{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:SNZEE5HHG7YVNVZNOT73O3JK43","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":"3dba1c00986940560158360cd5b3417afc3bebe601bb748a920fedd37db14786","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2024-02-03T23:18:48Z","title_canon_sha256":"2f268523307825157c55f516e587b5b04561a1e67fe5d1cad6ff00164a984d4c"},"schema_version":"1.0","source":{"id":"2402.02296","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2402.02296","created_at":"2026-07-05T12:00:42Z"},{"alias_kind":"arxiv_version","alias_value":"2402.02296v4","created_at":"2026-07-05T12:00:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2402.02296","created_at":"2026-07-05T12:00:42Z"},{"alias_kind":"pith_short_12","alias_value":"SNZEE5HHG7YV","created_at":"2026-07-05T12:00:42Z"},{"alias_kind":"pith_short_16","alias_value":"SNZEE5HHG7YVNVZN","created_at":"2026-07-05T12:00:42Z"},{"alias_kind":"pith_short_8","alias_value":"SNZEE5HH","created_at":"2026-07-05T12:00:42Z"}],"graph_snapshots":[{"event_id":"sha256:77bc501a34b0f038b24fc797908b47c5dcea6253d6e4a5a3cf77496ea860a8bc","target":"graph","created_at":"2026-07-05T12:00:42Z","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/2402.02296/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In recent work, we introduced a new semantics for conditionals, covering a large class of what we call preconditionals. In this paper, we undertake an axiomatic study of preconditionals and subclasses of preconditionals. We then prove that any bounded lattice equipped with a preconditional can be represented by a relational structure, suitably topologized, yielding a single relational semantics for conditional logics normally treated by different semantics, as well as generalizing beyond those semantics.","authors_text":"Wesley H. Holliday","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2024-02-03T23:18:48Z","title":"Preconditionals"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2402.02296","kind":"arxiv","version":4},"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":"sha256:934575215e558c023fb802cc76f17a66c2091fdf17373a60bc05f5c74c6de253","target":"record","created_at":"2026-07-05T12:00:42Z","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":"3dba1c00986940560158360cd5b3417afc3bebe601bb748a920fedd37db14786","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2024-02-03T23:18:48Z","title_canon_sha256":"2f268523307825157c55f516e587b5b04561a1e67fe5d1cad6ff00164a984d4c"},"schema_version":"1.0","source":{"id":"2402.02296","kind":"arxiv","version":4}},"canonical_sha256":"93724274e737f156d72d74ffb76d2ae6d308638712dbc0b26dd8cea9313f7407","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"93724274e737f156d72d74ffb76d2ae6d308638712dbc0b26dd8cea9313f7407","first_computed_at":"2026-07-05T12:00:42.602918Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T12:00:42.602918Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VpTPV5ahscpGtg+KRLyQ3iyyxRMgcKxe2M8qSjyR0cIFmnCtx4uWXbD5XrM2wB0wUTBGXz95GNDvueWcGFShCw==","signature_status":"signed_v1","signed_at":"2026-07-05T12:00:42.603427Z","signed_message":"canonical_sha256_bytes"},"source_id":"2402.02296","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:934575215e558c023fb802cc76f17a66c2091fdf17373a60bc05f5c74c6de253","sha256:77bc501a34b0f038b24fc797908b47c5dcea6253d6e4a5a3cf77496ea860a8bc"],"state_sha256":"1e1df0db48f0e513646e8453c77eae13fde6c1a048bad79fab552209c297e68f"}