{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:QD2CKPOK3PCA3OZOLF3DHY5GFH","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":"6a6d1247df1c01d787481fd1020ec0d6efa4639766c6af0b0f18996f4fa4e2c1","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.LO","submitted_at":"2025-06-09T20:38:17Z","title_canon_sha256":"150f9ca18766667124fc4249be6c9d5cf444a2a59b5cd28389526503370f0f8e"},"schema_version":"1.0","source":{"id":"2506.08217","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.08217","created_at":"2026-07-05T11:18:46Z"},{"alias_kind":"arxiv_version","alias_value":"2506.08217v1","created_at":"2026-07-05T11:18:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.08217","created_at":"2026-07-05T11:18:46Z"},{"alias_kind":"pith_short_12","alias_value":"QD2CKPOK3PCA","created_at":"2026-07-05T11:18:46Z"},{"alias_kind":"pith_short_16","alias_value":"QD2CKPOK3PCA3OZO","created_at":"2026-07-05T11:18:46Z"},{"alias_kind":"pith_short_8","alias_value":"QD2CKPOK","created_at":"2026-07-05T11:18:46Z"}],"graph_snapshots":[{"event_id":"sha256:e75054e302b253e577b5bcb78c8a644b06b6ad6f780a85a6a97fc611557055e1","target":"graph","created_at":"2026-07-05T11:18:46Z","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/2506.08217/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We address some fundamental problems concerning the structure of idealistic equivalence relations. In particular, we show that, under analytic determinacy, there are continuum many idealistic analytic equivalence relations that are not classwise Borel isomorphic to an orbit equivalence relation. Moreover, we also discuss alternative formulations of the E1 conjecture, and present an elementary counterexample to one of its earliest variants proposed by Hjorth and Kechris in 1997.","authors_text":"Filippo Calderoni, Luca Motto Ros","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.LO","submitted_at":"2025-06-09T20:38:17Z","title":"Structural results on idealistic equivalence relations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.08217","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:a70bc78a973ee5e49894d630108b807720d6ec3772cdf289f75fddba97cbb430","target":"record","created_at":"2026-07-05T11:18:46Z","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":"6a6d1247df1c01d787481fd1020ec0d6efa4639766c6af0b0f18996f4fa4e2c1","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.LO","submitted_at":"2025-06-09T20:38:17Z","title_canon_sha256":"150f9ca18766667124fc4249be6c9d5cf444a2a59b5cd28389526503370f0f8e"},"schema_version":"1.0","source":{"id":"2506.08217","kind":"arxiv","version":1}},"canonical_sha256":"80f4253dcadbc40dbb2e597633e3a629c724f6bb1aac2daad18fbba602ef1f4a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"80f4253dcadbc40dbb2e597633e3a629c724f6bb1aac2daad18fbba602ef1f4a","first_computed_at":"2026-07-05T11:18:46.378954Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:18:46.378954Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"v+LxCVHhbn9ieS0YUSLuxG8EPN7dtgH+9n3Yntuac3FWahxf7XhcRtpYAc6ti7swhLTnkhweYtZSOZ8rt1DSBQ==","signature_status":"signed_v1","signed_at":"2026-07-05T11:18:46.379483Z","signed_message":"canonical_sha256_bytes"},"source_id":"2506.08217","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a70bc78a973ee5e49894d630108b807720d6ec3772cdf289f75fddba97cbb430","sha256:e75054e302b253e577b5bcb78c8a644b06b6ad6f780a85a6a97fc611557055e1"],"state_sha256":"865496372465c536581d90ceda1bd42036c3377337abe2aa23ec93b569b3ed64"}