Mathine — Evidence In, Trust Out

KEPLER: A Method for Planning Solution Paths in Complex Problems

Mathine: Portable Resolution Path Machine
Link: https://doi.org/10.5281/zenodo.18896164

Complex problems often resist resolution not only because they are intrinsically difficult, but because the path from a promising local insight to a portable, defensible conclusion is usually left implicit. A claim may work inside the field where it was first generated, yet fail when it crosses into a new regime of evidence, language, scale, cost, institutional constraint, or operational context.

This paper introduces KEPLER — Knowledge Engine for Portable, Layered, Evidence-based Resolution — as a method for planning solution paths by treating solutions as governed journeys rather than isolated terminal answers. The shift is important: the problem is not only whether an answer exists, but whether the answer can travel without silently changing meaning or losing legitimacy.

Each part of the acronym is operational. Knowledge means structured understanding that can be examined and transferred. Engine means an explicit procedural discipline, not an informal metaphor. Portable means the solution must survive movement across contexts. Layered means that this movement happens across fields, regimes, scales, and boundary conditions. Evidence-based means promotion must remain grounded in auditable support. And Resolution means justified arrival under declared constraints, not the mere appearance of an answer.

KEPLER models a solution path as a structured traversal across fields, layers, and border crossings. That traversal must carry explicit invariants, contracts, admissible transformations, receipts, and fail-closed promotion gates. In other words, the method governs not just the endpoint, but the crossings that determine whether intermediate truth can remain stable as it moves.

The aim is not to replace proof, experiment, or domain expertise. It is to add a disciplined layer for governing how partial truths travel. By making the journey explicit, KEPLER is designed to reduce drift, overclaim, and false portability while improving auditability, replayability, and the cumulative value of intermediate progress.

The method is especially suited to high-complexity settings in science, engineering, AI, architecture, and policy, where legal, ethical, or safety constraints require conservative promotion and explicit accountability. In that sense, KEPLER is less a search for dramatic final answers and more a framework for building defensible paths to arrival.