Newton's Constant Is Not Primitive in Quantum Traction Theory: Artian Angular Capacity, Universal Endurance Ceilings, and G = ℓ_A² c³ / ℏ Without Planck-Length Circularity

This paper gives a substantive-axiomatic Quantum Traction Theory (QTT) derivation of Newton's constant. It does not predict the SI numerical value of G_N from pure numbers alone; one dimensional micro-ruler must be primitive or independently measured. The sharper claim is: once the universe has a primitive Artian micro-ruler ℓ_A, an Artian tick t_A = ℓ_A/c, and the UEL action scale ℏ, Newton's gravitational coupling is no longer an independent primitive.

The proof exposes the only two places where a dimensionless coefficient can hide. First, the QTT space quantum is postulated to be a radial-angular capacity fiber,

V_SQ = ℓ_A³ ∫_S² dΩ = 4π ℓ_A³,

not a Euclidean brick or filled ball. This is a definition theorem: the integral is standard mathematics; the QTT physics is the choice that an endurance source counts one radial Artian depth over the full S² direction bundle. Second, QTT postulates a universal capacity ceiling: a saturated speed-like endurance current and a saturated one-tick velocity response are the same local capacity endpoint, giving g = J_end/t_A.

Combined with the Law of Endurance and the UEL mass scale m_A = ℏ/(c ℓ_A), these axioms force ∇·g = −4π G_A ρ with

G_A = ℓ_A² c³ / ℏ.

Matching G_A to the measured G_N calibrates ℓ_A; it is not a premise. A deformation theorem exposes the rival-coefficient form G(C_Ω, χ_g) = (C_Ω χ_g / 4π) · ℓ_A² c³ / ℏ, with the QTT commitment C_Ω = 4π and χ_g = 1.

v3.5 changes

1. NuFIT label correction. The two NuFIT 6.0 normal-ordering tables (IC24+SK-atm; IC19 w/o SK-atm) are correctly assigned (33.55 and 33.83 respectively), and the 1σ-propagated residual is reported as +0.16σ for the preferred IC24+SK-atm variant.
2. Inlined π/8 two-clock projection derivation. θ_can = π/4 is the canonical refoliation angle of the two-clock plane; the metaplectic spinor lift halves it to π/8; the laboratory projection constant is

I_clk = cos(π/8) = ½√(2+√2) ≈ 0.9238795.

The same number is the standard T-gate magic-state overlap |⟨+|T|+⟩| and the symmetric Clauser–Horne–Shimony–Holt (CHSH) variational optimum at which the Tsirelson bound 2√2 is saturated.

1. Parameter-free neutrino mass-squared ratio. Combined with the QTT minimal-holonomy active-Majorana spectrum (m₁=0, m₂=m₀/ρ, m₃=m₀ with ρ=2π·I_clk), one obtains

Δm²₃₁ / Δm²₂₁ = 4π² cos²(π/8) = 33.69694…

The capacity-scale normalization m₀ cancels. No mixing angle, continuous coupling, or flavour-universal scale enters the ratio. NuFIT 6.0 IC24+SK-atm gives R_ν = 33.55 ± 0.92, residual +0.16σ.

1. Foundational-reconstruction acknowledgement. Explicit note in the abstract and hostile-referee table explaining that QTT's stated remit is to derive—not augment—classical mechanics, quantum mechanics, and general relativity from a single discrete-substrate axiomatic core (A1–A7). Cross-references between QTT companion manuscripts are therefore structural rather than editorial.
2. Hostile-referee audit table updated to reflect the inlined derivation and the corrected NuFIT labels.

Companion paper

Newton's Second Law as a Three-Way Capacity-Counting Theorem: A QTT Derivation of Inertia, Gravitation, and Reality-Work from One Substrate Count (10.5281/zenodo.20059780), where the same angular-capacity theorem and endpoint-preservation lemma carry the substrate count N_b·m* into the inertial sector.

Falsifiers

• F1. An independent micro-geometric measurement giving C_Ω χ_g ≠ 4π in the deformation theorem.
• F2. A non-gravitational measurement of ℓ_A inconsistent with √(ℏG_N/c³).
• F3. Two systems with the same inertial rest-energy producing different endurance sinks (failure of the UEL source identity).
• F4. Coherent single-address visible mass exceeding m_A without loss of QTT capacity behaviour.
• F5. A Δχ²_R ≥ 9 post-JUNO/DUNE departure of Δm²₃₁/Δm²₂₁ from 33.6969.

AI assistance disclosure

Per QTT submission discipline, the author used OpenAI GPT and Anthropic Claude as drafting and verification assistants for LaTeX formatting, grammer polishing, reference checking, converting abstract ideas to mathemathical and technical formats and dialectical pressure-testing of arguments. All structural claims, theorems, proofs, and numerical evaluations are the author's responsibility and creativity.