Bitopological Spaces from Directed Graphs: Extending the Nada Construction to Capture Temporal Irreversibility — Reproducibility and Formalization Bundle

v1. 0. 2 — Editorial revision of the manuscript. > Note on files. This version archives only the revised manuscript> (`directedₙadabitopology. pdf` / `directedₙadabitopology. tex`). The> complete research compendium — Lean 4 formalization against Mathlib, > R package implementing the construction, empirical dataset> (`GDPC1ₛnapshot. csv`), and Rmarkdown reproducibility notebook — is> byte-identical to v1. 0. 1 and is archived there: > `10. 5281/zenodo. {DOIV1. 0. 1}` (https: //doi. org/10. 5281/zenodo. {DOIV1. 0. 1}). > Readers interested in reproducing the empirical or formal results> should consult v1. 0. 1. This release contains an exposition refinement of the manuscript. Nomathematical, algorithmic, formalization, or empirical content has beenmodified: all theorems and proofs, the complexity analyses, the Lean 4formalization against Mathlib, the R implementation of the construction, the dataset, and the reproducibility notebook are byte-identical tov1. 0. 1. Changes are confined to the manuscript source and its compiled PDF (`paper/directedₙadabitopology. tex`, `paper/directedₙadabitopology. pdf`): - The introduction has been rebalanced to open directly with the non-trivial contributions of the paper — the identification of the bitopological structure (V, ^+, ^-) as the carrier of temporal asymmetry, the pairwise invariants that make this asymmetry visible, and the tractable irreversibility indices that quantify it. The methodological reflection on the structural universality of the generated-topology functor, previously distributed between the introduction and the discussion, is now consolidated in §6. 2 (Formalist compression and constructive content), where it belongs by the natural sequence of argument. - A grammatical remnant from an earlier revision, in §6. 2. 1 (Relation to prior work), has been corrected. - Minor wording adjustments in the conclusion improve the rhetorical balance of the closing paragraph. Readers who have already consulted v1. 0. 1 on technical grounds need takeno action: every mathematical claim, proof, algorithm, and empiricalfinding is unchanged between the two versions.