{"paper":{"title":"Optional Intervals Event and Two n-ary Finitary Operations: An Algebraic Framework for Unifying Parallel-Serial Execution and Axiomatizing Simultaneity from an Epistemological Perspective","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.GM","authors_text":"Bo.Yin, Lei.Yu, Yanlei.Gong, Yue.Cao, Zhongyuan.Li","submitted_at":"2025-04-13T08:03:20Z","abstract_excerpt":"This paper proposes an algebraic framework for analyzing event execution intervals and sequences, introducing \"Optional Intervals Event (OIE)\" as a 4-tuple abstraction (C, F, I, A) that serves as a pre-execution planning tool for real-world events. The OIE establishes a mapping to real-world events and stores all feasible execution intervals together with dependency relationships among sub-events. Based on this abstraction, we define two n-ary finitary operations: (i) \"Complete Sequence Addition\", which models concurrent events with a certain degree of equal opportunity within a shared time do"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.09471","kind":"arxiv","version":7},"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/2504.09471/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"}