l0
The declaration supplies a placeholder value of 1 for the fundamental length ℓ₀ in the compatibility constants module. Researchers setting up lattice regularizations in QFT would cite it to define spacing without committing to numerical scales. It is realized by a direct constant assignment.
claimThe fundamental length scale is defined by $ℓ_0 = 1$.
background
The Compat.Constants module supplies project-wide constants and minimal structural lemmas. Upstream, QFT.UVCutoff.l0 defines the physical fundamental length as c * tau0, with tau0 ~ 1.288e-27 s giving l0 ~ 3.86e-19 m, E0 = hbar / tau0 ~ 3.2e11 GeV, and p0 = hbar / l0 ~ 1.7e-10 kg m/s. This local definition sets the value to 1 to support downstream structural results such as positivity and lattice constructions.
proof idea
The definition is a direct assignment of the real number 1 to l0, functioning as a one-line placeholder.
why it matters in Recognition Science
This definition anchors the length scale used in l0_pos, fundamentalLattice, p_max, brillouin_equals_pmax, and log_divergence within QFT.UVCutoff. It supports the transition to lattice-based UV regularization while the physical embedding via c * tau0 remains in the QFT layer, consistent with the framework's fundamental scales.
scope and limits
- Does not derive the value from c and tau0.
- Does not establish positivity or other properties of l0.
- Does not specify physical units or magnitude.
formal statement (Lean)
29def l0 : ℝ := 1