The present work investigates the origin of the cosmological constant within a timeless Euclidean model on E⁴ with a single real harmonic field. The fundamental setting contains neither fundamental time, nor a Lorentzian metric, nor pre-given cosmological dynamics; these structures are treated as effective and reconstructed only within an operationally admissible regime.

It is shown that remote reconstruction relative to a local data region Ω₀ has an elliptic character and is accompanied by the exponential instability of inverse continuation. This leads to an infrared-induced narrowing of the stably reconstructible spectral window and to an increase in the minimum distinguishable wavelength as the scale of reconstruction grows. On this basis, a finite maximum scale of stable reconstruction L_max is obtained and interpreted as an operational reconstruction horizon.

It is then shown that, if this infrared limit is represented within the already reconstructed closed covariant gravitational regime, the leading universal local zero-derivative response takes the form of a cosmological term. Its natural scale is given by

Λ_IR = χ L_max⁻²,

where χ is a dimensionless coefficient depending on the details of the cosmological reconstruction class.

The relation to redshift is analyzed separately. As the spectral window narrows, the causal reconstructibility of a remote signal requires the transfer of its observable content into the admissible infrared range. In the effective FLRW description, this transfer is realized as cosmological redshift. Redshift thereby admits a reconstructive interpretation as a mechanism preserving the causal recognizability of remote signals while short-wavelength details are lost.

In the target homogeneous-isotropic sector, the positive FLRW branch is singled out as the branch compatible with a finite reconstruction horizon, redshifting infrared transfer, and an asymptotic Hubble scale H_IR ∼ L_max⁻¹. Thus, the cosmological constant is interpreted not as fundamental vacuum energy and not as non-vacuum hidden matter, but as a universal geometric infrared response to the limitation of stable remote reconstruction. The result is structural in character: the full FLRW phenomenology, the exact value of H₀, the full redshift law z(L), and the possible relation to the cosmic microwave background remain tasks for further analysis.