This preprint is version v1.4.0 of Observation–Feedback Closure I. It presents a conservative topological and structural extension of the v1.3.0 OF causal-hypergraph reconstruction with dual-order structure, rather than a replacement of the earlier kinematical and reconstruction architecture. Building on the stratified microscopic–mesoscopic–macroscopic ontology, source-generated propagation patterns, sheaf-compatible identity reconstruction, and obstruction-weighted effective action established in v1.3.0, the following contributions are first publicly disclosed in this v1.4.0 preprint as constructions and results formulated within the OF Closure framework: 1. Conditional localized non-Hausdorff reconstruction: under explicit role-distinction, persistent saturated-neighborhood overlap, and ordered-refinement assumptions, a conditional theorem establishes localized non-Hausdorff sectors in the mesoscopic identity reconstruction space. This result concerns reconstruction topology and does not assert that macroscopic spacetime is globally non-Hausdorff. 2. Two-orbit residual-map classification: within the adopted non-empty two-arrow residual-map model, modulo observer/feedbacker role reversal, the minimal irreducible residual maps are classified into a single-arrow process-type orbit (𝔭-type) and a bidirectional identity-dual orbit (𝔬-type). 3. Process–identity complementarity: qualitative process–identity complementarity is explicitly incorporated into the First Principle of Physical Admissibility. The persistent-overlap non-Hausdorff construction provides one conditional topological realization of this principle rather than a quantitative uncertainty theorem or a derivation of quantum measurement relations. 4. Leading-even OF response hierarchy: this version formalizes a leading-even response hierarchy and a weak-deformation dominance lemma. The proposed connection between response order and macroscopic physical externalization remains conjectural. Under additional externalization assumptions, the 𝔭-type and 𝔬-type sectors provide conditional structural precursors for gravitational-type and electromagnetic-type correspondences, respectively. The residual-map classification itself does not derive gravitational or electromagnetic dynamics, field equations, interaction laws, coupling constants, or physical signs. The obstruction-weighted reconstruction architecture of v1.3.0 is retained. In the clean binary, zero-obstruction, unit-weight regime, the framework continues to recover the explicitly identified v1.2.0 event-counting kinematical constructions. These statements record the established retention and limiting-recovery relations; they do not assert an unrestricted equivalence among all versions. The framework constructs relational and algebraic representations of physically admissible objects and processes, together with kinematical and continuous-parameter interfaces intended for possible future dynamical formulations; it does not itself supply a dynamics. This work does not challenge, invalidate, or replace established physical theories in their empirical domains, nor does it claim empirical superiority over them. No field equations, quantum dynamics, gauge dynamics, gravitational dynamics, interaction dynamics, quantitative cosmological models, or new empirical predictions are derived. Dynamical, categorical, generator-level, and quantitative physical extensions are deferred to subsequent work in the OF Closure series.
Song Ci (Mon,) studied this question.