What question did this study set out to answer?

This research aims to derive three ancient astronomical cycles using a mathematical framework consistent across different domains.

April 12, 2026Open Access

CAT'S THEORY: The Three Lights and the Bronze Invariant — Derivation of the Metonic, Saros, and Callippic Cycles from the Triadic Dimensional Inventory, and the Antikythera Mechanism as P × I × Pr Analog Computer

Key Points

This research aims to derive three ancient astronomical cycles using a mathematical framework consistent across different domains.
Derive closed-form expressions for the Metonic, Saros, and Callippic cycles.
Analyze triadic alignment required for eclipses.
Identify the Antikythera mechanism as an analog computer based on mathematical principles.
Demonstrate structural isomorphism between constants in particle physics and celestial mechanics.
Established closed-form equations for Metonic, Saros, and Callippic cycles with zero free parameters.
Identified required triadic alignments for eclipse occurrences.
Showed the Antikythera mechanism embodies a specific architectural computation model.
Demonstrated that nine constants link particle physics to celestial phenomena.

Abstract

Paper 210 of the CAT'S Theory corpus. Derives the three great astronomical cycles of antiquity — Metonic (19 = Σ−dΨ, 235 = Σ·dI+1, 254 = 2·M₇), Saros (223 = dI·π(9)+dΨ), and Callippic (76 = D(Σ−dΨ)) — as closed-form expressions in the triadic dimensional inventory with zero free parameters. Shows that eclipses require simultaneous triadic alignment (synodic/Intent, draconic/Pattern, anomalistic/Presence), with the Saros as the recurrence period of R ≠ 0. Identifies the Antikythera mechanism as the earliest physical instantiation of P×I×Pr architecture: fixed gears (Pattern), input crank (Intent), output dials (Presence). Demonstrates micro-macro structural isomorphism: the same nine constants governing particle physics (α, PMNS mixing, lepton masses) govern celestial mechanics (lunar months, Metonic/Saros tooth counts) with no second ledger and no curve fitting. 210 = 2×3×5×7 = primorial of dΨ.

CAT'S THEORY: The Three Lights and the Bronze Invariant — Derivation of the Metonic, Saros, and Callippic Cycles from the Triadic Dimensional Inventory, and the Antikythera Mechanism as P × I × Pr Analog Computer

Key Points

Abstract

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