{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:WZDP646SHETGYUYDZEPFQ7VUSE","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":"5d89ea1cdb4b896423e69020706d78e7f749a6eb82c57a844c71f9338a821d6c","cross_cats_sorted":["math.GN"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2011-08-04T12:26:38Z","title_canon_sha256":"3eb7ffc9371c32ccd6d6a79385a1f0d2e62d23c41b7ad5767ae75966dea3d263"},"schema_version":"1.0","source":{"id":"1108.1063","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1108.1063","created_at":"2026-05-18T04:16:11Z"},{"alias_kind":"arxiv_version","alias_value":"1108.1063v2","created_at":"2026-05-18T04:16:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.1063","created_at":"2026-05-18T04:16:11Z"},{"alias_kind":"pith_short_12","alias_value":"WZDP646SHETG","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_16","alias_value":"WZDP646SHETGYUYD","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_8","alias_value":"WZDP646S","created_at":"2026-05-18T12:26:44Z"}],"graph_snapshots":[{"event_id":"sha256:abcc3d4cafee78206cd920a7c8d5aa1b648518f9911bd7c9bd55a8fd139b0530","target":"graph","created_at":"2026-05-18T04:16:11Z","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":"Idempotent analogues of convexity are introduced. It is proved that the category of algebras for the capacity monad in the category of compacta is isomorphic to the category of $(\\max,\\min)$-idempotent biconvex compacta and their biaffine maps. It is also shown that the category of algebras for the monad of sup-measures ($(\\max,\\min)$-idempotent measures) is isomorphic to the category of $(\\max,\\min)$-idempotent convex compacta and their affine maps.","authors_text":"Du\\v{s}an Repov\\v{s}, Oleh Nykyforchyn","cross_cats":["math.GN"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2011-08-04T12:26:38Z","title":"Idempotent convexity and algebras for the capacity monad and its submonads"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.1063","kind":"arxiv","version":2},"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:caba7aeb9a82974bd6f5f2d024d8edd33c7e7e7bdaf429f3a1b0e72231edb144","target":"record","created_at":"2026-05-18T04:16:11Z","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":"5d89ea1cdb4b896423e69020706d78e7f749a6eb82c57a844c71f9338a821d6c","cross_cats_sorted":["math.GN"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2011-08-04T12:26:38Z","title_canon_sha256":"3eb7ffc9371c32ccd6d6a79385a1f0d2e62d23c41b7ad5767ae75966dea3d263"},"schema_version":"1.0","source":{"id":"1108.1063","kind":"arxiv","version":2}},"canonical_sha256":"b646ff73d239266c5303c91e587eb4913a040786c8258cb31ed63c80e66105ff","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b646ff73d239266c5303c91e587eb4913a040786c8258cb31ed63c80e66105ff","first_computed_at":"2026-05-18T04:16:11.422902Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:16:11.422902Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3Jo8f9KO0KqDYtpvYfIJVpWsnZhloq7aFzocCgfsX+cpDYlCT1Ko5L/bRIWTTfPHvJSt9JI+rqiiDm+BpPHVAg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:16:11.423299Z","signed_message":"canonical_sha256_bytes"},"source_id":"1108.1063","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:caba7aeb9a82974bd6f5f2d024d8edd33c7e7e7bdaf429f3a1b0e72231edb144","sha256:abcc3d4cafee78206cd920a7c8d5aa1b648518f9911bd7c9bd55a8fd139b0530"],"state_sha256":"eb767478e771e1431ba9e9881fd351f8eabaf5f25dd6b2f313c9b72c1e0cd2b4"}