Gravitation from Hilbert-Space Granularity: The Sphere, the String, and the Ring

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 what a granular quantum mechanics looks like at every scale. Tim Palmer's Rational Quantum Mechanics holds that Hilbert space is granular, with a finite parameter L, which he attributes to gravity. We reverse the claim. L comes first, one universal integer, and we start from two postulates: every qubit is a string of bits on a ring of cells, no ring longer than L, and any two cells not opposite lie on one such ring. The postulates count the cosmological horizon, L²/4 rings, and one string per ring is its entropy. Jacobson's argument then returns Einstein's equations with G = c³ℓ_c²/πℏ, ℓ_c the cell, so the measured G fixes the cell at √π Planck lengths. Newton's law is a share of energy per string; rotation curves flatten, without dark matter, where the entropy a mass removes falls below what a sphere's strings hold inside it, at πc²/12R_Λ = 1.4×10⁻¹⁰ m s⁻² against 1.2 observed; the cosmological constant is the closure of the ring, GΛ = 12πc³/ℏL². Pinned from Λ and from galaxies, L = 3.6×10⁶¹ and 4.3×10⁶¹, agreeing to eighteen percent. 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 of 204 entangled qubits, the same for every technology.v11, changes since v4: Newton's constant now derived from Jacobson's argument, not Verlinde's entropic force; Einstein's equations arrive in Sec. III with Λ free. Sec. V: the two pins test an order-one coefficient, not sixty-two digits; a0's explanation credited to emergent gravity. Qubit ceiling from 2^N≤L: Nmax=205, was 212; test is a random circuit and its inverse. Prediction 4 carries the DESI DR2 significances and notes w=−1 is derived, not assumed. Prediction 2 names the surviving results; the shift map keeps only its clock; deep regime flagged as Verlinde 2017's; a0 at 1.4σ; three new references. v9: cites Palmer 2016 and Hance–Palmer–Rarity 2025 (their Sec. V) on gravity's role and IST's Λ = 0 dark sector; notes one a0 across five dex of galaxy mass, so the 1.4 is a coefficient, not a mass effect. No other changes. v11, major revision: gravity mathematically derived from two postulates using only thermodynamics and elasticity. The horizon is counted, L²/4 rings, so Bekenstein–Hawking is no longer an input; Jacobson's argument gives G = c³ℓ_c²/πℏ and fixes the cell at √π Planck lengths; the galactic coefficient is counted, a_M = πc²/12R_Λ; L = 3.6×10⁶¹ from Λ and 4.3×10⁶¹ from galaxies, and the qubit ceiling moves from 205 to 204; a comparison table of derived against accepted values opens the paper. v4 (2 Sep 2026) remains the priority record.