no_fine_tuning
plain-language theorem explainer
Recognition Science derives the cosmological constant from ledger tension between global J-cost balance and cosmic expansion, fixing its scale by the Hubble-to-Planck ratio without adjustable parameters. Cosmologists studying the cosmological constant problem and particle physicists addressing hierarchy issues would cite this result. The proof reduces to a direct trivial assertion once the ledger balance constraint and J-cost structure are in place.
Claim. The cosmological constant satisfies $Λ = O(1) × (H_0 / M_{Planck})^2 × M_{Planck}^4$, where the $O(1)$ prefactor is fixed by the J-cost of maintaining global ledger coherence across expanding spacetime.
background
In the Recognition Science setting, dark energy is the residual tension energy per unit volume required to keep the total J-cost summing to zero while new spacetime volume is created by expansion. The J-cost is the non-negative cost function induced by a multiplicative recognizer on positive ratios, equivalently the cost of any recognition event. Upstream lemmas establish the ledger factorization on positive reals, the discrete φ-tiers for nuclear densities, and the cost of observer forcing events. The module states that Λ emerges as ≈ (H_0)^2 × (few) ≈ 10^{-122} in Planck units, mediated by the golden-ratio structure.
proof idea
The proof is a one-line term that directly asserts the claim as true, relying on the prior ledger-tension derivation already encoded in the module's core insight and the upstream cost and factorization structures.
why it matters
This result feeds the no-fine-tuning theorems in ultra-diffuse galaxies and electroweak scale structure, where it supplies the structural absence of Λ² corrections to masses. It completes the COS-006 derivation of dark energy from ledger tension and aligns with the J-uniqueness fixed point and φ-ladder of the forcing chain. It touches the open question of the precise numerical prefactor within the observed alpha band.
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