{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:CH4RSLDPHDM5NCSTQ6YUQO343G","short_pith_number":"pith:CH4RSLDP","schema_version":"1.0","canonical_sha256":"11f9192c6f38d9d68a5387b1483b7cd9bc2c60033ca6350a94337d9a9239a3e5","source":{"kind":"arxiv","id":"1603.03201","version":2},"attestation_state":"computed","paper":{"title":"Finitely Additive, Modular and Probability Functions on Pre-semirings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.AC","authors_text":"Amir Hossein Parvardi, Peyman Nasehpour","submitted_at":"2016-03-10T09:50:17Z","abstract_excerpt":"In this paper, we define finitely additive, probability and modular functions over semiring-like structures. We investigate finitely additive functions with the help of complemented elements of a semiring. We also generalize some classical results in probability theory such as the Law of Total Probability, Bayes' Theorem, the Equality of Parallel Systems, and Poincar\\'{e}'s Inclusion-Exclusion Theorem. While we prove that modular functions over a couple of known semirings are almost constant, we show it is possible to define many different modular functions over some semirings such as bottlene"},"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":"1603.03201","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2016-03-10T09:50:17Z","cross_cats_sorted":["math.RA"],"title_canon_sha256":"ba54a3bf1fcdd473e45cb974c5cb9203e327da672140437bb9177557fcd6bd48","abstract_canon_sha256":"dfaf8c31681dd6c15cd10c649bad2e09e2f44b827c36784266c58a6d0610f9f3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:25:08.114968Z","signature_b64":"R33ZNCGMcnTn6XSOhqHUwGOLjSr0ZgxNmwHDLUwBZtZt8BCWASCVP5aqf6hYaRETXaQoMBaD4DoD6DedAHEdCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"11f9192c6f38d9d68a5387b1483b7cd9bc2c60033ca6350a94337d9a9239a3e5","last_reissued_at":"2026-05-18T00:25:08.114463Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:25:08.114463Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Finitely Additive, Modular and Probability Functions on Pre-semirings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.AC","authors_text":"Amir Hossein Parvardi, Peyman Nasehpour","submitted_at":"2016-03-10T09:50:17Z","abstract_excerpt":"In this paper, we define finitely additive, probability and modular functions over semiring-like structures. We investigate finitely additive functions with the help of complemented elements of a semiring. We also generalize some classical results in probability theory such as the Law of Total Probability, Bayes' Theorem, the Equality of Parallel Systems, and Poincar\\'{e}'s Inclusion-Exclusion Theorem. While we prove that modular functions over a couple of known semirings are almost constant, we show it is possible to define many different modular functions over some semirings such as bottlene"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.03201","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":""},"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":"1603.03201","created_at":"2026-05-18T00:25:08.114544+00:00"},{"alias_kind":"arxiv_version","alias_value":"1603.03201v2","created_at":"2026-05-18T00:25:08.114544+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.03201","created_at":"2026-05-18T00:25:08.114544+00:00"},{"alias_kind":"pith_short_12","alias_value":"CH4RSLDPHDM5","created_at":"2026-05-18T12:30:09.641336+00:00"},{"alias_kind":"pith_short_16","alias_value":"CH4RSLDPHDM5NCST","created_at":"2026-05-18T12:30:09.641336+00:00"},{"alias_kind":"pith_short_8","alias_value":"CH4RSLDP","created_at":"2026-05-18T12:30:09.641336+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/CH4RSLDPHDM5NCSTQ6YUQO343G","json":"https://pith.science/pith/CH4RSLDPHDM5NCSTQ6YUQO343G.json","graph_json":"https://pith.science/api/pith-number/CH4RSLDPHDM5NCSTQ6YUQO343G/graph.json","events_json":"https://pith.science/api/pith-number/CH4RSLDPHDM5NCSTQ6YUQO343G/events.json","paper":"https://pith.science/paper/CH4RSLDP"},"agent_actions":{"view_html":"https://pith.science/pith/CH4RSLDPHDM5NCSTQ6YUQO343G","download_json":"https://pith.science/pith/CH4RSLDPHDM5NCSTQ6YUQO343G.json","view_paper":"https://pith.science/paper/CH4RSLDP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1603.03201&json=true","fetch_graph":"https://pith.science/api/pith-number/CH4RSLDPHDM5NCSTQ6YUQO343G/graph.json","fetch_events":"https://pith.science/api/pith-number/CH4RSLDPHDM5NCSTQ6YUQO343G/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CH4RSLDPHDM5NCSTQ6YUQO343G/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CH4RSLDPHDM5NCSTQ6YUQO343G/action/storage_attestation","attest_author":"https://pith.science/pith/CH4RSLDPHDM5NCSTQ6YUQO343G/action/author_attestation","sign_citation":"https://pith.science/pith/CH4RSLDPHDM5NCSTQ6YUQO343G/action/citation_signature","submit_replication":"https://pith.science/pith/CH4RSLDPHDM5NCSTQ6YUQO343G/action/replication_record"}},"created_at":"2026-05-18T00:25:08.114544+00:00","updated_at":"2026-05-18T00:25:08.114544+00:00"}