Reciprocal tetration: a boundary-capacity hypothesis for the cosmological constant

The cosmological constant problem combines two distinct questions: how is a very small positive curvature scale selected, and how is that scale protected against vacuum-energy shifts and radiative corrections? This Hypothesis and Theory article addresses value selection through a boundary-capacity hypothesis. For a four-dimensional de Sitter horizon, define Λ P ≡ Λ l P 2 as the cosmological constant expressed in Planck units, and N dS ≡ A H / 12 π l P 2 as the normalized horizon-area variable. Their reciprocal relation is then a geometric identity, not a selection mechanism. The physical hypothesis is the separate identification of the recursively completed boundary capacity with N dS . The primitive seed is the cubic χ ∂ = 4 − 4 π α 0 − 21 α 2 0 + 2 α 3 0 . Three right-associated promotions construct the first, second, and terminal capacities sequentially. The exact algebraic inputs are the 21-dimensional reciprocal constitutive space and the Lorentzian double-duality character − 2 on its 20-dimensional principal sector. Their scalarization, unit weighting, retention of one axion boundary contact, and the three-tier recurrence remain model-defining hypotheses. The Tamm–Rubilar constitutive-wave tensor supports cubic dependence under an affine principal response and exact axion exclusion from local geometrical-optics propagation, but does not determine the proposed scalar weights 20 and − 2 . Using the 2022 CODATA Thomson-limit coupling, the frozen hypothesis gives Λ P , ⋆ ≃ 2.84604 × 10 − 122 , compatible with the constant- Λ value inferred in base- Λ CDM. This is a postdiction. The minimal model is not renormalization-group invariant at an arbitrary scale and is not protected against a constant vacuum-energy displacement. Its present cosmological expansion history is therefore the same as base- Λ