The Information Manifold M

M is not spacetime.

Infinite resolution, no lattice

M is a Riemannian manifold with metric gμν^(M). It is continuous, irrational, unbroken. Irrational is precise: M admits no natural discretization — no lattice, pixel, or Planck-cell that tiles it without remainder. Every discrete coordinate system on M generates an approximation error. Resolution here means no lower bound on the smallest resolvable interval. M does not bottom out.

Spacetime is output

Four-dimensional Lorentzian geometry with signature (−,+,+,+), carrying the Einstein field equations, is an output of the α-Framework, not its input. The metric of general relativity is an induced metric on the projected surface C. M predates and underlies that structure. Treating discrete spacetime as fundamental generates the trans-Planckian problem, QFT UV divergences, the Planck-scale breakdown of geometry, and the hard problem of measurement. M dissolves all four: divergences live in the projection; discrete outcomes are edge events; the Planck scale is where the α-Connection reaches minimum area and geometry dissolves into the edge process.

The state of M

M carries a state |Ψ_M⟩ encoding all possible states, geometries, and field configurations at once. It is not a Hilbert-space wavefunction defined on a pre-existing spacetime. It is more primitive: a section of a fiber bundle over M. The projection of |Ψ_M⟩ through the α-Connection produces the local discrete field configuration experienced as C at scale μ. Experienced reality at any scale is precisely M as seen through the edge at that scale. Nothing more. Nothing less.

EQ-2

|Ψ_C(μ)⟩ = Π_α(μ) · |Ψ_M⟩

Π_α(μ) is the edge projection operator — disentanglers and isometries running at compression ratio α, with H determining completeness.