Andrew John Paton

Wormholes are frequently represented as tunnels that permit traversal or effective distance reduction through spacetime. Such interpretations persist despite repeated violations of admissibility, including instability under perturbation, causal inconsistency, and unrepayable constraint budgets. This paper introduces a scale-invariant admissibility principle that reframes wormhole-class phenomena as boundary surfaces rather than transport pathways. The principle asserts that any admissible wormhole-class structure must preserve the full causal, energetic, and distance ledger at every scale, while permitting only boundary-level mirroring—visibility, correlation, or informational alignment—without enabling traversal. Apparent shortcuts arise from matched, oppositely oriented constraints that refract description across a boundary; such refraction alters representation without permitting physical motion. This framework is viability-first and non-interfering: it does not modify governing equations, introduce new forces, or propose transport mechanisms. Instead, it functions as an interpretive admissibility filter that distinguishes physically meaningful structures from representational artifacts. By insisting on real, touchable interaction at the observer’s scale while preserving global constraint accounting, the principle explains why wormhole-class phenomena appear observable and structurally real yet remain non-traversable. No new physics is proposed.

Scientific frameworks routinely encounter boundaries that resist direct description, including singularities, horizons, undecidable regimes, and scale limits. In many cases, these boundaries are treated either as placeholders for future ontology or as regions requiring speculative explanation. This paper argues for a different approach: boundary regions may require precise definition without descriptive content. Within the Paton System, Tier-8 represents such a boundary. It is not a domain of entities or mechanisms, but a limiting condition inferred through breakdown behaviour, curvature budgets, and constraint saturation. This paper formalises Tier-8 as boundary knowledge rather than ontological territory, clarifying why definition at this level is necessary for responsible use while description is neither possible nor admissible. The result is a viability-first account of boundary reasoning that preserves continuity, prevents misuse, and establishes a principled stopping rule.

Atomic theory is often presented as a linear progression toward increasingly accurate representations of physical reality. This paper offers an alternative analysis, examining atomic models in terms of model admissibility rather than cumulative truth. Scientific frameworks are assessed according to the empirical and conceptual conditions under which they generate stable, predictive explanations, and the points at which they break down when applied beyond those limits. Tracing the progression from early atomism through classical, quantum, and modern field-based descriptions, the paper argues that model failure typically reflects boundary crossing rather than falsity. Later models do not invalidate earlier ones absolutely, but clarify the constraints that define their domains of applicability. The analysis is methodologically conservative, makes no new physical or ontological claims, and is fully compatible with established scientific theories.

Atomic theory is often presented as a linear progression toward increasingly accurate representations of physical reality. This paper offers an alternative analysis, examining atomic models in terms of model admissibility rather than cumulative truth. Scientific frameworks are assessed according to the empirical and conceptual conditions under which they generate stable, predictive explanations, and the points at which they break down when applied beyond those limits. Tracing the progression from early atomism through classical, quantum, and modern field-based descriptions, the paper argues that model failure typically reflects boundary crossing rather than falsity. Later models do not invalidate earlier ones absolutely, but clarify the constraints that define their domains of applicability. The analysis is methodologically conservative, makes no new physical or ontological claims, and is fully compatible with established scientific theories.

Scientific explanations are typically assessed in terms of truth, correctness, or predictive adequacy. However, many failures in scientific practice arise not from falsehood, but from the continued use of otherwise correct models outside the conditions under which their application remains admissible. This paper distinguishes truth from admissibility, arguing that these concepts play logically distinct roles in scientific reasoning. Truth concerns whether a claim accurately describes a stabilised structure, whereas admissibility concerns whether further explanation, prediction, or application is permitted under prevailing constraints. By clarifying this distinction within a viability-first framework, the paper explains how breakdown can occur without error and highlights the importance of admissibility as a precondition for responsible scientific continuation.

Scientific explanations often break down not because the underlying laws are wrong, but because they are applied outside the conditions where further reasoning remains admissible. This paper introduces the Paton System, a viability-first framework that treats admissibility as a pre-theoretical condition for scientific explanation. Rather than proposing new physical laws or mechanisms, the Paton System formalises a continuation gate that determines whether explanation, prediction, or optimisation may proceed at all. The framework distinguishes correctness, applicability, and viability, arguing that viability is logically prior to dynamical modelling. By making explicit a constraint that is typically applied implicitly across science and engineering, the Paton System clarifies scope limits, breakdown conditions, and stability while remaining fully compatible with existing theories across domains.