{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:RCFGS652ESWGMT4W7OTGL6A55N","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":"94f27be1089bf8a838fedd17a1f9dbd2603790a2b6a2b0412a773e0172828ce8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"econ.TH","submitted_at":"2026-06-04T11:59:44Z","title_canon_sha256":"64414a8421488c1f3c2958f3f4394a92c9a82f4f32f6df068616bf8e675aca7e"},"schema_version":"1.0","source":{"id":"2606.06059","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.06059","created_at":"2026-06-05T01:15:31Z"},{"alias_kind":"arxiv_version","alias_value":"2606.06059v1","created_at":"2026-06-05T01:15:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.06059","created_at":"2026-06-05T01:15:31Z"},{"alias_kind":"pith_short_12","alias_value":"RCFGS652ESWG","created_at":"2026-06-05T01:15:31Z"},{"alias_kind":"pith_short_16","alias_value":"RCFGS652ESWGMT4W","created_at":"2026-06-05T01:15:31Z"},{"alias_kind":"pith_short_8","alias_value":"RCFGS652","created_at":"2026-06-05T01:15:31Z"}],"graph_snapshots":[{"event_id":"sha256:b1bb2b43c5773e8943d302c01f9a3d0d192d32c9d8f798373ea30ef92076276c","target":"graph","created_at":"2026-06-05T01:15:31Z","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/2606.06059/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study the division of a heterogeneous good between two agents into contiguous bundles, each defined by a starting location and a quantity, in a purely ordinal framework that does not rely on cardinal valuations. We introduce a general class of monotonic preferences representable by indifference curves. We show that an allocation is Pareto efficient and envy-free if and only if it lies in a specific ``balanced region'', implying that an equal split is fair only when it belongs to this region. We further show that no rule can simultaneously satisfy Pareto efficiency, envy-freeness, and strate","authors_text":"Mihir Bhattacharya, Ojasvi Khare","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"econ.TH","submitted_at":"2026-06-04T11:59:44Z","title":"Fair Division of a Heterogeneous Good Between Two Agents: An Ordinal Approach"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.06059","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":"sha256:67830ac74b4b94ec895dedb6b3c700c5b3ce91f76b656c87bfc46d5655423570","target":"record","created_at":"2026-06-05T01:15:31Z","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":"94f27be1089bf8a838fedd17a1f9dbd2603790a2b6a2b0412a773e0172828ce8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"econ.TH","submitted_at":"2026-06-04T11:59:44Z","title_canon_sha256":"64414a8421488c1f3c2958f3f4394a92c9a82f4f32f6df068616bf8e675aca7e"},"schema_version":"1.0","source":{"id":"2606.06059","kind":"arxiv","version":1}},"canonical_sha256":"888a697bba24ac664f96fba665f81deb559fb0db33a1f0a99e7b320057286514","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"888a697bba24ac664f96fba665f81deb559fb0db33a1f0a99e7b320057286514","first_computed_at":"2026-06-05T01:15:31.776717Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-05T01:15:31.776717Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+Rk/FUOgokQcQwf6dy1CaWDda736cjDP6tSIfMRiseujmh6PsyRs34tIPthPvIm1G/q1k8q8pxznX/r15HSJAA==","signature_status":"signed_v1","signed_at":"2026-06-05T01:15:31.777125Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.06059","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:67830ac74b4b94ec895dedb6b3c700c5b3ce91f76b656c87bfc46d5655423570","sha256:b1bb2b43c5773e8943d302c01f9a3d0d192d32c9d8f798373ea30ef92076276c"],"state_sha256":"c69a36b41dbb92ffb0710a75f3b41ae4db807a473a88381db2ddd4c5a7c408b3"}