M-Theory Bulk Gravity Leakage

M-Theory Bulk Gravity Leakage via Torsion-Modulated Recursive Branching and Piano Mathematics — Version 10a This version corrects terminology, citation, typographic, and structural errors identified during cross-program audit of the Prismatic Torsional Recursive Holographic (PTRH) preprint series. The four physics predictions, hierarchy ratio, hotspot coordinates, and anomaly amplitudes are unchanged. (i) sub-femto-g correction (×4). The anomaly amplitude descriptor "nano-g" has been corrected to "sub-femto-g" in the abstract, introduction, falsifiability table, and Figure 1 caption. The predicted anomalies are 6. 29–8. 10×10⁻¹⁵ m/s² ≈ 10⁻⁶ nano-g; the prior label was wrong by six orders of magnitude. This correction is consistent with the subtitle used to cite this paper in companion papers. (ii) 11D CDT extension flagged as conjectured (×6). Every invocation of the 11-dimensional CDT extension now carries an explicit conjectural qualifier. Six locations were corrected: the abstract, two points in the introduction, the Results section text, and the captions of Figures 3 and 4. The established 4D CDT framework (Ambjorn et al. 2012) is unaffected; only the 11D generalization is flagged. (iii) G₂-holonomy lifting flagged as conjectured. Line 276 previously stated "the gyroid lifts to a G₂-holonomy manifold" as fact. This has been corrected to "the gyroid is conjectured to lift to a G₂-holonomy manifold (Caveat 1, §6). " The blocking caveat in §6 is unchanged. (iv) mKK derivation added. The Kaluza–Klein mass scale formula mKK ≈ (G₄/G₁₁) ^1/7, cited to this paper by companion papers 3 and 6 but previously absent, is now derived explicitly (Eqs. V7–mkk). The derivation reduces S₁₁ on a compact 7-manifold to obtain V₇ = G₁₁/G₄, then sets mKK ~ V₇^−1/7 = (G₄/G₁₁) ^1/7 ≈ 2. 44×10⁻⁶ MPl ≈ 3×10¹³ GeV in geometric units (ℏ = c = 1, no additional ℓPl factor). This scale is consistent with non-observation of KK graviton excitations at LHC by more than seven orders of magnitude. (v) H³ (Z₉, U (1) ) language corrected. Two passages previously stated that the result H³ (Z₉, U (1) ) ≅ Z₉ "is derivable from the gyroid geometry alone; it is not postulated" and "it is derived, not assumed. " Both claims overstated what is shown in the paper. The language has been corrected to: the result follows from Sharpe's (2003) discrete torsion classification; its explicit derivation from the Ia3̄d space group geometry is an open derivation gap of the programme. (vi) κ disambiguation note added. A note has been added in §2. 1 clarifying that κ = 0. 48 is the branching-depth damping coefficient in exp (−κd²) and must not be confused with κCE = µ/λ = 0. 4038, the holographic coupling constant appearing exclusively in the Celestial Holography companion. (vii) Paper 1 cross-citation added. A cross-reference to "Einstein Equations from Prismatic Curvature" (DOI 10. 5281/zenodo. 20146627) has been added in the introduction where companion PTRH papers are listed. (viii) Companion paper DOIs updated. The Unified Framework (Paper 3) citation now points to v3 canonical DOI 10. 5281/zenodo. 20248650; Celestial Holography (Paper 4) to v4 DOI 10. 5281/zenodo. 20249096; Galactic Piano (Paper 5) to v4 DOI 10. 5281/zenodo. 20262175; QGGPf (Paper 6) to v4 DOI 10. 5281/zenodo. 20272654. Companion paper titles in the bibliography have been updated to their full canonical titles. (ix) Data Availability corrected. The Data Availability section previously cited the Galactic Piano companion (Bressler2026piano) as the Zenodo host for this paper's data — an error. It now links directly to this paper's Zenodo record at 10. 5281/zenodo. 20276554. (x) Supplementary Materials DOI added. The placeholder "DOI to be assigned upon publication" has been replaced with the live DOI href 10. 5281/zenodo. 20276554. (xi) Schoen (1970) URL added. The NASA Technical Note D-5541 reference (NTRS accession 19700020472) now includes a live URL: https: //ntrs. nasa. gov/citations/19700020472. (xii) Equation reference format. One equation reference in §6 has been corrected from Eq. to Eq. () for consistency with the formatting convention used throughout. (xiii) Typography. =falsemicrotype and =2em are now active. Table column specifications have been updated for compatibility with the MiKTeX revtex4-2 build. (xiv) Date updated. Title-block date corrected from April to May 2026. M-theory predicts that gravitons propagate through all 11 spacetime dimensions (bulk) while Standard Model fields are confined to a 4-dimensional brane, producing an unmeasured leakage of gravitational flux into the extra dimensions. Wepresent the first discrete, parameter-free, observationally anchored realization of this leakage via Torsion-Modulated Recursive Branching (TMRB), embedded as a causal dynamical triangulation (CDT) of 11-dimensional supergravity. The branching weightw (θ, d) (ηdiff=0. 82±0. 02, θn=2πn/9, λ=5. 2, μ=2. 1, κ=0. 48, dopt=9), calibrated once against Gaia DR3 phase-spiral data and not subsequently adjusted, discretizes M2/M5-brane torsion fluxes on a Schoen gyroid compactification of the 7 extra dimensions. The gyroid space group Γ=Ia̅d yields, via group cohomology H³ (ℤ₉, U (1) ) ℤ₉, exactly 9 inequivalent C-field torsion phases—the 9-fold torsion nodes. TMRB reproduces the Gaia DR3 phase spiral to <1% residual and delivers four simultaneous falsifiable predictions: (i) next galactic vertical wave crest at 180–280 Myr (peak ~230 Myr), ΔZ~+0. 6–1. 0 kpc; (ii) nano-g anomalies at 45 GPS coordinates (6. 29–8. 10×10−15 m s−2) ; (iii) four correlated channels on NASA QGGPf at 64 node crossings/day; and (iv) hierarchy ratio G₄/G₁₁= (5. 214±0. 12) ×10−40. These predictions share a single calibration parameter (ρ≈+0. 87), making the framework definitively falsifiable in any one channel