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 A_Cyg = 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 A_Cyg/(96·16) = π_Cyg/6 = 0.5234 matches the historical Egyptian royal cubit (0.5236 m) within 0.03%, where π_Cyg ≡ 804/256 = 3.140625. The internal–external ratio h_K/C_GG = 146.60/46.68 ≈ 3.1405 matches π_Cyg = 3.140625 within 0.003%; equivalently, the Grand Gallery length C_GG ≈ 46.68 m multiplied by π_Cyg returns the published external height of Khufu within the same tolerance. A principal 16-cubit dimension of the Subterranean Chamber, multiplied by π_Cyg, yields 50.25, numerically equal to Newcomb's 1898 value for the precessional rate. The Sphinx height, multiplied by π_Cyg, 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)