{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1996:VEXQNB7MMKYHYYMETEWMI32EMC","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":"dccc6ef3cb9ae66a75c61ff48af5677e58488ab65b1785e07f181acb199c6287","cross_cats_sorted":["math.OA"],"license":"","primary_cat":"math.FA","submitted_at":"1996-02-02T00:00:00Z","title_canon_sha256":"c4edf273c5872d19319db8ad2d39a40a3d850419bb3282e3068f7ed0d6cef002"},"schema_version":"1.0","source":{"id":"math/9602218","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/9602218","created_at":"2026-05-18T01:05:47Z"},{"alias_kind":"arxiv_version","alias_value":"math/9602218v1","created_at":"2026-05-18T01:05:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9602218","created_at":"2026-05-18T01:05:47Z"},{"alias_kind":"pith_short_12","alias_value":"VEXQNB7MMKYH","created_at":"2026-05-18T12:25:48Z"},{"alias_kind":"pith_short_16","alias_value":"VEXQNB7MMKYHYYME","created_at":"2026-05-18T12:25:48Z"},{"alias_kind":"pith_short_8","alias_value":"VEXQNB7M","created_at":"2026-05-18T12:25:48Z"}],"graph_snapshots":[{"event_id":"sha256:b6dc053ff2bc62bdb333fb7bbe805194815991dcc225df97c0c21fffc75ecfcd","target":"graph","created_at":"2026-05-18T01:05:47Z","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":"It is proved that every second countable locally Hausdorff and locally compact continuous groupoid has a Borel set of units that meets every orbit and is what is called \"lacunary,\" a property that implies that the intersection with every orbit is countable.","authors_text":"Arlan Ramsay","cross_cats":["math.OA"],"headline":"","license":"","primary_cat":"math.FA","submitted_at":"1996-02-02T00:00:00Z","title":"Lacunary sections for locally compact groupoids"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9602218","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":"sha256:558efc7a5b48dc10989bfa9572935f33359d2060ff78558fb92ccca9e2f1fcfa","target":"record","created_at":"2026-05-18T01:05:47Z","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":"dccc6ef3cb9ae66a75c61ff48af5677e58488ab65b1785e07f181acb199c6287","cross_cats_sorted":["math.OA"],"license":"","primary_cat":"math.FA","submitted_at":"1996-02-02T00:00:00Z","title_canon_sha256":"c4edf273c5872d19319db8ad2d39a40a3d850419bb3282e3068f7ed0d6cef002"},"schema_version":"1.0","source":{"id":"math/9602218","kind":"arxiv","version":1}},"canonical_sha256":"a92f0687ec62b07c6184992cc46f4460a565cda2297c14289484fdb3f5407a9e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a92f0687ec62b07c6184992cc46f4460a565cda2297c14289484fdb3f5407a9e","first_computed_at":"2026-05-18T01:05:47.757850Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:05:47.757850Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PZ6FOO/N3LzVpbL1UrpKROgE0Eriwe9VjDAxsprqshAskblMeys0rRuN29Ti6jQzPiF9o3hnD6OyfOOg0qBICw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:05:47.758681Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/9602218","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:558efc7a5b48dc10989bfa9572935f33359d2060ff78558fb92ccca9e2f1fcfa","sha256:b6dc053ff2bc62bdb333fb7bbe805194815991dcc225df97c0c21fffc75ecfcd"],"state_sha256":"1e5c396910278d86af418e69e41950b133cabf4488d0cbab010da1050a18408a"}