CDIP v3.1 META PHYSICS Addendum Trinary Domain Observation with Bottom Extension and Lexicographic Divergence in the Verified-Image Quotient

Read full text
Authors: Jian Lin
Cited by: 0

Abstract

We present a specification-level refinement of the Trinary-domain wrapper semantics (Real/Couple/Imag) in the CDIP v3.x stack, formulated as a monotone observation over an evidence preorder. A bottom element ⊥ totalizes the domain-label map, capturing the “undefined/insufficient evidence” gap (INAD shadow) without introducing new control surfaces. We then construct a lexicographic divergence object that combines (i) domain comparability (including absorption by ⊥) and (ii) a black-box verified-image core distance dcore , yielding an earliest-failure-aligned comparison principle: domain legitimacy precedes any metric refinement. We further formalize (a) non-contradictory refinement discipline for evidence, (b) a precise comparability domain, (c) minimal assumptions on dcore , (d) epoch- wise monotonicity under evidence evolution, and (e) a naturality condition for Couple as a 1-cell decoration in enriched (holonomy) settings. This addendum introduces no parameter writes, no new thresholds, and no executable state machine.

Fields of Study & Subjects

Logic programming and type systems Diverse Interdisciplinary Research Studies Formal Methods in Verification

Publication details

Journal / source
Zenodo (CERN European Organization for Nuclear Research)
Publication date
7 February 2026
Document type
Preprint