Torsion-Modulated Recursive Branching (TMRB): A Unified Framework for Quantum Gravity Phenomenology and Subluminal Plasma Propulsion

Changes in v3 (May 2026) Δλ corrected: 1. 729 → 1. 7287 (exact value 104π/189; prior rounding propagated dimensional error through §2. 4 and §8) mKK formula corrected: spurious ℓPl factor removed; formula now reads mKK ≈ (G₄/G₁₁) ^1/7 in geometric units, consistent with dimensional analysis κ disambiguation: κCE = μ/λ = 0. 4038 (conformal-weight/holographic contexts) and κₚrop = 0. 48 (plasma/Beltrami/QGGPf contexts) are now explicitly distinguished throughout; prior version used bare κ ambiguously Gaussian weight table added: normalisation constant C = 1/Σexp (−πn²/9) ≈ 0. 500 made explicit; representative values w₀ = 0. 500, w₁ = 0. 353, w₂ = 0. 124, w₃ = 0. 0216 tabulated Paper 1 cross-citation added: variational foundation for the prismatic action Z and stress-tensor Tₚrism is now cited to Bressler (2026), "Einstein Equations from Prismatic Curvature, " doi: 10. 5281/zenodo. 20146627 Citation corrected: Donà (2022) → Donà emergencystretch=2em Version 2 — What Changed Version 2 applies the full TMRB series correction set and incorporates developments from the companion Celestial Holography and M-Theory Bulk Gravity Leakage papers. Core corrections (all papers) Modular-covariant Gaussian branching weight. The phenomenological weight wn ∝ φ−λn used in v1 is replaced by the DFT fixed-point form wn = C exp (−πn2/9), n = 0, …, 8. This is the unique weight on Z9 satisfying modular covariance (not invariance) under the discrete Fourier transform. The associated torsion entropy is 9 ln 9 ≈ 19. 775. The old golden-ratio form failed this condition and is superseded. κ disambiguation. Two distinct coupling constants are now explicitly labelled throughout: κCE = μ/λ = 2. 1/5. 2 = 0. 4038 (conformal-weight comb; Celestial Holography and galactoseismology) and κprop = 0. 48 (plasma torsion suppression; VASIMR and QGGPf). These are different quantities with different physical origins. A disambiguation table is provided in Section 2. 4. 11D CDT qualifier. All claims about the 11D CDT extension are now labelled “conjectured”. Established CDT results cover 4D only. Non-supersymmetric declaration. The Schoen gyroid compactification carries no G2 holonomy. UV control derives from CDT causal structure, not supersymmetry. This is explicitly stated throughout. New content from companion papers Kaluza–Klein hierarchy ratio. New Section 3 derives G4/G11 = (5. 214 ± 0. 12) × 10−40 from compactification on the Schoen gyroid with nine inequivalent C-field torsion phases from H3 (Z9, U (1) ) ≅ Z9. This ratio provides the stress-tensor normalisation connecting all observational sectors across 1023 m. BMS superrotation discretization. TMRB’s 9-fold torsion nodes are identified as a discrete realization of BMS superrotation charges at null infinity ℐ+, closing the infrared triangle among Weinberg’s soft graviton theorem, BMS asymptotic symmetries, and gravitational memory. ZF Z9 parafermion identification. The nine parafermion primaries (c = 16/11, Gepner–Qiu 1987) map bijectively onto the nine torsion phases, connecting the framework to flat-space holography. Density parameter derivation. The density field ρ (r) = ρ0 ∑n wn cos (θn + kn·r) is derived from first principles here and cross-referenced in the QGGPf predictions paper wherever ρ appears. Observable predictions summary table. A new table lists all eight falsifiable predictions spanning the companion paper series, from QGGPf orbital signatures to the 230 Myr galactic disk-wave crest and the G4/G11 hierarchy ratio. Three new figures. Fig. 1: TMRB branching tree and UV→IR spectral dimension flow. Fig. 2: Cross-domain equivalence diagram (quantum gravity ↔ plasma drive) with shared kernel w (θ, d). Fig. 3: κ disambiguation plot and Gaia DR3 calibration likelihood comparison. Three open theoretical gaps documented. (i) 11D CDT extension unproven; (ii) KK mass approximation neglects gyroid moduli corrections; (iii) disk-potential mapping uses low-energy approximation. IR triangle identification. The four QGGPf signatures are now identified within the infrared triangle structure: fractal noise = spin memory imprint; gravitomagnetic modulation = gyroscopic memory; running G anchored to G4/G11 = (5. 214 ± 0. 12) × 10−40; error suppression = UV path-integral self-consistency. Cross-scale coherence. ηdiff = 0. 82 ± 0. 02 propagates unchanged from Planck scale through LEO (∼106 m) to the galactic disk (∼1021 m) across 1023 m. Running G amplitude anchor. The 0. 01–0. 1 % LEO deviation is anchored to the KK hierarchy ratio G4/G11 derived in the M-Theory Bulk Gravity Leakage paper (doi: 10. 5281/zenodo. 19581289). ρ derivation cross-reference. The density parameter ρ is derived in the Unified Framework v2 (doi: 10. 5281/zenodo. 19192990) and cross-referenced here. New references Donnay, Pasterski Galactic Piano v3 (doi: 10. 5281/zenodo. 19422604) ; M-Theory Bulk Gravity Leakage (doi: 10. 5281/zenodo. 19581289). Previously unlinked references now carry full DOIs: Ambjørn Stray et al. 2025 (doi: 10. 1140/epjqt/s40507-025-00338-1) ; Muirhead 2025 (esto. nasa. gov/quantum) ; Chiow et al. 2025 (esto. nasa. gov/files/quantum/Chiow. pdf).