Decidability, observational bridges and finite-information quantum gravity.

Λεπτομέρειες βιβλιογραφικής εγγραφής
Τίτλος:	Decidability, observational bridges and finite-information quantum gravity.
Συγγραφείς:	Budiyanto, Agus Hasan¹ (AUTHOR) agus.budiyanto@umsv.edu
Πηγή:	International Journal of Modern Physics D: Gravitation, Astrophysics & Cosmology. Sep2026, p1. 26p.
Θεματικοί όροι:	Decidability (Mathematical logic), Quantum gravity, Incompleteness theorems, Entropy (Information theory), *Scientific observation
Περίληψη:	Recent arguments in quantum gravity infer a need for a nonalgorithmic metatheory from Gödel incompleteness, while finite-information replies infer decidability from entropy bounds. We separate axiomatic completeness, dynamical reachability, observational interpretation and physical tractability. Our main theorem-level results identify exact hyperplane reachability with a restricted unit-circle Skolem problem, prove exact decidability of finite-time expectation comparisons at effectively algebraic times by Lindemann–Weierstrass, and formulate observational bridge criteria at the correct reduction strength. In particular, syntactic independence alone entails neither empirical inertness nor empirical disagreement; a computable reduction from any undecidable set to observational truth transfers undecidability, while a reduction from true arithmetic would make observational truth nonarithmetical. As supporting dynamical results, we give a self-contained unitary specialization of established orbit-closure methods: strict approximate semialgebraic reachability is uniformly decidable for effectively algebraic finite-dimensional data, and reachable open targets have a positive asymptotic visit density. Finite dimension alone neither makes the state space finite nor ensures decidability for arbitrary computable coefficients. Entropy and state-packing results delimit what finite information can support. [ABSTRACT FROM AUTHOR]
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