A Falsifiable Mathematical Framework for Architectural Design Hypotheses: A Cygnus-Derived Angular Alphabet Applied to the Giza Complex

We present a falsifiable mathematical framework for testing design hypotheses in ancient architecture, applied here as a case study to the Giza necropolis. A fixed angular alphabet of nine operators 16, 28, 34, 46, 62, 64, 66, 96, 256—derived from the publicly catalogued IAU and SIMBAD properties of the constellation Cygnus (area ACyg = 804 deg², 28 Delporte boundary segments, area-rank r = 16, declination boundaries, and principal-star coordinates in equatorial and ecliptic systems) —generates simultaneous numerical closures for the external geometry of the three principal pyramids of Giza, the height of the Sphinx, the length of the Egyptian royal cubit, and a closed coupling between internal and external dimensions of Khufu's Great Pyramid. The face slope angle of Khufu satisfies θ = √ (96·28) = 51. 846° against the published value of 51. 844° (error 0. 004%). The base length satisfies L = √ (804·66) = 230. 36 m against 230. 34 m (error 0. 007%). Khafre's tan θ = 4/3 = 64/ (64−16) matches exactly; Menkaure's tan θ = 5/4 = (46+34) /64 matches within 0. 2%. The dimensionless numerical closure ACyg/ (96·16) = πCyg/6 = 0. 5234 matches the historical Egyptian royal cubit (0. 5236 m) within 0. 03%, where πCyg ≡ 804/256 = 3. 140625. The internal–external ratio hK/CGG = 146. 60/46. 68 ≈ 3. 1405 matches πCyg = 3. 140625 within 0. 003%; equivalently, the Grand Gallery length CGG ≈ 46. 68 m multiplied by πCyg returns the published external height of Khufu within the same tolerance. A principal 16-cubit dimension of the Subterranean Chamber, multiplied by πCyg, yields 50. 25, numerically equal to Newcomb's 1898 value for the precessional rate. The Sphinx height, multiplied by πCyg, yields a value within 1. 6% of operator 62. A falsification test applied to seven Old Kingdom pyramids at Saqqara, Dahshur, and Meidum reveals that none satisfies the conjunction of these six criteria; within the tested corpus, only the Giza configuration closes simultaneously. We register these relationships as empirical observations within a stated tolerance regime (ε ≤ 0. 6% for the principal pyramid and internal predictions; the Sphinx module is treated separately at ε ≤ 1. 6%) and discuss explicitly the post-hoc considerations. The framework presented here is methodologically general: any monument with reliably catalogued archaeometric dimensions can be tested against an alphabet derived from externally fixed astronomical or geometric parameters, with falsification following the same protocol applied here. Lucas Giovani Ribeiro — Independent Researcher, Uruana de Minas, MG, Brazil — ORCID: 0009-0002-1417-0062 — Email: thecygnuscode@gmail. com — Companion monograph: "O Código Oculto de Cygnus" (Clube de Autores, 2026)