{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:WMLALY7IWIGZS3CQNNAH4GVH5F","short_pith_number":"pith:WMLALY7I","canonical_record":{"source":{"id":"2603.14955","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"cs.LO","submitted_at":"2026-03-16T08:10:05Z","cross_cats_sorted":["math.LO"],"title_canon_sha256":"dd8f9fdd1455f69b03ff1d8fadf945503e5ab4dc7aea5b0c2f8a46229bf73a49","abstract_canon_sha256":"871b4b1ccab728123188e1e23c6d2f61188d8568869671fcc16926ce4d27406f"},"schema_version":"1.0"},"canonical_sha256":"b31605e3e8b20d996c506b407e1aa7e9593f1df6c74cd13a087368cb3b507b89","source":{"kind":"arxiv","id":"2603.14955","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2603.14955","created_at":"2026-06-09T01:05:16Z"},{"alias_kind":"arxiv_version","alias_value":"2603.14955v2","created_at":"2026-06-09T01:05:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2603.14955","created_at":"2026-06-09T01:05:16Z"},{"alias_kind":"pith_short_12","alias_value":"WMLALY7IWIGZ","created_at":"2026-06-09T01:05:16Z"},{"alias_kind":"pith_short_16","alias_value":"WMLALY7IWIGZS3CQ","created_at":"2026-06-09T01:05:16Z"},{"alias_kind":"pith_short_8","alias_value":"WMLALY7I","created_at":"2026-06-09T01:05:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:WMLALY7IWIGZS3CQNNAH4GVH5F","target":"record","payload":{"canonical_record":{"source":{"id":"2603.14955","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"cs.LO","submitted_at":"2026-03-16T08:10:05Z","cross_cats_sorted":["math.LO"],"title_canon_sha256":"dd8f9fdd1455f69b03ff1d8fadf945503e5ab4dc7aea5b0c2f8a46229bf73a49","abstract_canon_sha256":"871b4b1ccab728123188e1e23c6d2f61188d8568869671fcc16926ce4d27406f"},"schema_version":"1.0"},"canonical_sha256":"b31605e3e8b20d996c506b407e1aa7e9593f1df6c74cd13a087368cb3b507b89","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-09T01:05:16.069763Z","signature_b64":"peqXpirAhlqIvtcKFudw3rGrThu7ktvR9CEd58qmG2rikFLEYxwSTN/Yh3Vrk2br42ULQwzFVw81kSRsK2fgBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b31605e3e8b20d996c506b407e1aa7e9593f1df6c74cd13a087368cb3b507b89","last_reissued_at":"2026-06-09T01:05:16.069240Z","signature_status":"signed_v1","first_computed_at":"2026-06-09T01:05:16.069240Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2603.14955","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-06-09T01:05:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sdNJqts4/gA0+Vu85ymyA2iUV91iqNdXZX3CGGnjQHrNteBQ3FxH15grz4ZrjfMM94+p7lypsmvq1sKXMzWQDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T17:38:36.148336Z"},"content_sha256":"8cb7f7aa98143f94a2fbc23b981350a8236503d5f79a243c1a60754c64e7d4e8","schema_version":"1.0","event_id":"sha256:8cb7f7aa98143f94a2fbc23b981350a8236503d5f79a243c1a60754c64e7d4e8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:WMLALY7IWIGZS3CQNNAH4GVH5F","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Convex algebras on an interval with semicontinuous monotone operations","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":["math.LO"],"primary_cat":"cs.LO","authors_text":"Ana Sokolova, Harald Woracek","submitted_at":"2026-03-16T08:10:05Z","abstract_excerpt":"In a recent work of Matteo Mio on compact quantitative equational theories (here compact means that all its consequences are derivable by means of finite proofs) convex algebras on the carrier set [0,1] whose operations are monotone and satisfy certain semicontinuity properties occurred. We fully classify those algebraic structures by giving an explicit construction of all possible convex operations on [0,1] possessing the mentioned properties. Our result thus describes exactly the range of theories to which Mio's theorem applies."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2603.14955","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2603.14955/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-06-09T01:05:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"x7u5Rm2RXy/WnppVU6O790Erl5SWkScI1mh9jD5qvpooJrwuMIgWoQZC16KMt3wTDi+NmjqDMMmbfTBqFXkUDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T17:38:36.148711Z"},"content_sha256":"f16bed37dfb64302fcb74df0439a688c0515522038129765ae51c88b2274a587","schema_version":"1.0","event_id":"sha256:f16bed37dfb64302fcb74df0439a688c0515522038129765ae51c88b2274a587"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WMLALY7IWIGZS3CQNNAH4GVH5F/bundle.json","state_url":"https://pith.science/pith/WMLALY7IWIGZS3CQNNAH4GVH5F/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WMLALY7IWIGZS3CQNNAH4GVH5F/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-27T17:38:36Z","links":{"resolver":"https://pith.science/pith/WMLALY7IWIGZS3CQNNAH4GVH5F","bundle":"https://pith.science/pith/WMLALY7IWIGZS3CQNNAH4GVH5F/bundle.json","state":"https://pith.science/pith/WMLALY7IWIGZS3CQNNAH4GVH5F/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WMLALY7IWIGZS3CQNNAH4GVH5F/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:WMLALY7IWIGZS3CQNNAH4GVH5F","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":"871b4b1ccab728123188e1e23c6d2f61188d8568869671fcc16926ce4d27406f","cross_cats_sorted":["math.LO"],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"cs.LO","submitted_at":"2026-03-16T08:10:05Z","title_canon_sha256":"dd8f9fdd1455f69b03ff1d8fadf945503e5ab4dc7aea5b0c2f8a46229bf73a49"},"schema_version":"1.0","source":{"id":"2603.14955","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2603.14955","created_at":"2026-06-09T01:05:16Z"},{"alias_kind":"arxiv_version","alias_value":"2603.14955v2","created_at":"2026-06-09T01:05:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2603.14955","created_at":"2026-06-09T01:05:16Z"},{"alias_kind":"pith_short_12","alias_value":"WMLALY7IWIGZ","created_at":"2026-06-09T01:05:16Z"},{"alias_kind":"pith_short_16","alias_value":"WMLALY7IWIGZS3CQ","created_at":"2026-06-09T01:05:16Z"},{"alias_kind":"pith_short_8","alias_value":"WMLALY7I","created_at":"2026-06-09T01:05:16Z"}],"graph_snapshots":[{"event_id":"sha256:f16bed37dfb64302fcb74df0439a688c0515522038129765ae51c88b2274a587","target":"graph","created_at":"2026-06-09T01:05:16Z","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/2603.14955/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In a recent work of Matteo Mio on compact quantitative equational theories (here compact means that all its consequences are derivable by means of finite proofs) convex algebras on the carrier set [0,1] whose operations are monotone and satisfy certain semicontinuity properties occurred. We fully classify those algebraic structures by giving an explicit construction of all possible convex operations on [0,1] possessing the mentioned properties. Our result thus describes exactly the range of theories to which Mio's theorem applies.","authors_text":"Ana Sokolova, Harald Woracek","cross_cats":["math.LO"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"cs.LO","submitted_at":"2026-03-16T08:10:05Z","title":"Convex algebras on an interval with semicontinuous monotone operations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2603.14955","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":"sha256:8cb7f7aa98143f94a2fbc23b981350a8236503d5f79a243c1a60754c64e7d4e8","target":"record","created_at":"2026-06-09T01:05:16Z","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":"871b4b1ccab728123188e1e23c6d2f61188d8568869671fcc16926ce4d27406f","cross_cats_sorted":["math.LO"],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"cs.LO","submitted_at":"2026-03-16T08:10:05Z","title_canon_sha256":"dd8f9fdd1455f69b03ff1d8fadf945503e5ab4dc7aea5b0c2f8a46229bf73a49"},"schema_version":"1.0","source":{"id":"2603.14955","kind":"arxiv","version":2}},"canonical_sha256":"b31605e3e8b20d996c506b407e1aa7e9593f1df6c74cd13a087368cb3b507b89","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b31605e3e8b20d996c506b407e1aa7e9593f1df6c74cd13a087368cb3b507b89","first_computed_at":"2026-06-09T01:05:16.069240Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-09T01:05:16.069240Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"peqXpirAhlqIvtcKFudw3rGrThu7ktvR9CEd58qmG2rikFLEYxwSTN/Yh3Vrk2br42ULQwzFVw81kSRsK2fgBQ==","signature_status":"signed_v1","signed_at":"2026-06-09T01:05:16.069763Z","signed_message":"canonical_sha256_bytes"},"source_id":"2603.14955","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8cb7f7aa98143f94a2fbc23b981350a8236503d5f79a243c1a60754c64e7d4e8","sha256:f16bed37dfb64302fcb74df0439a688c0515522038129765ae51c88b2274a587"],"state_sha256":"0eaf32266ed0d078d1d9f8c3d53e66cc2a1fb0f69f6406086fe0273d71021293"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SevoVg+M5s2hH/1UfvFhPZMAfK6DB5PfeMYzMUoOGC9ZOSxKI9+wIENjUXFY45sEfwXpGgHNcohbFduNeek9Ag==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T17:38:36.154440Z","bundle_sha256":"0d9455e8dbf8e7a7c3323ed5570d3dde2dd06b2875bc12500774af97e3d30312"}}