Renewal Dust: A Quantum Traction Theory Mechanism

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 incoming in a forthcoming 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).

v2.3 corpus elevation: path (a) is the unique QTT-native source law for shock-induced WV creation, by category-error argument and no-go theorem. The v2.2 closure was argued from absence of a corpus-stated alternative. v2.3 strengthens this to a structural QTT-physical argument: a hydrodynamic shock does not convert gas rest-mass into White-Void creation events; gas particles are not minted, only thermally rearranged. Therefore C_shock cannot be sourced by the baryonic rest-mass endurance sink S_gas = (V_SQ/m̃t̃)ρ_gas, because S_gas counts the substrate cost of maintaining existing gas mass, not the rate of WV emptying. The only QTT-native source is the irreversible creation energy density u̇_irr = T·ṡ_irr, giving the path (a) identification C_shock = (V_SQ/E_☆)·u̇_irr. The category-error argument is independent of which counting scheme is invoked and removes the v2.2 conditional dependence on the strict 1 k_B ≡ 1 WV ledger identity assumption.

Mass-Sink Shock-Gating No-Go Theorem (v2.3). Any conjectured rule of the form C_shock = N_gate · χ̄_RH · S_gas · I_M>1 with N_gate ≥ 1 leads, after the elegant cancellation c/(4πGℓ̃) × 4πGℓ̃/c = 1 in the lensing projection, to κ_C = −N_gate · χ̄_RH · Σ_shock/Σ_crit. For Bullet bow-shock parameters (M = 3, χ̄_RH = 0.85, Σ_shock ~ 1-3 kg/m², Σ_crit^Clowe = 6.47 kg/m²), Clowe Table 2's observed κ̄_obs = 0.05 ± 0.06 at gas peaks empirically excludes the entire class for N_gate ≥ 3 (at 6-19σ) and definitively for N_gate = 24 (at 52-157σ), independently of whether the gating identity could be derived from A6/A7 plus the 24-capacity blip ledger. This is not 'Candidate C is unproven' --- it is the stronger statement Candidate C is empirically dead before the question of derivation arises. F3 is strengthened correspondingly from a structural η_C ≠ 1 falsifier to a no-go theorem against the entire mass-sink shock-gating class.

Stage-2 substrate-counting closure: κ_C is Planck-suppressed at all astrophysical scales (preserved from v2.2). The path (a) lensing form κ_C = −(ℓ̃/c³Σ_crit) F_RH^los with all constants except the Artian micro-ruler ℓ̃ cancelling. For Bullet-class geometry and astrophysical shock fluxes, |κ_C| ~ 10⁻⁶⁵, structurally indistinguishable from zero at any current or foreseeable observational precision. The C field is a real ontological object in QTT, but its lensing contribution is dynamically negligible at all energy fluxes below Planck scale. Path (a) status badge upgraded from ☆☆ T+X to ☆☆☆ T (theorem-level, no remaining qualification beyond the Artian-G deformation-theorem closure of G).

Stage-1 substrate-counting closure: Z_occ = 1/(16π) forced by axioms (preserved from v2.2). The forthcoming substrate-counting paper [4] closes the absolute prefactor of the occupancy term as the product of the QTT discrete master-equation trace coefficient 1/4 and the already-derived Newton-Poisson normalisation 1/(4π), with no fitted multiplier surviving the substrate-cell cancellation ∇²ln(ρ_b V_σ) = ∇²ln ρ_b. The 24-lock and the radial-angular capacity V_SQ = 4πℓ̃³ enter only through G, not through Z_occ.

Bullet conditional peak theorem (preserved from v2.2). The v2.1 two-term peak inequality reduces to the simplified form |κ_occ|_gal > (κ_N|_gas − κ_N|_gal) + ε_occ, with all load now falling on κ_occ alone. Verifying the inequality on the actual Bullet stellar profile is the substrate-counting paper's Stage 3-5 task. From Clowe Table 2 with the Clowe normalisation and 100-kpc apertures, the inequality pressure is 0.027 ± 0.007 (subcluster, the sharper test) and 0.008 ± 0.010 (main cluster).

Gauge-safe linearization-validity audit (v2.3). The substrate-counting paper's Stage-3 evaluation of κ_occ on cuspy Hernquist BCG profiles produced |κ_occ| ~ 10⁴-10⁵ at full-aperture stellar mass vs. observed κ ~ 0.3. Whether this is a real falsification or a linearization breakdown artifact must be determined by an audit. v2.3 introduces a gauge-safe beam-local formulation: ε_lin(θ; B) = (1/4) |ln(ρ_b(θ)/exp<ln ρ_b>_B)| and λ_occ(θ; B) = (R_B²/4) |∇_⊥² ln ρ_b|, where B is the observational lensing beam (5″, 10″, 20″) and R_B is its characteristic radius. This replaces an earlier gauge-ambiguous formulation. Three regimes: λ_occ ≪ 1 (linearization safe), λ_occ ~ 1 (borderline), λ_occ >> 1 (breakdown artifact, not corpus prediction). The substrate-counting paper's Stage-4 audit must compute λ_occ at the four lock positions × four BCG-cusp-mass-fraction values × three beams before the |κ_occ| value can be interpreted.

Total-occupancy hypothesis as named future research (v2.3). If the |κ_occ| ~ 10⁵ value is a linearization breakdown artifact, the substrate-counting paper requires a nonlinear completion. The candidate repair: replace the baryon-only ν_b with the total substrate occupancy ν_tot = ν_vac + ν_b + ν_WV + ··· with the vacuum baseline ν_vac = 1. For small baryonic occupancy, ln ν_tot = ln(1 + ν_b + ···) ≈ ν_b, a regular function with no ln(0) pathology at low-density boundaries. Status: corpus-conditional candidate; valid only if the Book's A6/A7 wording supports ν_tot over ν_b. Three branches: if A6/A7 supports ν_tot, v2.3 requires a v2.4 with the corrected master equation; if A6/A7 explicitly means ν_b, the linearization audit is performed at face value; if A6/A7 is ambiguous, both interpretations are reported in parallel.

Bullet observational anchors per Clowe+ 2006 (preserved from v2.2). 1″ = 4.413 kpc/arcsec at z = 0.296 in standard ΛCDM (h = 0.7, Ω_m = 0.3, Ω_Λ = 0.7); D_A = 910 Mpc; D_L = 1529 Mpc; 25″ gas-bullet offset = 110 kpc (corrected from v2.0-v2.1's 114 kpc which used a wrong plate scale and confused distance measure); Σ_crit^Clowe = 3.1 × 10⁹ M_⊙/kpc² = 6.47 kg/m² (canonical for direct κ-map comparison). 100-kpc aperture Newtonian checkpoint table from Clowe Table 2 with the four lock positions (Main BCG, Main plasma, Subcluster BCG, Subcluster plasma) and their RA/Dec coordinates included. Anti-circularity rule: Brownstein-Moffat 2007 MOG-style galaxy density reconstruction excluded as QTT input because lensing-derived.

Ten falsifiers (F3 strengthened in v2.3). 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 strengthened in v2.3: Mass-Sink Shock-Gating No-Go Theorem against any C_shock = N_gate · χ̄_RH · S_gas with N_gate ≥ 3 (subsumes v2.2 structural η_C ≠ 1 sub-falsifier); F4: closure-consistency violation propagating from the ABC/WV theorem; F5: cluster κ_occ/κ_N inconsistent with the structural form (now triggered conditional on λ_occ ≪ 1 audit); F6: cosmological abundance violation; F7: σ₈ failure (held in abeyance); F8: two symmetric falsifiers from the G derivation [3].

v2.3 summary of substantive additions over v2.2 (preserving all v2.2 numerical claims and observational anchors). (i) Category-error argument elevating path (a) to unique QTT-native source law (new §7); (ii) Mass-Sink Shock-Gating No-Go Theorem with N_gate falsification table (new §8); (iii) F3 strengthened from ☆☆ structural to ☆☆☆ no-go theorem; (iv) Path (a) status badge upgraded from ☆☆ T+X to ☆☆☆ T; (v) Gauge-safe beam-local linearization-validity audit formulation (new §9); (vi) Total-occupancy hypothesis parked as named future research (new §13); (vii) Operational status table updated with three new entries (path (a) uniqueness, no-go theorem, gauge-safe audit, total-occupancy hypothesis); (viii) Hostile-referee gauntlet expanded with six new v2.3 entries. The Newton-G derivation result and all v2.2 numerical claims are preserved unchanged.

One ledger. Three mechanisms. No new particle. Path (a) is now QTT-native, not corpus-conditional. The mass-sink shock-gating class is a no-go theorem. Newton's constant is derived. The C field is real but Planck-suppressed at astrophysical scales. The Bullet absolute-magnitude question reduces to a gauge-safe linearization audit on the actual stellar map. We welcome attempts to falsify.