Finite-Bit Geometric Reasoning: Axioms and Information-Conserving Proofs
Year: 2025
Type: article
Abstract: We present a geometric framework where classical theorems in Euclidean geometryemerge from finite,minimal, conserved data units (information bits), suchas lengths, angles and their ratios. These bits and the theorems’ proofs obey aconservation principle. Our axioms state that all geometric entities are defined byfinite bit sets (e.g., side ratios, angle sines) and adjoining new bits generates equivalentbits under algebraic relations. Theorems arise as equivalence relations betweenexisting, adjoining, and equivalent bits. This framework unifies proofs viainformation invariance where proofs are reducing to combinatorial bit-balanceverifications.
Author: Amiri, Manouchehr
Language: English
Topic: Mathematics and Applications
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W6930930377
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