{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:ZNLQORHIZE73NBF3VCFIHQYKUA","short_pith_number":"pith:ZNLQORHI","canonical_record":{"source":{"id":"1510.03399","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2015-10-12T19:20:06Z","cross_cats_sorted":[],"title_canon_sha256":"9925b64b43a927fa97e61ea35c3780e5c9a96f7508c1de31a3decc3dbad43193","abstract_canon_sha256":"37bcbff48796045d7e69552968e928128bcfb74cd74e492a4ea2a33d77e3c50c"},"schema_version":"1.0"},"canonical_sha256":"cb570744e8c93fb684bba88a83c30aa00eb5b4ff2b06556471e723665c674e80","source":{"kind":"arxiv","id":"1510.03399","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.03399","created_at":"2026-05-18T01:26:17Z"},{"alias_kind":"arxiv_version","alias_value":"1510.03399v2","created_at":"2026-05-18T01:26:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.03399","created_at":"2026-05-18T01:26:17Z"},{"alias_kind":"pith_short_12","alias_value":"ZNLQORHIZE73","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_16","alias_value":"ZNLQORHIZE73NBF3","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_8","alias_value":"ZNLQORHI","created_at":"2026-05-18T12:29:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:ZNLQORHIZE73NBF3VCFIHQYKUA","target":"record","payload":{"canonical_record":{"source":{"id":"1510.03399","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2015-10-12T19:20:06Z","cross_cats_sorted":[],"title_canon_sha256":"9925b64b43a927fa97e61ea35c3780e5c9a96f7508c1de31a3decc3dbad43193","abstract_canon_sha256":"37bcbff48796045d7e69552968e928128bcfb74cd74e492a4ea2a33d77e3c50c"},"schema_version":"1.0"},"canonical_sha256":"cb570744e8c93fb684bba88a83c30aa00eb5b4ff2b06556471e723665c674e80","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:26:17.701771Z","signature_b64":"lXCVbRGTbZEJAlNxj0s4anCNMPWE841rzkV9bs62MQOVtI+hx90fuHDV+Gr5JYpDWI1JyictGSuofkcm29sNDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cb570744e8c93fb684bba88a83c30aa00eb5b4ff2b06556471e723665c674e80","last_reissued_at":"2026-05-18T01:26:17.701305Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:26:17.701305Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1510.03399","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:26:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Qe5Kdmc71BrnsQ0F+XjluGeMSn1kJqJMnAVPFbQPMe42ZWqFVABL61b6fhE/wmHD0HGR6BKzkhDIw442XO2RDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T22:09:51.049741Z"},"content_sha256":"f118769757e60d589483f0a3e6696df79587b72c23c484865ddfbd04d4b1f700","schema_version":"1.0","event_id":"sha256:f118769757e60d589483f0a3e6696df79587b72c23c484865ddfbd04d4b1f700"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:ZNLQORHIZE73NBF3VCFIHQYKUA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Selling Two Goods Optimally","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.GT","authors_text":"Elias Koutsoupias, Yiannis Giannakopoulos","submitted_at":"2015-10-12T19:20:06Z","abstract_excerpt":"We provide sufficient conditions for revenue maximization in a two-good monopoly where the buyer's values for the items come from independent (but not necessarily identical) distributions over bounded intervals. Under certain distributional assumptions, we give exact, closed-form formulas for the prices and allocation rule of the optimal selling mechanism. As a side result we give the first example of an optimal mechanism in an i.i.d. setting over a support of the form $[0,b]$ which is not deterministic. Since our framework is based on duality techniques, we were also able to demonstrate how s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.03399","kind":"arxiv","version":2},"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":"2026-05-18T01:26:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ydKnt94iDm+W/oF4BO+smoEV/g8eCwKhsWKbzJlKmIKIYi32fCtFZCojWnecFcvqM0XH8XB/uJ0NwVTJHcfOBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T22:09:51.050071Z"},"content_sha256":"b246eaa3515703fb26ccde73beb32f0fd8453346fb5c69d3eeb5c6d67e7df8e6","schema_version":"1.0","event_id":"sha256:b246eaa3515703fb26ccde73beb32f0fd8453346fb5c69d3eeb5c6d67e7df8e6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZNLQORHIZE73NBF3VCFIHQYKUA/bundle.json","state_url":"https://pith.science/pith/ZNLQORHIZE73NBF3VCFIHQYKUA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZNLQORHIZE73NBF3VCFIHQYKUA/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":"2026-06-03T22:09:51Z","links":{"resolver":"https://pith.science/pith/ZNLQORHIZE73NBF3VCFIHQYKUA","bundle":"https://pith.science/pith/ZNLQORHIZE73NBF3VCFIHQYKUA/bundle.json","state":"https://pith.science/pith/ZNLQORHIZE73NBF3VCFIHQYKUA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZNLQORHIZE73NBF3VCFIHQYKUA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:ZNLQORHIZE73NBF3VCFIHQYKUA","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":"37bcbff48796045d7e69552968e928128bcfb74cd74e492a4ea2a33d77e3c50c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2015-10-12T19:20:06Z","title_canon_sha256":"9925b64b43a927fa97e61ea35c3780e5c9a96f7508c1de31a3decc3dbad43193"},"schema_version":"1.0","source":{"id":"1510.03399","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.03399","created_at":"2026-05-18T01:26:17Z"},{"alias_kind":"arxiv_version","alias_value":"1510.03399v2","created_at":"2026-05-18T01:26:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.03399","created_at":"2026-05-18T01:26:17Z"},{"alias_kind":"pith_short_12","alias_value":"ZNLQORHIZE73","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_16","alias_value":"ZNLQORHIZE73NBF3","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_8","alias_value":"ZNLQORHI","created_at":"2026-05-18T12:29:52Z"}],"graph_snapshots":[{"event_id":"sha256:b246eaa3515703fb26ccde73beb32f0fd8453346fb5c69d3eeb5c6d67e7df8e6","target":"graph","created_at":"2026-05-18T01:26:17Z","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 provide sufficient conditions for revenue maximization in a two-good monopoly where the buyer's values for the items come from independent (but not necessarily identical) distributions over bounded intervals. Under certain distributional assumptions, we give exact, closed-form formulas for the prices and allocation rule of the optimal selling mechanism. As a side result we give the first example of an optimal mechanism in an i.i.d. setting over a support of the form $[0,b]$ which is not deterministic. Since our framework is based on duality techniques, we were also able to demonstrate how s","authors_text":"Elias Koutsoupias, Yiannis Giannakopoulos","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2015-10-12T19:20:06Z","title":"Selling Two Goods Optimally"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.03399","kind":"arxiv","version":2},"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:f118769757e60d589483f0a3e6696df79587b72c23c484865ddfbd04d4b1f700","target":"record","created_at":"2026-05-18T01:26:17Z","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":"37bcbff48796045d7e69552968e928128bcfb74cd74e492a4ea2a33d77e3c50c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2015-10-12T19:20:06Z","title_canon_sha256":"9925b64b43a927fa97e61ea35c3780e5c9a96f7508c1de31a3decc3dbad43193"},"schema_version":"1.0","source":{"id":"1510.03399","kind":"arxiv","version":2}},"canonical_sha256":"cb570744e8c93fb684bba88a83c30aa00eb5b4ff2b06556471e723665c674e80","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cb570744e8c93fb684bba88a83c30aa00eb5b4ff2b06556471e723665c674e80","first_computed_at":"2026-05-18T01:26:17.701305Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:26:17.701305Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lXCVbRGTbZEJAlNxj0s4anCNMPWE841rzkV9bs62MQOVtI+hx90fuHDV+Gr5JYpDWI1JyictGSuofkcm29sNDg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:26:17.701771Z","signed_message":"canonical_sha256_bytes"},"source_id":"1510.03399","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f118769757e60d589483f0a3e6696df79587b72c23c484865ddfbd04d4b1f700","sha256:b246eaa3515703fb26ccde73beb32f0fd8453346fb5c69d3eeb5c6d67e7df8e6"],"state_sha256":"2cfd402cd0a47259b8c552be83d5fd6d7a945ec505201c209fd464440783c87e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uzDGY12qGeQy8Ku9KrwrCeEwB56KUDYSu8sT0YgUs7p9p+lPYjLyMbWrITcq1RTK/0nVoqcUjXTnYxMLJqvSAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T22:09:51.051977Z","bundle_sha256":"c6571d9ecdb10e16942b6b09c18717d9604221b643826f62e17ac1588b90b96c"}}