Foundations of General Informational Theory (TGI): Relational Access, Reversible Memory, and Conditional Emergence of Geometry

Foundations of General Informational Theory (TGI) v1.1 This foundational preprint presents the current formulation of Teoría General Informacional (TGI), a relational framework organized around the sequence distinction → access → stored history → backreaction. The framework remains under active development. This manuscript is intended to freeze and publicly document the present foundational structure rather than to claim a completed theory of nature or a finished Theory of Everything. The work isolates a minimal relational-access core and distinguishes its exact algebraic consequences from conditional constructions, no-go results, and open problems. Particular emphasis is placed on making the assumptions and epistemic status of each result explicit. The principal purpose of this deposit is to establish a public, versioned scholarly record of the formulation developed to date, including: the exact identities of the relational-access core; sharpened algebraic and structural no-go results; the explicit separation between core statements, completion-dependent results, conditional sectors, and open problems; reversible dynamical memory and operational non-invertibility; conditional constructions of operational time and probe-defined locality; the emergence of transport, holonomy, and curvature from relational access structures; a conditional route to a minimal saturated four-dimensional active geometric phase; an infrared complex/Schrödinger-form sector; and a conditional derivation of Born weights for an explicitly defined ideal first-hit measurement class. The manuscript deliberately does not claim that these results establish TGI as a complete fundamental theory. Several central problems remain open, including the derivation of a smooth continuum limit from the underlying relational dynamics, uniqueness of admissible completions, complete gravitational closure, unrestricted quantum composition and entanglement, Bell/Tsirelson structure, post-measurement dynamics, and the numerical derivation of the action scale identified experimentally with ℏ, Newton’s constant (G_N), and the cosmological constant (\Lambda). Standard-Model dynamics, particle masses and couplings, and any new blind, experimentally confirmed TGI-specific prediction also remain outside the established claims of this version. This version supersedes earlier internal drafts. Subsequent developments are intended to be deposited as new versions within the same research lineage, preserving a transparent record of revisions, strengthened results, discarded approaches, and remaining open questions.