The Story of the Quaternion (四元數) — Void (虛) and Substance (實), Filling the Empty. The second of a three-part series, this paper rereads, one layer deeper, the two pyramids the first paper defined — artificial intelligence (人工知能) above and manufacturing (製造) below. It first confirms, with established science alone, that information, matter, and energy are the three categories (範瘇) twentieth-century physics actually arrived at; then examines the living hypotheses above them together with their support and counterexamples; and presents, as speculation (思辨), the author's view that the duals of the five Platonic solids (正多面體) form the ladder of the series — from two·three, through four·five, toward the sixth seat that gathers the five. In particular it shows that the design principle of Hunminjeongeum (訓民正音) embodied in letters, six hundred years earlier, the geometric grammar of dot, line, triangle, square, and circle. This paper closes all those constants and axes in a single equation — the Kotineste Formula. Base form O = E·D·T, extended form O = ℍ·Rθ·e^ (it). It writes output (出力) as the product of energy (labor·sovereignty, the quaternion ℍ), distance (R·θ of the layer, with φ and π within it), and time (phase e^ (it), that is, streaming). It shows that gathering the four constants ℍ·φ·π·i into one line is of the same spirit as Euler's formula gathering several fundamental constants into one line; and that, since each term stands upon established mathematics and physics (Hamilton's quaternions, Hurwitz's theorem, Euler's identity, the Ryu-Takayanagi equation), while the formula that binds them is not a theorem to be proven but a structure laid upon definitions, it is not refuted but preempted with a date. It further builds, as derived formulas, the Labor Sovereignty Index (勞動主權指數, LSI) and the mirror-balance inequality, completing a three-level measurement that runs from one output to one nation and on to the two pyramids, and upon this it joins the generative rule of Hangul as a fourth formula. It reads the intellectual coordinates on which these four formulas stand, overlaid on the four branches of the quaternion (1·i·j·k): Autor who measured labor (the real axis), Acemoglu who divided automation and institutions (i), Gershenfeld who joined bits and atoms (j), and the author who joins in the field (k). Substituting the three scholars' prescriptions into the four formulas, it shows by calculation that each stops at a partial solution (部分解) and that only where all four layers are stripped away do the four formulas hold at once — it shows that all three coordinates need the lower pyramid. The axis of the golden ratio and pi and the axis of the quaternion are of different layers, and are strictly separated. If the first paper's name was Beauty (美) and Love (愛), a beautiful love, this paper's name is Void (虛) and Substance (實), filling the empty. The conclusion is one line — the democratization of materials (素材). The industrial and protocol design clauses in the body are a defensive publication; from the date of disclosure they become prior art, so that no one can enclose them by patent. The second of the series, dedicated to Plato, who read the world in the five Platonic solids. Author: Chang, Hyung Kee (denix, 장형기) · KOTINESTEORCID: 0009-0003-0921-8014License: CC BY 4. 0 (open and free to use) Series DOI —Paper 1 «AI and MI»: Korean 10. 5281/zenodo. 21131400 · English 10. 5281/zenodo. 21133315 · Portuguese 10. 5281/zenodo. 21133329Paper 2 «AGI and MGI»: Korean 10. 5281/zenodo. 21218392 · English 10. 5281/zenodo. 21218409 · Portuguese 10. 5281/zenodo. 21218413
hyung kee chang (Mon,) studied this question.