The Infinite Structure of Goodness: Cross-Domain Derivations from Ethical Intuition to Physical Limits — With a Comparative Analysis of Five AI Cognitive Modes

This paper derives 23 cascading propositions from three axioms: Goodness has temporal attributes; Goodness has spatial attributes; and the Infinite-Quantity Law. It constructs a field-theoretic mathematical formalism, establishes a physical upper limit at the photon-sphere boundary (G_max ≈ 1.54 × 10¹¹³ J/m³), and develops a 0–100 civilisational Goodness-Value index with historical anchor points. A comparative analysis of five LLM derivation paths (ChatGPT, Gemini, Grok, Nemotron-3-Nano, Claude) demonstrates that their plurality constitutes the first empirical evidence for the spatial attribute of Goodness. The paper concludes at the boundary of language with statements on AI alignment, civilisational risk, and the individual.