Information Topology: Saturation, an Information Field, and Topological Patterns (Papers I–V, research notes and code)

A series of exploratory theoretical papers proposing that spacetime behaves as a medium of finite-capacity information units. Paper I constructs an auxiliary-field saturation mechanism whose on-shell term is bounded. Paper II confronts a phenomenological Yukawa correction with the S2 precession and finds consistency with GR and with published bounds. Paper III shows that this term equals ln 2 minus the binary entropy, introduces a dynamical information field with an entropy-bounded potential and density-induced ordering, and derives domain-wall solutions. Paper IV studies point-like patterns: gauged hedgehogs with a size-independent mass, their metastability and critical melting in finite ordered regions (with a spinodal scaling law), and a confining hidden sector whose glueballs are a dark-matter candidate. Paper V derives the saturation scale and shape and a self-tuned ordering threshold from Lloyd's computational bounds and links the hidden-sector dark matter to the tensor-to-scalar ratio. Research notes (Part I exploratory, Part II speculative) record further tests on dark energy, dark matter and large-scale structure, including those that failed. A perspective essay (Turkish original and English translation) states the motivating vision with every claim labelled as derived, constrained or speculative. All tables can be reproduced with the included Python code. AI assistance (Claude, Anthropic) was used for derivations, computation and literature search; see README. No professional physicist has yet reviewed this work.