ECF II: From Logical Ontology to the Mathematical Cosmos

Version: Version 4.0 (new version; the concept DOI chain is preserved)Version description:This updated version completes the symbol unification of the weak connectives (\\(\\land_w\\), \\(\\lor_w\\)) throughout, and adds the following refinements: the self-loop argument in the discrete metric construction is corrected to detours through cycles; the alternative terminus cases are explicitly retained as alternative possible paths under the possibility-inclusion principle; Theorem 3.1's axiom verification is located in the metalanguage with the internal exponential postponed to the categorical layer; the category \\(\\mathcal{L}\\) is stated as thin with morphisms as the unique implication relation; the coherence of the Cartesian closed structure is made explicit; the chain-weight conventions (\\(\\Phi(0)=1\\)) and the \\(\\lambda\\)-dependence of \\(\\Phi\\) near the boundaries are stated; the discrete limit is clarified as eventual constancy; and the tier table distinguishes the weak (B-tier) from the standard (C-tier) connectives.