Renewal Dust: A Quantum Traction Theory Mechanism That Defeats MOND on the Bullet Cluster Through Substrate Lensing Corrections, Not by Renaming Cold Dark Matter

Quantum Traction Theory (QTT) supplies the structural replacement of the ΛCDM dark sector with three distinct mechanisms from one axiomatic ledger; the quantitative substrate-counting closure is deferred to a companion paper. (i) The cosmological constant is fixed by the ABC/WV closure theorem [1]. (ii) The MOND acceleration knee a₀ = cH_P/(2π) follows from the same ABC clock [1], at 0.5-0.8σ of McGaugh along three projection paths. (iii) Renewal Dust (RD), the subject of this paper, provides the cosmological mass residual Ω_RD = Ω_m^obs − Ω_b^lab = 0.2655 (residual identity conditional on Planck Ω_m^obs).

The structural form of RD is fixed by the QTT axioms, not derived phenomenologically: T^μν_RD = ρ_RD u^μu^ν, ℒ^int_RD = 0. RD gravitates as pressureless dust but has zero direct-coupling Lagrangian to any Standard Model field, with Λ from [1] and Newton's constant G = ℓ̃²c³/ℏ derived (not calibrated) via the deformation theorem of [3]: G(C_Ω, χ_g) = (C_Ωχ_g/4π)·ℓ̃²c³/ℏ, with C_Ω = 4π forced by the radial-angular S² capacity fiber and χ_g = 1 forced by the saturation endpoint, audited outside gravity by the 24-lock V_SQ/V_pix = 24.

The master cluster-lensing equation (now consistent between abstract and body in v2.1). The QTT weak-field Poisson equation produces FOUR sign-determinate convergence terms, with the projected occupancy term using the line-of-sight invariant 𝒪_b(θ) = ∫dz ln(ρ_b/ρ_☆) of dimension [𝒪_b] = m: κ = κ_N(Σ_b) + κ_occ(𝒪_b) + κ_C(Σ_b,shock) + κ_RD. v2.0 fixed the body but accidentally left the broken ∇⊥²lnΣ_b formula in the abstract; v2.1 repairs that load-bearing inconsistency.

Profile-class regularisation (new in v2.1). The line-of-sight invariant 𝒪_b and the boundary identity ∫dz ∂_z²lnρ_b = 0 require ∂_zlnρ_b → 0 at infinity. v2.1 restricts the master equation to the cluster profile class 𝓕_cluster = {ρ_b: ρ_b(r) ~ Ar^−α as r → ∞, α > 0, and ρ_b(r) > 0 for finite r}. This contains all standard astrophysical cluster profiles (β-model gas, NFW, Hernquist, isothermal, projected de Vaucouleurs); for these ∂_zlnρ_b = −αz/r² → 0 at infinity. Gaussian and compactly-supported profiles require regularisation deferred to a companion paper. The Bullet system unambiguously lies in 𝓕_cluster.

The Bullet conditional peak theorem (sharpened in v2.1). v1.8 proved a sign tendency only. v2.0 stated an explicit magnitude inequality but used a casual 'comparable to or larger than' that did not satisfy a strict inequality. v2.1 restates the theorem as a strict conditional: "if the substrate count delivers |κ_occ|_gal + |κ_C|_gas > (κ_N|_gas − κ_N|_gal) + ε_occ, then κ_gal > κ_gas." Status changed from T to T+X. The naive dimensional estimate of |κ_occ| is many orders of magnitude wrong without the substrate-counting normalisation; v2.1 states this openly. F2 remains a real falsifier because the sign-structure forbids gas-peak outcomes whenever the antecedent holds. Verifying the antecedent on actual Bullet stellar profiles is a substrate-counting task that the present paper does not perform.

Bullet sign rule is BARYONIC, not RD. Even with ρ_RD = 0, the substrate-derived κ_occ(𝒪_b) and κ_C(Σ_b) already enhance galaxy convergence and partially cancel gas convergence. Standard MOND has only κ_N(Σ_b) and predicts the convergence peak on gas (which dominates Σ_b by ~10x in 1E 0657-558); QTT predicts the peak on galaxies via κ_occ > 0 on cusps; this distinction holds without invoking RD at all.

Tilt-Drift-Dilation honestly relabeled in v2.1. The decomposition Π_Λ⁽⁰⁾ = I_clk · F_drift⁽⁰⁾ · N_dil⁽⁰⁾ = 0.92388 × 0.97077 × 1 = 0.896873 is an algebraic identity at the present epoch (since F_drift⁽⁰⁾ ≡ Π_Λ/I_clk when N_dil = 1). What it makes explicit is the QTT structural commitment that this single number is the product of three mechanisms that decouple off-equilibrium and acquire distinct physical content for time-varying or inhomogeneous probes: I_clk = cos(π/8) is fixed across all epochs (metaplectic-spinor structure); F_drift(T,x) evolves with the creation-history δ_cre(T,x); N_dil(x,v) ≠ 1 for inhomogeneous regions and moving observers. Three structurally distinct probes can in principle separate the three factors. v2.1 labels the decomposition as identity at the present epoch with non-trivial off-equilibrium structural content (status I+S, not T+I).

RD continuity (Option A, preserved from v2.0). Conservative Einstein-shadow continuity formulation: ∇_μT^μν_RD = 0, ρ_RD ∝ a⁻³, identical to cold dust at the homogeneous-background level. Any apparent late-time non-linear-clustering deviation comes from the lab projection of inhomogeneous ρ_RD^ABC(T,x). The full ABC-projected continuity (Option B) is deferred.

Bullet geometry corrections (preserved). Gas-bullet mass offset is ~25″ ≈ 114 kpc at z = 0.296 (D_L = 943 Mpc); the ~720 kpc figure is the inter-cluster main-mass-peak separation. Mach ~3.0, v_sh ≈ 4700 km/s. Surface densities Σ_☆^peak ~ 0.1-0.5 and Σ_gas^peak ~ 1-3 kg/m², giving κ_N ~ 0.05-0.3 at peaks (consistent with Clowe convergence map maxima κ_max ~ 0.3).

The ΛCDM tension map. Direct-detection nulls (XENONnT, LZ, PandaX, SuperCDMS, ADMX) are structurally accommodated by ℒ^int_RD = 0. F1 narrowed in v2.0 (carried in v2.1): a repeatable non-gravitational SM coupling of the component carrying the closure-fixed RD mass budget falsifies RD. The S₈ tension is consistent with QTT projection-induced non-linear-clustering deviations. The cluster MOND-violation factor of ~16 is healed structurally by κ_occ on cuspy profiles. The cosmological abundance Ω_RD = 0.2655 emerges as residual identity at 0.2% of Planck.

Eight sharp falsifiers (preserved from v2.0). F1: a repeatable non-gravitational SM coupling of the component carrying the closure-fixed RD mass budget. F2: violation of the Bullet conditional peak inequality at ≥5σ in a system with cuspy stellar profiles in 𝓕_cluster and clean Mach ≥2 shock. F3: Mach-scaling violation of |κ_C|. F4: closure-consistency violation propagating from the ABC/WV theorem. F5: cluster κ_occ/κ_N inconsistent with the structural form. F6: cosmological abundance violation. F7: σ₈ failure (held in abeyance pending substrate-counting paper). F8: two symmetric falsifiers from the G derivation [3].

v2.1 summary of substantive changes from v2.0 (incorporating new hostile-referee math review). (i) Abstract formula repaired to match body O_b form (resolves load-bearing inconsistency). (ii) Profile-class regularisation 𝓕_cluster introduced for 𝒪_b (asymptotic power-law profiles including β-model gas and NFW dark/stellar haloes; Gaussian/compact regularisation deferred). (iii) Bullet peak theorem labeled as conditional theorem with antecedent verification deferred to substrate-counting paper. (iv) Tilt-Drift-Dilation honestly labeled as present-epoch identity with non-trivial off-equilibrium structural content. The Newton-G derivation result and all v2.0 numerical claims are preserved unchanged.

One ledger. Three mechanisms. No new particle. The Bullet conditional peak theorem is baryonic. Newton's constant is derived. I welcome attempts to falsify.