{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:SCBNCHRYDCXIAFUSLTHM7PJKQD","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":"d65ca6d864377b21b1a96b8a4c8902ced49827e695dd6d9850efee2aa32e95eb","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"cs.LO","submitted_at":"2025-07-15T10:40:48Z","title_canon_sha256":"ec90d65eab1f7d2505b10f60294bde79a1edb2239f2d6cdb0191a0871f89abc5"},"schema_version":"1.0","source":{"id":"2507.11186","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2507.11186","created_at":"2026-07-05T11:37:33Z"},{"alias_kind":"arxiv_version","alias_value":"2507.11186v1","created_at":"2026-07-05T11:37:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.11186","created_at":"2026-07-05T11:37:33Z"},{"alias_kind":"pith_short_12","alias_value":"SCBNCHRYDCXI","created_at":"2026-07-05T11:37:33Z"},{"alias_kind":"pith_short_16","alias_value":"SCBNCHRYDCXIAFUS","created_at":"2026-07-05T11:37:33Z"},{"alias_kind":"pith_short_8","alias_value":"SCBNCHRY","created_at":"2026-07-05T11:37:33Z"}],"graph_snapshots":[{"event_id":"sha256:7a370658fefd112c36a08c96a6ec7d13c0dbd4151e01c3fe6d34855d32feed78","target":"graph","created_at":"2026-07-05T11:37:33Z","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/2507.11186/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Convex semilattices are algebras that are at the same time a convex algebra and a semilattice, together with a distributivity axiom. These algebras have attracted some attention in the last years as suitable algebras for probability and nondeterminism, in particular by being the Eilenberg-Moore algebras of the nonempty finitely-generated convex subsets of the distributions monad.\n  A convex semilattice is cancellative if the underlying convex algebra is cancellative. Cancellative convex algebras have been characterized by M. H. Stone and by H. Kneser: A convex algebra is cancellative if and on","authors_text":"Ana Sokolova, Harald Woracek","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"cs.LO","submitted_at":"2025-07-15T10:40:48Z","title":"Cancellative Convex Semilattices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.11186","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":"sha256:4d1cc2a063ec8bce88c572ff917830b4af3e4d67802aaf6305b918c457321db5","target":"record","created_at":"2026-07-05T11:37:33Z","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":"d65ca6d864377b21b1a96b8a4c8902ced49827e695dd6d9850efee2aa32e95eb","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"cs.LO","submitted_at":"2025-07-15T10:40:48Z","title_canon_sha256":"ec90d65eab1f7d2505b10f60294bde79a1edb2239f2d6cdb0191a0871f89abc5"},"schema_version":"1.0","source":{"id":"2507.11186","kind":"arxiv","version":1}},"canonical_sha256":"9082d11e3818ae8016925ccecfbd2a80eb9fd411fe7be04d64b76e9617e47112","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9082d11e3818ae8016925ccecfbd2a80eb9fd411fe7be04d64b76e9617e47112","first_computed_at":"2026-07-05T11:37:33.977126Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:37:33.977126Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WCq7dJqnCufMYDosryfAjC7rYt3cNAq6JsxWFcZxrrgzswB7oTYU0zFjm16zQ5H9BcRPlhhiIXlnod5HCXMWDg==","signature_status":"signed_v1","signed_at":"2026-07-05T11:37:33.977616Z","signed_message":"canonical_sha256_bytes"},"source_id":"2507.11186","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4d1cc2a063ec8bce88c572ff917830b4af3e4d67802aaf6305b918c457321db5","sha256:7a370658fefd112c36a08c96a6ec7d13c0dbd4151e01c3fe6d34855d32feed78"],"state_sha256":"52b9334c56046040dc35ee89fc82c6a85486859ae2a9412077b28383aedb9bfc"}