Spacetime from the Contraction of Possibility on Fl₁,₂(ℂ³) × ℂP¹

This paper derives the Lorentzian structure and dimensionality of spacetime from irreversible record formation on a compact Kähler configuration space. Building on a programme in which physical law emerges from the contraction of possibility under irreversible measurement events, the framework begins with the configuration manifold

M = Fl₁,₂(ℂ³) × ℂP¹

and a bridge law governing the depletion of accessible states.

The bridge law relates the contraction rate of the possibility measure Ω to the local rate of irreversible record formation Γ through

d/dτ ln Ω = −κΓ

where κ = π arises as the Fubini–Study volume of CP¹. Physical time is identified with the contraction of possibility,

dt = −kₜ d ln Ω.

From this relation the paper derives several structural results:

• The temporal one-form θ = −d ln Ω defines a canonical causal ordering on the event manifold.
• Finite record-propagation speed produces a cone field whose compatible quadratic form has Lorentzian signature.
• Quantisation of the entropy screen measure in Planck area units implies that spatial dimension must be d = 3.
• Among simple Lie groups, SU(3) uniquely matches the resulting spatial dimensionality through the dimension of its flag manifold.

The resulting (3+1)-dimensional Lorentzian spacetime therefore appears not as a fundamental arena but as the structural residue of irreversible contraction on configuration space.

The manifold furnishes structured possibility, the Fubini sphere furnishes recordability, and spacetime is the ordered geometry of irreversible configuration selection

Within the broader research programme, the same geometric framework has previously produced quantitative predictions for fundamental constants, particle masses, the Born rule, and semiclassical gravitational dynamics without adjustable parameters.

This paper closes the remaining gap by deriving the causal structure and dimensionality of spacetime itself from the same mechanism.