{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:7F3L2T6NSYN3GJK4UPDOKXR3WH","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":"2029b15e156cc2c9f0f64cc6852807fbb315bf4145318f55a7584892ee614df7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"econ.TH","submitted_at":"2026-06-09T19:01:39Z","title_canon_sha256":"1a6955e196b37c5c29f6d7ddb6787198a9ee297abe8c696f849c76ba8563c3c5"},"schema_version":"1.0","source":{"id":"2606.11377","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.11377","created_at":"2026-06-11T00:08:22Z"},{"alias_kind":"arxiv_version","alias_value":"2606.11377v1","created_at":"2026-06-11T00:08:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.11377","created_at":"2026-06-11T00:08:22Z"},{"alias_kind":"pith_short_12","alias_value":"7F3L2T6NSYN3","created_at":"2026-06-11T00:08:22Z"},{"alias_kind":"pith_short_16","alias_value":"7F3L2T6NSYN3GJK4","created_at":"2026-06-11T00:08:22Z"},{"alias_kind":"pith_short_8","alias_value":"7F3L2T6N","created_at":"2026-06-11T00:08:22Z"}],"graph_snapshots":[{"event_id":"sha256:394e3a0516fc1569d4e7938a470db7328d8352e859c47828fd8c3556d7f5e836","target":"graph","created_at":"2026-06-11T00:08:22Z","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/2606.11377/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study global uniqueness of competitive equilibrium in two-good pure-exchange economies with heterogeneous impatience types and a common HARA Bernoulli utility. The paper connects the CRRA sorting result of \\citet{GeanakoplosWalsh2018} with the line of HARA uniqueness results developed in \\citet{LoiMatta2022,LoiMatta2024}. In the CRRA case, ordered endowments provide a sorting mechanism for uniqueness. In the HARA case, uniqueness is known to hold for arbitrary endowments under the curvature bound $\\gamma\\le I/(I-1)$, where $I$ is the number of impatience types. For two types, the curvature ","authors_text":"Andrea Loi, Stefano Matta","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"econ.TH","submitted_at":"2026-06-09T19:01:39Z","title":"Sorting and Global Uniqueness in Two-Good HARA Economies with Many Patience Types"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.11377","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":"sha256:44c45d2695a76faaaf1ed545a8224a147557e13a7afe95ad120b94fe775e8cb3","target":"record","created_at":"2026-06-11T00:08:22Z","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":"2029b15e156cc2c9f0f64cc6852807fbb315bf4145318f55a7584892ee614df7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"econ.TH","submitted_at":"2026-06-09T19:01:39Z","title_canon_sha256":"1a6955e196b37c5c29f6d7ddb6787198a9ee297abe8c696f849c76ba8563c3c5"},"schema_version":"1.0","source":{"id":"2606.11377","kind":"arxiv","version":1}},"canonical_sha256":"f976bd4fcd961bb3255ca3c6e55e3bb1d97361758e01ac8a08f40f1648326f7b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f976bd4fcd961bb3255ca3c6e55e3bb1d97361758e01ac8a08f40f1648326f7b","first_computed_at":"2026-06-11T00:08:22.426446Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-11T00:08:22.426446Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1LZaahZchO7G7VNJyRYyDzQBUzYEoMG/e0yel99R9f4qT711vQMG1FuVy5ZAX0Ba9LfuOzlrJAOQ1gHltFVHBw==","signature_status":"signed_v1","signed_at":"2026-06-11T00:08:22.427369Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.11377","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:44c45d2695a76faaaf1ed545a8224a147557e13a7afe95ad120b94fe775e8cb3","sha256:394e3a0516fc1569d4e7938a470db7328d8352e859c47828fd8c3556d7f5e836"],"state_sha256":"b2210b10169f9f93c528ddc6b28e8bec27acde260b929316ac0393338ca6f213"}