Logical Lock, Sparse Effective Information, and the Unified Evidence Functional: The Universal Mathematics of Prediction Before Certainty
Authors: Bsmpx
Type: Book
Published: 2026-08-03
Keywords: Logical lock, sparse effective information, unified evidence functional, three-valued reasoning, natural transformation, Möbius inversion, chaos forecasting, system identification, Laplace's demon, distribution of primes, integer-multiplication complexity, three-dimensional Kakeya conjecture, Lorenz–63 attractor, Lorenz–96 spatiotemporal chaos, Rössler chaotic system, forced Burgers equation, chaotic double pendulum, three-body problem, continuous weak-measurement quantum trajectories, Robertson–Schrödinger uncertainty relation, pi, Riemann explicit formula, Willamowski–Rössler chemical chaos, CRISPR repair-outcome prediction

<p class="MsoBodyText"><span>This paper introduces logical lock, sparse effective information, and the unified evidence functional, establishing a mathematical framework for jointly handling candidate elimination, local high-demand information, cross-protocol evidence composition, and component intervention under finite evidence before outcomes are revealed. The framework gives discrete decisions, probabilistic forecasts, and continuous-state forecasts a common provable, computable, and reproducible interface. Using prespecified primary and stress-test endpoints with a two-track retention design, the study evaluates generated or held-out samples from finite worlds, primes and Riemann zeros, integer multiplication, the three-dimensional Kakeya theorem, pi, continuous weak-measurement quantum trajectories, quantum uncertainty boundaries, CRISPR repair outcomes, and multiple chaotic systems through a unified three-valued lock, target-local certificates, Möbius interaction decomposition, structured system identification, and endpoint-level intersection-union tests against every comparator. The full model matches the full-information oracle in finite worlds. It achieves exact locking in target-local prime queries and in masked-conclusion reconstruction of the Kakeya theorem, while the meta-identifiability analysis of pi returns calibrated abstention when evidence is insufficient. In the Riemann experiment, the held-out prime-error curve improves strictly as the number of input zeros increases, and the model attains significant advantages in chaotic dynamics, chemical-rate extrapolation, drifting quantum trajectories, and DNA-editing repair outcomes. The integer-multiplication complexity and Robertson–Schrödinger experiments further show that the interface remains rigorously undecided for unresolved global existence questions and states near physical boundaries, preventing finite samples from producing spurious certainty. These results establish that computable evidence structures can characterize pre-outcome certainty across task formulations and data types, providing a common foundation for provable prediction under finite information in mathematics, physics, chemistry, biology, and dynamical systems.</span></p>
<p>English first edition.</p>
<p>ISBN: 978-952-7696-88-0</p>
<p>The associated reproducibility dataset is archived under DOI 10.5281/zenodo.21756748. The release-level MANIFEST.json and SHA256SUMS.txt cryptographically bind the book PDF and the reproducibility-package ZIP.</p>
<p>Bsmpx is the publishing name of Contributor.</p>