Zero-State Axioms: Minimal Boundary Structure, Structural Consequences, and Semantic Models

Reader orientation. Readers new to the programme may wish to begin with ZSA Programme Reader Orientation, which explains the problem space, need space, and two-paper architecture before entering the technical manuscripts. The orientation note is not a third theory paper; it is an entry guide to the role of the ZSA manuscript and the relative IMB bridge paper.

The ZSA manuscript develops a bookkeeping framework whose axiomatics is first-order. It concerns boundary-governed admissibility in systems where extension, coherence, valuation, and partial measurement interact.

The main ZSA manuscript studies semantic universes equipped with a configuration preorder, a coherence relation, a valuation into a partially ordered value domain, and a partial measurement operator. Under explicit semantic, closure, reflection, and meet-selection hypotheses, it proves an Infinity–Measurement Boundary Theorem. The boundary-extraction argument uses the Measurement Condition together with the local principles PR, DL, and BM; the Infinity Condition marks the intended unbounded-extension regime in which the boundary is interpreted. The theorem yields a selected least boundary candidate, unique up to preorder-equivalence, such that every measured configuration extends the selected boundary, and measurement that stabilises along a coherent increasing chain at or above that boundary is certified at the limit whenever a limit exists.

Motivated by this, the manuscript introduces the Zero-State Axioms, or ZSA, in a first-order language naming a distinguished boundary constant. It shows that a boundary fragment of ZSA is forced in the canonical expansion extracted from any universe satisfying the IMB hypotheses. It also shows that one axiom is derivable from another over the fixed semantic background, while the remaining core axioms are independent via explicit countermodels. Reference-chain, valuation-extended, measurement-stable, and product-style model constructions demonstrate consistency and flexibility.

The manuscript also clarifies the distinction between boundary-candidatehood, selected-boundaryhood, and reassignment. The boundary-candidate predicate is downward persistent: it defines a candidate class, not a sharp predecessor-excluding predicate. The IMB construction selects the least member of that candidate class, with meet selection supplied by BM. The invariance condition AR0 is used only as fixed-regime pinning for admissible reassignment of the boundary constant; it does not perform boundary extraction and does not turn the candidate predicate into a predecessor-exclusion principle.

This record also includes the technical follow-up Relative IMB and Structural Decoupling. That paper develops the relative form of the IMB mechanism: where a sub-layer carries the required internal semantic, closure, reflection, and meet-selection packet, IMB can be re-applied inside that sub-layer, yielding an internal selected boundary unique up to the sub-layer's preorder-equivalence. It also introduces structural decoupling as a witness-level failure of ambient measurement certification for internal measured-limit behaviour.

Structural decoupling is tracked through two principal sufficient witness mechanisms: limit/stability discrepancy and cross-value incompatibility through the bridge predicate. The bridge proves that either kind of witness is sufficient for decoupling, without claiming an exhaustive classification. The paper's worked model exercises the limit/stability-discrepancy branch; the cross-value-incompatibility branch is defined and proved as a sufficient criterion, but is not exercised by a separate worked model. Relative IMB is presented as re-application of the base clause-set to the internal sub-layer packet, not as analogy.

The follow-up functions as the bridge from global ZSA boundary structure to relative boundary formation and structural decoupling. The record should therefore be read as a two-part technical package, with the reader orientation serving as an entry guide. The ZSA manuscript establishes the base admissibility-boundary extraction and axiomatics; the relative IMB follow-up establishes relative reapplication and structural decoupling under explicit sub-layer readiness conditions.