Zero-Parameter Quantum Gravity from Discrete Recognition Calculus
Independent Research, Austin, Texas, USA
Summary
A parameter‑free route to classical and quantum gravity is presented from a minimal recognition axiom. The discrete recognition calculus fixes a unique cost, an 8‑tick cadence, a discrete light‑cone bound, and an RS Planck normalization; mesh refinement yields GR. An interacting, BRST‑consistent QG, a DEC‑to‑continuum path integral, and RS‑normalized black‑hole semiclassics are developed, with structural theorems machine‑verified in Lean 4.
Abstract
We derive classical and quantum gravity from a minimal information‑theoretic axiom—“a recognition event requires non‑empty data”—with parameter‑fixed, gauge‑rigid displays. The discrete recognition calculus yields conserved ledger dynamics, exact integer 1‑forms, a unique convex cost \(J(x)=\tfrac12(x+1/x)-1\), and an 8‑tick minimal period in three dimensions. These dictate a discrete light‑cone bound \(\Delta r\le c\,\Delta t\) and a parameter‑free Planck normalization \(\lambda_{\mathrm{rec}}=\sqrt{\hbar G/(\pi c^3)}\). Mesh refinement recovers the continuity equation and Einstein’s field equations with emergent Lorentz invariance. Beyond linearized gravity we develop an interacting, BRST‑consistent quantum theory under the RS bridge, a background‑field renormalization with RS‑compatible UV bands, a nonperturbative DEC path integral, and RS‑normalized black‑hole semiclassics. Structural theorems are Lean‑verified; expanded interacting/UV/nonperturbative/semiclassics are presented as classical proofs with explicit audits and falsifiers.
Key Points
- Unique convex cost and 8‑tick cadence fix a discrete, parameter‑free scaffold with emergent GR.
- RS normalization: \(\lambda_{\mathrm{rec}}=\sqrt{\hbar G/(\pi c^3)}\); light‑cone bound \(\Delta r \le c\,\Delta t\).
- Interacting BRST‑consistent QG, DEC‑to‑continuum path integral, and RS‑normalized BH semiclassics.
- Structural theorems machine‑verified; remaining modules shipped with explicit audits and falsifiers.