Mathematical Physics

Metrarchic Field Theory: a Geometric-Probability Research Architecture for Quantum Measure, Relativistic Geometry, Gauge Structure, and Matter Spectra Within the Metrarchic Geometry Framework

Authors: Perry Henderson

Metrarchic Field Theory (MFT) is presented as a speculative research architecture with explicittoy sectors within the Metrarchic Geometry Framework (MGF). Its organizing hypothesis is thatquantum measure and macroscopic metric geometry may be scale-dependent manifestations of acommon deeper structure. A positive coframe metric and a prescribed conserved reference measuregive the conditional identity ρG = ρ0/J, where J is the metric volume ratio. Curved realizationsrequire generalized coframes rather than merely compatible maps into a flat space of the samedimension. A conformal sector gives an explicit leading relation between a normalized amplitude’squantum-potential expression and spatial scalar curvature. The fixed reference measure leavesprobabilities of fixed base regions unchanged; a quantum observation map remains to be constructed.A compact worked example also exhibits the distinction between fixed-metric variation and theconstrained metric—density variation within a fixed-shape conformal sector.The wider architecture separates a formal positive configuration-weighting functional, an assumedreduced symplectic quantum sector, and an unspecified coarse-graining map. Prequantizationconstrains symplectic periods but does not derive a universal action scale. Gleason’s theorem suppliesa conditional projector-probability reconstruction after Hilbert-space and measure assumptions; itdoes not establish a microscopic Born rule. Standard Klein—Gordon, Bell/CHSH and Newtoniancalculations are retained as compatibility benchmarks. General relativity is an effective-field-theorytarget under additional infrared assumptions.An internal finite-dimensional construction uses a nonzero simple two-form in C5 to select a ranktwo plane and a postulated 3+2 splitting operator. The plane projector has determinant-one stabilizerS(U(3) × U(2)), whereas a fixed two-form has the smaller stabilizer SU(3) × SU(2). Retainingthe Abelian factor therefore requires an explicit phase-insensitive projector-sector assumption.The associated representation algebra is standard SU(5)-type mathematics. Gauge dynamics,representation-resolved chiral indices, fermion masses and cosmological observables remain open.The paper distinguishes established identities, model assumptions, conditional calculations andunproved physical identifications. It offers an auditable geometric research program, not a completedunification or an experimentally validated theory.

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[v1] 2026-09-25 23:20:37

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