The Tier-0 Framework: A Law-Level Closure and Selection Principle for Physics

This paper presents the Tier-0 framework: a law-level closure and selection principle for physics. It does not introduce a new force, modify existing equations of motion, or propose a phenomenological model. Instead, it addresses a more basic structural question: what makes a candidate structure a physical law rather than a contingent representation, redundancy, or formal artifact? The central claim is that lawful structures are exactly those stable under three canonical operations: presentation collapse, admissibility projection, and canonical completion. On this basis, the paper defines physical law through a fixed-point closure condition formulated at the level of formal structure, prior to any carrier-specific realization. Two main results are developed. First, the operator triple underlying the closure condition is shown to be inevitable: under minimal structural requirements, any viable lawhood diagnostic reduces to the same three-stage form (Operator Inevitability Theorem, conditional on the Universal Canonicality Axiom AX-U). Second, the resulting fixed point is shown to be unique under a finite structural package using a Noetherian descent argument rather than a spectral-gap assumption (Unconditional Uniqueness Theorem). The paper then develops several consequences of the Tier-0 framework. These include the record/flow distinction, the null classification of record-silent propagation, the definition of closure horizons, the selection of the Lovelock gravitational law-form, reduction to Einstein-Hilbert gravity in four dimensions, and the Lovelock-Iyer-Wald route by which the gravitational coupling G is fixed from internal consistency. It also analyzes the admissibility kernel, the suppression of the catastrophic cosmological constant contribution through a vanishing zero-mode condition, and the modular fixed-point mechanism (“Selector 9”) that selects the ultraviolet stiffness invariant. The conditional axiom set is compressed to a terminal two-principle backbone: AX-UAC-CORE(min) and AX-H9-COUNT(min). Under the now formally closed Option (b) operational record definition, COUNT(min) becomes theorem-level, reducing the empirical axiom floor to zero. In that form, the programme backbone reduces to Tier-0 together with AX-UAC-CORE(min) alone. Whether CORE is itself irreducible or derivable from realization-germ rigidity remains the main open foundational question, reducible to a concrete Tier-1 admissibility-transfer verification. A central theme throughout is the separation between law-level structure and spectral realization. The broader programme is organized as a four-layer generative architecture: Layer 1 (lawhood generator), Layer 2 (admissible law spaces), Layer 3 (canonical selection), and Layer 4 (interface realization), together with a Global Consistency Closure Protocol. For exposition, Layers 1–3 are grouped as Tier-0 (law-level, carrier-independent), while Layer 4 is Tier-1 (spectral projection onto a specific carrier geometry). This paper covers Layers 1–3. The companion Tier-1 projection, developed in the Dirac-Lambda paper series, instantiates the law-level architecture on the adopted S3 / Model-B spectral carrier and derives the fine-structure constant, the weak mixing angle, and, conditionally, the cosmological constant on that carrier. This version includes the four-layer programme architecture, operator inevitability, unconditional uniqueness, the compressed axiom backbone, the closed Option (b) reduction, the Tier-0 derivation route for the gravitational coupling, the current status of AX-UAC-CORE(min) derivability, and the full Tier-0 / Tier-1 interface, while keeping the focus strictly on law-level structure. Related work: A companion paper, Lawhood Necessity, proves that the Tier-0 architecture is not optional: any viable notion of physical law must realize the same quotient–filter–closure structure (or an equivalent form). This upgrades the framework from a candidate construction to a structural inevitability theorem for lawhood. The Necessity of Lawhood Primitives: Why Any Non-Arbitrary Notion of Physical Law Requires Four Structural Conditions DOI: https://doi.org/10.5281/zenodo.19390155