Tension–Induced Geometry (TIG–0): Project Definitions and Unified Notation

Tension–Induced Geometry (TIG–0) is the foundational reference document for the TIG framework, a classical field theory in which spacetime structure, inertia, gravitation, and matter emerge from the dynamics of a single finite-tension vacuum field governed by a Born–Infeld–type action. This document fixes the core postulates, definitions, notation, dimensional conventions, and canonical equations used consistently throughout the TIG series (TIG–1 through TIG–5). It is intended to function as the axiomatic and notational backbone of the programme, rather than as a standalone phenomenological analysis. TIG–0 consolidates material that would otherwise be repeated across multiple papers and establishes the logical dependencies between the linear, soliton, anisotropic, and strong-field sectors of the theory. All subsequent TIG papers explicitly rely on the definitions and structures formalised here.