{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:7C7BMFJAMCI7HJ52VRMKTDVJSA","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":"f1c82e0e0fe0265c39741fafa47fa9ea7fa64df5766861d33cb9df5b43f57ddf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2015-12-14T17:43:59Z","title_canon_sha256":"a0694d2b3c5b41493fb6a625f98002a5290aa7f399f0765f7019962a7b80d12e"},"schema_version":"1.0","source":{"id":"1512.04424","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.04424","created_at":"2026-05-18T00:34:31Z"},{"alias_kind":"arxiv_version","alias_value":"1512.04424v1","created_at":"2026-05-18T00:34:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.04424","created_at":"2026-05-18T00:34:31Z"},{"alias_kind":"pith_short_12","alias_value":"7C7BMFJAMCI7","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_16","alias_value":"7C7BMFJAMCI7HJ52","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_8","alias_value":"7C7BMFJA","created_at":"2026-05-18T12:29:07Z"}],"graph_snapshots":[{"event_id":"sha256:44e4587c65c208243a88a2f9518f39f064683c9d0a1adf6f61f7a3f86da30bdd","target":"graph","created_at":"2026-05-18T00:34:31Z","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"},"paper":{"abstract_excerpt":"We show that not every family of generalized microscopic sets forms an ideal. Moreover, we prove that some of these families have some weaker additivity properties and some of them do not have even that.","authors_text":"Adam Kwela, Klaudiusz Czudek, Nikodem Mro\\.zek, Wojciech Wo{\\l}oszyn","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2015-12-14T17:43:59Z","title":"Ideal-like properties of generalized microscopic sets"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.04424","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":"sha256:051f6bdc0d428a03ac926f44edf07c2984ccf2de5b49ae02a70b0fae1df36301","target":"record","created_at":"2026-05-18T00:34:31Z","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":"f1c82e0e0fe0265c39741fafa47fa9ea7fa64df5766861d33cb9df5b43f57ddf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2015-12-14T17:43:59Z","title_canon_sha256":"a0694d2b3c5b41493fb6a625f98002a5290aa7f399f0765f7019962a7b80d12e"},"schema_version":"1.0","source":{"id":"1512.04424","kind":"arxiv","version":1}},"canonical_sha256":"f8be1615206091f3a7baac58a98ea9901e1ef7fcced4591753eeb91a03451e9a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f8be1615206091f3a7baac58a98ea9901e1ef7fcced4591753eeb91a03451e9a","first_computed_at":"2026-05-18T00:34:31.854239Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:34:31.854239Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9YP/coHDYOUc5XBWqvnzlieZoWAKjXQSJ9lvKVZZla51xqhW1C1H8jdmbDxGWdVcJ6yl/yNxgQdN/K2FWheqAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:34:31.854744Z","signed_message":"canonical_sha256_bytes"},"source_id":"1512.04424","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:051f6bdc0d428a03ac926f44edf07c2984ccf2de5b49ae02a70b0fae1df36301","sha256:44e4587c65c208243a88a2f9518f39f064683c9d0a1adf6f61f7a3f86da30bdd"],"state_sha256":"e79c44049bf549aa511629d9ec52adf09a355bc4a905714b5ea3228d9591099b"}