{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:SPGPJFHQOS6EPFDT44DSCEH4AK","short_pith_number":"pith:SPGPJFHQ","canonical_record":{"source":{"id":"1812.01794","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2018-12-05T03:05:01Z","cross_cats_sorted":[],"title_canon_sha256":"0c9abd4f3b3794f2a803fc1d93c3add07b901a720a4202ad574e8d95d8ce8f14","abstract_canon_sha256":"88b7cdb342fa660767da7dd7a3279e0ebc595ce9e47a1c08d5602d046284b21b"},"schema_version":"1.0"},"canonical_sha256":"93ccf494f074bc479473e7072110fc029880ce2c3dd0f6939041d3393f340217","source":{"kind":"arxiv","id":"1812.01794","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.01794","created_at":"2026-05-17T23:59:00Z"},{"alias_kind":"arxiv_version","alias_value":"1812.01794v1","created_at":"2026-05-17T23:59:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.01794","created_at":"2026-05-17T23:59:00Z"},{"alias_kind":"pith_short_12","alias_value":"SPGPJFHQOS6E","created_at":"2026-05-18T12:32:53Z"},{"alias_kind":"pith_short_16","alias_value":"SPGPJFHQOS6EPFDT","created_at":"2026-05-18T12:32:53Z"},{"alias_kind":"pith_short_8","alias_value":"SPGPJFHQ","created_at":"2026-05-18T12:32:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:SPGPJFHQOS6EPFDT44DSCEH4AK","target":"record","payload":{"canonical_record":{"source":{"id":"1812.01794","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2018-12-05T03:05:01Z","cross_cats_sorted":[],"title_canon_sha256":"0c9abd4f3b3794f2a803fc1d93c3add07b901a720a4202ad574e8d95d8ce8f14","abstract_canon_sha256":"88b7cdb342fa660767da7dd7a3279e0ebc595ce9e47a1c08d5602d046284b21b"},"schema_version":"1.0"},"canonical_sha256":"93ccf494f074bc479473e7072110fc029880ce2c3dd0f6939041d3393f340217","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:59:00.618114Z","signature_b64":"MQuC0NT/PWTIDuqzYkmF3EWSAM39JKJbecMdQB08Rpu+KZPd9TB7G3UI9WoyHKarOa0dCv5KBj7VTZefbMnQCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"93ccf494f074bc479473e7072110fc029880ce2c3dd0f6939041d3393f340217","last_reissued_at":"2026-05-17T23:59:00.617526Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:59:00.617526Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1812.01794","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":"2026-05-17T23:59:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"86FYeZvnrsLyPKX4J2FR9he0XZrvHNvbbPdnBYlH9IJdVzoSaHTVoFHqSJ3xmxt8YUfB2XPNQ8pfg80xQp8ZDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T04:05:23.763914Z"},"content_sha256":"428e49bc5d58c11a6862ad9d5e18e15a13726a7557bd0045f5dfbc2ea38e1da0","schema_version":"1.0","event_id":"sha256:428e49bc5d58c11a6862ad9d5e18e15a13726a7557bd0045f5dfbc2ea38e1da0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:SPGPJFHQOS6EPFDT44DSCEH4AK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Optimal (and Benchmark-Optimal) Competition Complexity for Additive Buyers over Independent Items","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.GT","authors_text":"Hedyeh Beyhaghi, S. Matthew Weinberg","submitted_at":"2018-12-05T03:05:01Z","abstract_excerpt":"The Competition Complexity of an auction setting refers to the number of additional bidders necessary in order for the (deterministic, prior-independent, dominant strategy truthful) Vickrey-Clarke-Groves mechanism to achieve greater revenue than the (randomized, prior-dependent, Bayesian-truthful) optimal mechanism without the additional bidders.\n  We prove that the competition complexity of $n$ bidders with additive valuations over $m$ independent items is at most $n(\\ln(1+m/n)+2)$, and also at most $9\\sqrt{nm}$. When $n \\leq m$, the first bound is optimal up to constant factors, even when th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.01794","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":"2026-05-17T23:59:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/MPsYtm94SbKQB8cBmZTT0azO7A7gv5/yBC72iMfOibD+NxKDdZJ0UNuke+tMkryvCWS1dVYqX1J2i3unaCyCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T04:05:23.764256Z"},"content_sha256":"2458d1b1d975dea4fede4a3abbcc50affcd02b8cdd97a33f274badbdec39865e","schema_version":"1.0","event_id":"sha256:2458d1b1d975dea4fede4a3abbcc50affcd02b8cdd97a33f274badbdec39865e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SPGPJFHQOS6EPFDT44DSCEH4AK/bundle.json","state_url":"https://pith.science/pith/SPGPJFHQOS6EPFDT44DSCEH4AK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SPGPJFHQOS6EPFDT44DSCEH4AK/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":"2026-06-20T04:05:23Z","links":{"resolver":"https://pith.science/pith/SPGPJFHQOS6EPFDT44DSCEH4AK","bundle":"https://pith.science/pith/SPGPJFHQOS6EPFDT44DSCEH4AK/bundle.json","state":"https://pith.science/pith/SPGPJFHQOS6EPFDT44DSCEH4AK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SPGPJFHQOS6EPFDT44DSCEH4AK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:SPGPJFHQOS6EPFDT44DSCEH4AK","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":"88b7cdb342fa660767da7dd7a3279e0ebc595ce9e47a1c08d5602d046284b21b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2018-12-05T03:05:01Z","title_canon_sha256":"0c9abd4f3b3794f2a803fc1d93c3add07b901a720a4202ad574e8d95d8ce8f14"},"schema_version":"1.0","source":{"id":"1812.01794","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.01794","created_at":"2026-05-17T23:59:00Z"},{"alias_kind":"arxiv_version","alias_value":"1812.01794v1","created_at":"2026-05-17T23:59:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.01794","created_at":"2026-05-17T23:59:00Z"},{"alias_kind":"pith_short_12","alias_value":"SPGPJFHQOS6E","created_at":"2026-05-18T12:32:53Z"},{"alias_kind":"pith_short_16","alias_value":"SPGPJFHQOS6EPFDT","created_at":"2026-05-18T12:32:53Z"},{"alias_kind":"pith_short_8","alias_value":"SPGPJFHQ","created_at":"2026-05-18T12:32:53Z"}],"graph_snapshots":[{"event_id":"sha256:2458d1b1d975dea4fede4a3abbcc50affcd02b8cdd97a33f274badbdec39865e","target":"graph","created_at":"2026-05-17T23:59:00Z","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":"The Competition Complexity of an auction setting refers to the number of additional bidders necessary in order for the (deterministic, prior-independent, dominant strategy truthful) Vickrey-Clarke-Groves mechanism to achieve greater revenue than the (randomized, prior-dependent, Bayesian-truthful) optimal mechanism without the additional bidders.\n  We prove that the competition complexity of $n$ bidders with additive valuations over $m$ independent items is at most $n(\\ln(1+m/n)+2)$, and also at most $9\\sqrt{nm}$. When $n \\leq m$, the first bound is optimal up to constant factors, even when th","authors_text":"Hedyeh Beyhaghi, S. Matthew Weinberg","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2018-12-05T03:05:01Z","title":"Optimal (and Benchmark-Optimal) Competition Complexity for Additive Buyers over Independent Items"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.01794","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":"sha256:428e49bc5d58c11a6862ad9d5e18e15a13726a7557bd0045f5dfbc2ea38e1da0","target":"record","created_at":"2026-05-17T23:59:00Z","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":"88b7cdb342fa660767da7dd7a3279e0ebc595ce9e47a1c08d5602d046284b21b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2018-12-05T03:05:01Z","title_canon_sha256":"0c9abd4f3b3794f2a803fc1d93c3add07b901a720a4202ad574e8d95d8ce8f14"},"schema_version":"1.0","source":{"id":"1812.01794","kind":"arxiv","version":1}},"canonical_sha256":"93ccf494f074bc479473e7072110fc029880ce2c3dd0f6939041d3393f340217","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"93ccf494f074bc479473e7072110fc029880ce2c3dd0f6939041d3393f340217","first_computed_at":"2026-05-17T23:59:00.617526Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:59:00.617526Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MQuC0NT/PWTIDuqzYkmF3EWSAM39JKJbecMdQB08Rpu+KZPd9TB7G3UI9WoyHKarOa0dCv5KBj7VTZefbMnQCA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:59:00.618114Z","signed_message":"canonical_sha256_bytes"},"source_id":"1812.01794","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:428e49bc5d58c11a6862ad9d5e18e15a13726a7557bd0045f5dfbc2ea38e1da0","sha256:2458d1b1d975dea4fede4a3abbcc50affcd02b8cdd97a33f274badbdec39865e"],"state_sha256":"96e8672d94c5a4fe42a0f6178def10ed94239f0c822858620d250987e1adb5fe"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sRVg8Ld14+1hguLy1vuTyct7mawJgMLnqMuhi61ahN8aDS9/W3xr/dRqze5kE+cUI5MCBezIe0y5O2TlwZGrDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T04:05:23.766119Z","bundle_sha256":"99c2abf0999e542570556a88847455d92a359a594600a9ff167ad408a9edfa89"}}