{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:DDW36YRHHLNE2YK6F5E43Q7TOW","short_pith_number":"pith:DDW36YRH","canonical_record":{"source":{"id":"1312.6249","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2013-12-21T13:09:10Z","cross_cats_sorted":[],"title_canon_sha256":"a782303444f0be57ebd1387744000d716dd07e68b4953a043c079e25fbd6db79","abstract_canon_sha256":"5d9c31c6114efc47dd77c4c6a824017ae68278291c2882516f70720f620fdcad"},"schema_version":"1.0"},"canonical_sha256":"18edbf62273ada4d615e2f49cdc3f37584b7ba154b1f2cedbabdbf6c0a3babf1","source":{"kind":"arxiv","id":"1312.6249","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.6249","created_at":"2026-05-18T02:41:18Z"},{"alias_kind":"arxiv_version","alias_value":"1312.6249v3","created_at":"2026-05-18T02:41:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.6249","created_at":"2026-05-18T02:41:18Z"},{"alias_kind":"pith_short_12","alias_value":"DDW36YRHHLNE","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_16","alias_value":"DDW36YRHHLNE2YK6","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_8","alias_value":"DDW36YRH","created_at":"2026-05-18T12:27:40Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:DDW36YRHHLNE2YK6F5E43Q7TOW","target":"record","payload":{"canonical_record":{"source":{"id":"1312.6249","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2013-12-21T13:09:10Z","cross_cats_sorted":[],"title_canon_sha256":"a782303444f0be57ebd1387744000d716dd07e68b4953a043c079e25fbd6db79","abstract_canon_sha256":"5d9c31c6114efc47dd77c4c6a824017ae68278291c2882516f70720f620fdcad"},"schema_version":"1.0"},"canonical_sha256":"18edbf62273ada4d615e2f49cdc3f37584b7ba154b1f2cedbabdbf6c0a3babf1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:41:18.729664Z","signature_b64":"uWTxOs8Ak5/2Vmx8+hZrR+LLUk2g/xHux9OLwwXO67Tz3D2WFgBKPYnzoNSl2O8qB7zfcvC93JlvT38nRlKZBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"18edbf62273ada4d615e2f49cdc3f37584b7ba154b1f2cedbabdbf6c0a3babf1","last_reissued_at":"2026-05-18T02:41:18.729261Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:41:18.729261Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1312.6249","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:41:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"J8s96roE8TPiFvrhSuiKrI4lioGKa+m68gp2tEmrXO/TEjYTVYVu2LW2qpIqSBcfUuzjhqcsQZrmrEbhbb5ACA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T01:37:02.221249Z"},"content_sha256":"6276db6c3ddbe992cf1ab1bd279b1c0125f333fed7505aba9c330b6f89183dfb","schema_version":"1.0","event_id":"sha256:6276db6c3ddbe992cf1ab1bd279b1c0125f333fed7505aba9c330b6f89183dfb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:DDW36YRHHLNE2YK6F5E43Q7TOW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Complexity of Fairness through Equilibrium","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.GT","authors_text":"Abraham Othman, Aviad Rubinstein, Christos Papadimitriou","submitted_at":"2013-12-21T13:09:10Z","abstract_excerpt":"Competitive equilibrium with equal incomes (CEEI) is a well known fair allocation mechanism; however, for indivisible resources a CEEI may not exist. It was shown in [Budish '11] that in the case of indivisible resources there is always an allocation, called A-CEEI, that is approximately fair, approximately truthful, and approximately efficient, for some favorable approximation parameters. This approximation is used in practice to assign students to classes. In this paper we show that finding the A-CEEI allocation guaranteed to exist by Budish's theorem is PPAD-complete. We further show that f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.6249","kind":"arxiv","version":3},"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":"2026-05-18T02:41:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"y9tRITSUwHFMYAjolSpb/v6FV7h1P62eAvBUCX8yOEltJVQwgNOiKV6H84MnKtXAs1Eyi/+Z9dS8WdXv5T/kDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T01:37:02.221757Z"},"content_sha256":"9dad81b4b8bb8a457344618e5eea84c21a19845d15256bfb358c0295d6d1a5e1","schema_version":"1.0","event_id":"sha256:9dad81b4b8bb8a457344618e5eea84c21a19845d15256bfb358c0295d6d1a5e1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DDW36YRHHLNE2YK6F5E43Q7TOW/bundle.json","state_url":"https://pith.science/pith/DDW36YRHHLNE2YK6F5E43Q7TOW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DDW36YRHHLNE2YK6F5E43Q7TOW/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":"2026-05-31T01:37:02Z","links":{"resolver":"https://pith.science/pith/DDW36YRHHLNE2YK6F5E43Q7TOW","bundle":"https://pith.science/pith/DDW36YRHHLNE2YK6F5E43Q7TOW/bundle.json","state":"https://pith.science/pith/DDW36YRHHLNE2YK6F5E43Q7TOW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DDW36YRHHLNE2YK6F5E43Q7TOW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:DDW36YRHHLNE2YK6F5E43Q7TOW","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":"5d9c31c6114efc47dd77c4c6a824017ae68278291c2882516f70720f620fdcad","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2013-12-21T13:09:10Z","title_canon_sha256":"a782303444f0be57ebd1387744000d716dd07e68b4953a043c079e25fbd6db79"},"schema_version":"1.0","source":{"id":"1312.6249","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.6249","created_at":"2026-05-18T02:41:18Z"},{"alias_kind":"arxiv_version","alias_value":"1312.6249v3","created_at":"2026-05-18T02:41:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.6249","created_at":"2026-05-18T02:41:18Z"},{"alias_kind":"pith_short_12","alias_value":"DDW36YRHHLNE","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_16","alias_value":"DDW36YRHHLNE2YK6","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_8","alias_value":"DDW36YRH","created_at":"2026-05-18T12:27:40Z"}],"graph_snapshots":[{"event_id":"sha256:9dad81b4b8bb8a457344618e5eea84c21a19845d15256bfb358c0295d6d1a5e1","target":"graph","created_at":"2026-05-18T02:41:18Z","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":"Competitive equilibrium with equal incomes (CEEI) is a well known fair allocation mechanism; however, for indivisible resources a CEEI may not exist. It was shown in [Budish '11] that in the case of indivisible resources there is always an allocation, called A-CEEI, that is approximately fair, approximately truthful, and approximately efficient, for some favorable approximation parameters. This approximation is used in practice to assign students to classes. In this paper we show that finding the A-CEEI allocation guaranteed to exist by Budish's theorem is PPAD-complete. We further show that f","authors_text":"Abraham Othman, Aviad Rubinstein, Christos Papadimitriou","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2013-12-21T13:09:10Z","title":"The Complexity of Fairness through Equilibrium"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.6249","kind":"arxiv","version":3},"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":"sha256:6276db6c3ddbe992cf1ab1bd279b1c0125f333fed7505aba9c330b6f89183dfb","target":"record","created_at":"2026-05-18T02:41:18Z","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":"5d9c31c6114efc47dd77c4c6a824017ae68278291c2882516f70720f620fdcad","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2013-12-21T13:09:10Z","title_canon_sha256":"a782303444f0be57ebd1387744000d716dd07e68b4953a043c079e25fbd6db79"},"schema_version":"1.0","source":{"id":"1312.6249","kind":"arxiv","version":3}},"canonical_sha256":"18edbf62273ada4d615e2f49cdc3f37584b7ba154b1f2cedbabdbf6c0a3babf1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"18edbf62273ada4d615e2f49cdc3f37584b7ba154b1f2cedbabdbf6c0a3babf1","first_computed_at":"2026-05-18T02:41:18.729261Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:41:18.729261Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uWTxOs8Ak5/2Vmx8+hZrR+LLUk2g/xHux9OLwwXO67Tz3D2WFgBKPYnzoNSl2O8qB7zfcvC93JlvT38nRlKZBw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:41:18.729664Z","signed_message":"canonical_sha256_bytes"},"source_id":"1312.6249","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6276db6c3ddbe992cf1ab1bd279b1c0125f333fed7505aba9c330b6f89183dfb","sha256:9dad81b4b8bb8a457344618e5eea84c21a19845d15256bfb358c0295d6d1a5e1"],"state_sha256":"a3ed6aa26c363e0ec6b3f9ea4dabc8f882b3d4afe66b45f0f6c4b6c314e70ee9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"i0oi5MM7eGJ1jFiw+3nTGW2eAMRxInadTdaoq0QSB9q66NiBNXMDtHW01uyQzBnEUPQczEac5MWT7FQ/xI9GCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T01:37:02.224161Z","bundle_sha256":"f8fec6f9bd80fcca86a0ab4b9d89a289c567ee882d86f1238e3adceba657deee"}}