Torsion-Modulated Recursive Branching (TMRB) Predictions for NASA's QGGPf

TMRB Predictions for NASA Quantum Gravity Gradiometry (QGGPf) — Version 4 This version corrects terminology, citation, typographic, and companion-file errors identified during cross-program audit of the Prismatic Torsional Recursive Holographic (PTRH) preprint series. The four physics predictions (ηdiff, fractal noise excess, gravitomagnetic modulation, running Gₑff), the torsion-ring anomaly amplitudes, and all hotspot coordinates are unchanged. (i) Terminology and definitions. "Bondi–Metzner–Sachs (BMS) " is now defined in full on its first appearance in the body text, not only in the abstract. (ii) Strominger (2014) citation added. The Strominger infrared-triangle reference (JHEP 07 (2014) 152) is now cited at the first invocation of the BMS memory effect, consistent with the PTRH series standard. (iii) Modular covariance qualified. Two passages in the Conclusions and one in the Appendix that described the Gaussian branching weight wₙ as "modular-covariant" have been corrected to "approximately modular-covariant, " with explicit statement that corrections are of order O (e^−4π) ≈ 3×10⁻⁶. The claim of exact modular invariance was not established and has been removed. (iv) 1. 2σ statistic clarified. The 1. 2σ figure now reads as a central-value separation normalized by combined uncertainty, not a lower-bound distance from the null. The accompanying prose is reworded to remove ambiguity. (v) Saddle-point density ρ (r) labelled open gap. The saddle-point derivation of the hotspot density profile ρ (r) is explicitly flagged as an open derivation gap rather than a completed result. (vi) Donà Celestial Holography (Paper 4) to v4 DOI 10. 5281/zenodo. 20249096; Galactic Piano (Paper 5) to v4 DOI 10. 5281/zenodo. 20262175; VASIMR (Paper 8) to corrected DOI 10. 5281/zenodo. 19268015. (viii) M-Theory Bulk Gravity Leakage citation updated. The citation now references v9e with the full subtitle, consistent with all other papers in the series. (ix) Paper 1 cross-citation added. A cross-reference to "Einstein Equations from Prismatic Curvature" (DOI 10. 5281/zenodo. 20146627) has been added where prismatic curvature underlies the torsion geometry. (x) Duplicate titlesec block removed. A duplicate package declaration introduced in an earlier revision has been eliminated. (xi) Typography. =falsemicrotype and =2em are now active, eliminating overfull hbox warnings in the bibliography. (xii) Equation reference format. One equation reference in the Appendix has been corrected from to () for consistency with the Eq. ~ (. . . ) convention used throughout. (xiii) Companion visualizations corrected. The interactive globe (TMRBGravityLeakGlobeᵥ4₃. html) and flat map (TMRBGravityLeakFlatMap. html) contained geographic label errors for 14 of the 36 hotspot nodes. Errors included wrong country assignments, wrong ocean (one node labeled Pacific when its coordinates place it in the Caribbean), incorrect distance estimates, and city/region names inconsistent with the node coordinates. All 14 labels have been corrected. Node highlighting was also corrected: the five highest-ranked peak nodes now render in gold with pulse animation; the remaining four Ring 62°N nodes render in amber. Previously all nine Ring 62°N nodes were incorrectly highlighted as peak nodes. (xiv) Companion CSV corrected. Ring 62°N anomaly value standardized to 8. 10×10⁻¹⁵ m/s²; longitude columns standardized; RingLabel, nᵢndex, Units, and Geography columns added. (xv) Figure 3 added. fig3ₜorsion. pdf (TMRB torsion phase diagram) was missing from v3 and is now included as a generated companion file. Background: Quantum gravity remains the last missing piece of fundamental physics. While string theory and loop quantum gravity (LQG) offer elegant formalisms, they have yielded few near-term observables. The NASA Quantum Gravity Gradiometer Pathfinder (QGGPf) mission (Infleqtion/JPL-led, target sensitivity 100 mE/sqrtHz at 10 s interrogation, launch ~2030) presents a rare opportunity to test quantum-gravity phenomenology at orbital scales. Methods: The Torsion-Modulated Recursive Branching (TMRB) framework is presented — abackground-independent extension of causal dynamical triangulations (CDT) with discrete torsion twists on every simplex link and recursive self-similar branching weights. The path-integral measure incorporates torsion-modulated damping and EPRL/FK vertex amplitudes. Low-energy signatures follow directly from the framework and map onto QGGPf observables. Results: Four concrete, falsifiable predictions lie within QGGPf sensitivity: (i) fractal 1/f0. 75 noise excess of 150-300 mE/sqrtHz in the 10-3-10-2 Hz band; (ii) running effective gravitational constant Geff (r) at the 0. 01-0. 1% level over LEO baselines; (iii) torsion-induced gravitomagnetic modulations phase-locked to Earth rotation at 50-200 mE/sqrtHz at 1 cycle/orbit; and (iv) 20-50% suppression of high-frequency gradient variance below the atom-shot-noise limit. Conclusions: Detection or null-result bounds would provide the first orbital-scale experimental constraint on a fully background-independent, emergent unification model requiring no fine-tuning. TMRB closes the loop between quantum information, discrete geometry, and precision space geodesy. It shares the identical mathematical substrate with the Thermoacoustic Resonance Drive -- Variable Specific Impulse Magnetoplasma Rocket (TMRD-VASIMR) hybrid plasma propulsion system (Zenodo doi: 10. 5281/zenodo. 19192990 and doi: 10. 5281/zenodo. 19267212).