Gravitation from Hilbert-Space Granularity: Pinning the Parameter L of Rational Quantum Mechanics Across Scales

Ever since general relativity and quantum mechanics were discovered over a century ago, physics has been on the quest for a theory that unites them. We argue that the answer has been staring us in the face: gravitation is a consequence of discrete quantum mechanics. Tim Palmer's Rational Quantum Mechanics claims that a quantum state cannot carry infinite information. Hilbert space is granular, with a finite parameter L, and Palmer attributes that granularity to gravity. We reverse the claim. L comes first, and gravity is what a granular Hilbert space looks like at every scale. From one universal integer L and one length, the cosmological horizon radius, we derive the Planck length and Newton's constant. Einstein's equations follow; with the same L, galactic rotation curves flatten without dark matter, and Newton's constant and the cosmological constant cease to be independent: their product is fixed by L. We test the reversal by pinning L on every scale where it appears on its own rather than through the Planck length. The galactic scale gives 4.6×10^61; the cosmological scale gives 6.4×10^61. They agree to within a factor of 1.4 on a sixty-two-digit number. This is the old coincidence between Milgrom's acceleration and the Hubble scale, and here it is one L seen on two scales. The third place where L appears on its own is the quantum computer, which will report within the decade. We predict what it will find: a ceiling near 200 entangled qubits, the same for every technology.Version 5 (3 Sep 2026): abstract and text tightened; the constancy-of-Λ prediction is now stated as a bound on the dark-energy equation of state, |1+w₀| ≲ 5×10⁻⁴; Gibbons–Hawking reference added; references corrected and completed with DOIs; keywords, declarations and ORCID added. v1 (2 Sep 2026) remains the priority record.