{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:JEQG3SRUBGU4DFQ5QONLL5WREE","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":"741704cf170c15004ab04040bef5091f79b3d0907cec2ac9956127cb9b77d26a","cross_cats_sorted":["cs.CC"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.GT","submitted_at":"2026-05-31T02:05:21Z","title_canon_sha256":"b3c02fcef12f216a7d6ff1011d65aba8a1063e50b9a294392b8bb8db097e5fae"},"schema_version":"1.0","source":{"id":"2606.00951","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.00951","created_at":"2026-06-02T01:04:10Z"},{"alias_kind":"arxiv_version","alias_value":"2606.00951v1","created_at":"2026-06-02T01:04:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.00951","created_at":"2026-06-02T01:04:10Z"},{"alias_kind":"pith_short_12","alias_value":"JEQG3SRUBGU4","created_at":"2026-06-02T01:04:10Z"},{"alias_kind":"pith_short_16","alias_value":"JEQG3SRUBGU4DFQ5","created_at":"2026-06-02T01:04:10Z"},{"alias_kind":"pith_short_8","alias_value":"JEQG3SRU","created_at":"2026-06-02T01:04:10Z"}],"graph_snapshots":[{"event_id":"sha256:ded31108e94adf2f396b0c95e1f125596c443dc2d89753e1a14c4f96ca0c551a","target":"graph","created_at":"2026-06-02T01:04:10Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2606.00951/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we investigate the computational hardness of finding fractional allocations to unit-demand players using competitive equilibria from equal incomes (CEEI), where we allow a small constant error in players' response to market prices (also known as an approximate Hylland-Zeckhauser equilibrium). We show that assuming the $\\mathbf{(\\varepsilon,\\delta)}$-Generalized Circuits problem is PPAD-hard (the \"PCP for PPAD\" conjecture), finding an approximate HZ equilibrium is also PPAD-hard. This result provides additional motivation for trying to prove the PCP for PPAD conjecture as a tool ","authors_text":"Chenghan Zhou, Eric Xue, Jingyi Liu, Mark Braverman","cross_cats":["cs.CC"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.GT","submitted_at":"2026-05-31T02:05:21Z","title":"Hardness of Approximate Hylland-Zeckhauser Equilibria"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.00951","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:ba3165ff770f44dba224daef5bff61b47e2fe2440202acc0726bd2d90d8ef23e","target":"record","created_at":"2026-06-02T01:04:10Z","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":"741704cf170c15004ab04040bef5091f79b3d0907cec2ac9956127cb9b77d26a","cross_cats_sorted":["cs.CC"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.GT","submitted_at":"2026-05-31T02:05:21Z","title_canon_sha256":"b3c02fcef12f216a7d6ff1011d65aba8a1063e50b9a294392b8bb8db097e5fae"},"schema_version":"1.0","source":{"id":"2606.00951","kind":"arxiv","version":1}},"canonical_sha256":"49206dca3409a9c1961d839ab5f6d1213bd9fcf533e7a19ce3630400f412c9cc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"49206dca3409a9c1961d839ab5f6d1213bd9fcf533e7a19ce3630400f412c9cc","first_computed_at":"2026-06-02T01:04:10.248216Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-02T01:04:10.248216Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ggoWX5lFrmFnVtH/iNHct//Y3Df2i7BkGZiREzWyb1kzVGC4MZojyF64UCk4yIO01tW632QkVCJlR1YqHBnTCA==","signature_status":"signed_v1","signed_at":"2026-06-02T01:04:10.248658Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.00951","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ba3165ff770f44dba224daef5bff61b47e2fe2440202acc0726bd2d90d8ef23e","sha256:ded31108e94adf2f396b0c95e1f125596c443dc2d89753e1a14c4f96ca0c551a"],"state_sha256":"c8f3c7a2b68a67bb8817c1934a0ed55d59c9ec6204d09c20d3a1f44ec40faec5"}