{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:W5AMJIEHPCB56WPBOVTZWTDNFN","short_pith_number":"pith:W5AMJIEH","schema_version":"1.0","canonical_sha256":"b740c4a0877883df59e175679b4c6d2b6f4a05993280b0eefa700d54cc4614fb","source":{"kind":"arxiv","id":"1804.01682","version":1},"attestation_state":"computed","paper":{"title":"On the Axiomatizability of Quantitative Algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.LO","authors_text":"Gordon Plotkin, Prakash Panangaden, Radu Mardare","submitted_at":"2018-04-05T06:39:33Z","abstract_excerpt":"Quantitative algebras (QAs) are algebras over metric spaces defined by quantitative equational theories as introduced by the same authors in a related paper presented at LICS 2016. These algebras provide the mathematical foundation for metric semantics of probabilistic, stochastic and other quantitative systems. This paper considers the issue of axiomatizability of QAs. We investigate the entire spectrum of types of quantitative equations that can be used to axiomatize theories: (i) simple quantitative equations; (ii) Horn clauses with no more than $c$ equations between variables as hypotheses"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1804.01682","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2018-04-05T06:39:33Z","cross_cats_sorted":[],"title_canon_sha256":"749b516844123eff5d9eeda3936b8d19a099cc9d905e440a9f39ff469bc4a965","abstract_canon_sha256":"29f93e7110ecce3de9b274ab2747553627e4714fcdea88dc16fc18c271cac7ad"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:19:10.385190Z","signature_b64":"hCDgho2yBTnVmqZanJzw96U4nxLpg3w+d4e9zxvQVVv8BpSXIT4BIUxm/qF4bftFnU6NROwwTerPK9xNpSsvCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b740c4a0877883df59e175679b4c6d2b6f4a05993280b0eefa700d54cc4614fb","last_reissued_at":"2026-05-18T00:19:10.384684Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:19:10.384684Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the Axiomatizability of Quantitative Algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.LO","authors_text":"Gordon Plotkin, Prakash Panangaden, Radu Mardare","submitted_at":"2018-04-05T06:39:33Z","abstract_excerpt":"Quantitative algebras (QAs) are algebras over metric spaces defined by quantitative equational theories as introduced by the same authors in a related paper presented at LICS 2016. These algebras provide the mathematical foundation for metric semantics of probabilistic, stochastic and other quantitative systems. This paper considers the issue of axiomatizability of QAs. We investigate the entire spectrum of types of quantitative equations that can be used to axiomatize theories: (i) simple quantitative equations; (ii) Horn clauses with no more than $c$ equations between variables as hypotheses"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.01682","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1804.01682","created_at":"2026-05-18T00:19:10.384769+00:00"},{"alias_kind":"arxiv_version","alias_value":"1804.01682v1","created_at":"2026-05-18T00:19:10.384769+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.01682","created_at":"2026-05-18T00:19:10.384769+00:00"},{"alias_kind":"pith_short_12","alias_value":"W5AMJIEHPCB5","created_at":"2026-05-18T12:32:59.047623+00:00"},{"alias_kind":"pith_short_16","alias_value":"W5AMJIEHPCB56WPB","created_at":"2026-05-18T12:32:59.047623+00:00"},{"alias_kind":"pith_short_8","alias_value":"W5AMJIEH","created_at":"2026-05-18T12:32:59.047623+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/W5AMJIEHPCB56WPBOVTZWTDNFN","json":"https://pith.science/pith/W5AMJIEHPCB56WPBOVTZWTDNFN.json","graph_json":"https://pith.science/api/pith-number/W5AMJIEHPCB56WPBOVTZWTDNFN/graph.json","events_json":"https://pith.science/api/pith-number/W5AMJIEHPCB56WPBOVTZWTDNFN/events.json","paper":"https://pith.science/paper/W5AMJIEH"},"agent_actions":{"view_html":"https://pith.science/pith/W5AMJIEHPCB56WPBOVTZWTDNFN","download_json":"https://pith.science/pith/W5AMJIEHPCB56WPBOVTZWTDNFN.json","view_paper":"https://pith.science/paper/W5AMJIEH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1804.01682&json=true","fetch_graph":"https://pith.science/api/pith-number/W5AMJIEHPCB56WPBOVTZWTDNFN/graph.json","fetch_events":"https://pith.science/api/pith-number/W5AMJIEHPCB56WPBOVTZWTDNFN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/W5AMJIEHPCB56WPBOVTZWTDNFN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/W5AMJIEHPCB56WPBOVTZWTDNFN/action/storage_attestation","attest_author":"https://pith.science/pith/W5AMJIEHPCB56WPBOVTZWTDNFN/action/author_attestation","sign_citation":"https://pith.science/pith/W5AMJIEHPCB56WPBOVTZWTDNFN/action/citation_signature","submit_replication":"https://pith.science/pith/W5AMJIEHPCB56WPBOVTZWTDNFN/action/replication_record"}},"created_at":"2026-05-18T00:19:10.384769+00:00","updated_at":"2026-05-18T00:19:10.384769+00:00"}