A Parameter-Free Einstein–Hilbert Coefficient from a Sink-Current Endurance Ledger

Abstract. We derive the Einstein–Hilbert action coefficient parameter-free from the Quantum Traction Theory (QTT) endurance ledger. The QTT-native theorem is a sink-current derivation: axioms A1/A2/A6/A7 fix the space-quantum volume V_SQ = 4πℓ³, the tick ẃ = ℓ/c, the mass quantum ṛ = ħ/(cℓ), and force the no-knob constitutive projection g_N = (c/ℓ)J_end from endurance flux to acceleration. Combined with the A2 sink continuity law, this gives Newton–Poisson with G = ℓ²c³/ħ.

The continuum-geometric layer is stated separately: in a coarse-grained, manifoldlike, distinguishing limit, A1 causal order determines the conformal Lorentzian metric (Hawking–King–McCarthy / Malament), and the QTT four-volume count fixes its conformal factor. Locality, metricity, capacity regularity, and second-order infrared truncation then allow Lovelock uniqueness to select the Einstein tensor plus a metric term. Matching to the QTT Newton–Poisson limit fixes the bulk coefficient λ = c³/(16πG) = ħ/(16πℓ²), so that the local Einstein-gauge action is S_EH = λ ∫ d⁴x √(–g) R.

Scope. The paper does not claim global equivalence to vanilla general relativity. QTT retains an absolute background clock, an integrable-Weyl lapse φ, and a creation source C₀(T) outside the local Einstein gauge — these are flagged as the discriminating cosmological content of the framework. Five concrete falsifiers are stated, tied to a one-ruler consistency requirement on ℓ.

What is new in v1.2.

• A QTT-native no-knob constitutive projection lemma forcing the coefficient c/ℓ from A1/A6/A7 saturation alone.
• An explicit five-register table separating QTT-native theorems from imported continuum mathematics (causal reconstruction, Lovelock).
• A bridge-hypothesis statement for manifoldlike coarse-graining, flagged as the standard causal-set regularity problem rather than a proven theorem.
• A cross-domain one-ruler audit tying the gravitational ℓ to UV capacity, transport, and QED endpoints.
• A comparison-with-related-programs paragraph distinguishing the endurance-ledger route from causal-set, loop-quantum-gravity, and entropic-gravity derivations of G.

Keywords. Einstein–Hilbert action, Newton's gravitational constant, quantum gravity, Quantum Traction Theory (QTT), endurance ledger, sink current, parameter-free derivation, Lovelock theorem, causal reconstruction, Hawking–King–McCarthy, Malament, Planck length, foundations of physics, microstructure of gravity, axiomatic physics.

Submission target. Foundations of Physics (Springer); arXiv mirror: gr-qc primary, math-ph cross-list.

Companion papers. This paper is part of the QTT corpus. Supplements: Quantum Traction Theory (framework manuscript, doi:10.5281/zenodo.17527179). Cross-references the omega-baryon paper (doi:10.5281/zenodo.20042421) for the cosmological non-equivalence falsifier.