbfaf23aa77abb942c7c24c3ec5286af6671341e714840","target":"graph","created_at":"2026-05-17T23:46:36Z","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":"Bulow and Klemperer's well-known result states that, in a single-item auction where the $n$ bidders' values are independently and identically drawn from a regular distribution, the Vickrey auction with one additional bidder (a duplicate) extracts at least as much revenue as the optimal auction without the duplicate. Hartline and Roughgarden, in their influential 2009 paper, removed the requirement that the distributions be identical, at the cost of allowing the Vickrey auction to recruit $n$ duplicates, one from each distribution, and relaxing its revenue advantage to a $2$-approximation.\n  In","authors_text":"Christopher Liaw, Hu Fu, Sikander Randhawa","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2019-05-09T17:55:46Z","title":"The Vickrey Auction with a Single Duplicate Bidder Approximates the Optimal Revenue"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.03773","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":"sha256:3e3e0d733ca6ca64ea05c7c8958321e63d138a76b559ba4a716aed452ea7cbc7","target":"record","created_at":"2026-05-17T23:46:36Z","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":"1fca36f8398bbac764d87b893d5eec06a9caaf057af67b8a9c6920c7589fbeff","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2019-05-09T17:55:46Z","title_canon_sha256":"efbae16cd489dcb78030acf38ce0529a44a224dcfdafcc993ca9e7d3ca72c45e"},"schema_version":"1.0","source":{"id":"1905.03773","kind":"arxiv","version":1}},"canonical_sha256":"178ad08432580e1df663c8bd6ec2818b0c1405e48cec7f03652e056a2de4113d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"178ad08432580e1df663c8bd6ec2818b0c1405e48cec7f03652e056a2de4113d","first_computed_at":"2026-05-17T23:46:36.746524Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:46:36.746524Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Sj42b8FAuDKw/onDfIAq/LdJ13yEQs03BSU0k5Y2IRlYBT2Lp4AO1Mz6pZrRlH+gLEyyZM8kPa19lqBZixjkAg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:46:36.747142Z","signed_message":"canonical_sha256_bytes"},"source_id":"1905.03773","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3e3e0d733ca6ca64ea05c7c8958321e63d138a76b559ba4a716aed452ea7cbc7","sha256:9121be905948f66f96cbfaf23aa77abb942c7c24c3ec5286af6671341e714840"],"state_sha256":"5dec26a8384252434bfc29b96e0975b7f8f8c2233916c2573b07a6786663eb99"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2CnHbqBnFojjwW9a1ioa3fRTwkaqI5do+aTFGhBdX8XgxMUnaC0s0HB/8peCj4RbfS8rSW7ECn1TmmEwNOwRCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T07:11:34.965625Z","bundle_sha256":"d8aec925b35c750f0ec36ce7186e2a8a2ff1a8ab132d7c928d627a384eebb7de"}}