Single-Chain Persistence Theory III: A Tool System for Explaining the Past, Diagnosing the Present, and Conditionally Predicting the Future

Abstract

the series nomenclature goes live (three-tier architecture I/II/III, abolishing the old labels “narrow/broad/1.5”); implements the sole verdict ofVerification Gate No. 1 for the literature (the fid full-value resurrection in the mathematics chapter is re-marked as [Empirical]); v1.1 implements the six-member review panel’s 2 mandatory revisions plus 3 suggestions. — v0.1 implements Archive Items 01/02; v0.2 implements Archive Item 03; v1.0 implements the six-member panel’s final decision (6:0) construction list of 7 blocking items: upstream citation updates in Single-Chain Persistence Theory II (SCPT-II) v2.0 (§1.1/§2.2/§8.2/§9/§23.3), 22 conditional-prediction testing schemes (Appendix T), and the Part III qualification-of-judgment limitation statement. Foundations: Single-Chain Persistence Theory I (SCPT-I) v3.4 (frozen) → Single-Chain Persistence Theory II(SCPT-II) v2.0 (citable) → this manuscript (tool application). — Part 0 Introduction + Part I Theoretical Foundations (Chapters 1–4) + Part II The Tool System (Chapters 5–10) + Part III Domain Applications, all 11 chapters (Chapters 11–21) + Part IV Historical Contributions and Open Problems (Chapters 22–23 + Appendix H). Executed in accordance with the Reconstruction Program v2.1 (DOI: 10.5281/zenodo.21788801); Cross-Criticism Archive Items 01 and 02 have been implemented. The formal submission text is in English.English Ultimate Edition; the master text is the Chinese v1.2 Review Edition. Three-tier series architecture I/II/III, abolishing the old labels 'narrow/broad/1.5'. Executed per Reconstruction Programme v2.1 (DOI: 10.5281/zenodo.21788801).