10. FALSIFICATION MATRIX

Philosophy: A theory that cannot be proven wrong is not science. We provide specific, testable predictions with definite timelines.

10.1 Tier 1: Decisive Tests (2027-2035)  LiteBIRD Falsification (Revised)

The SBF makes a single, non-negotiable prediction that allows for the decisive rejection of the core mechanical hypothesis: the CMB Sawtooth Signature.

The vacuum's attempt to crystallize, driven by geometric frustration, imposes specific topological constraints on the initial B-mode power spectrum. The SBF predicts a unique, highly non-Gaussian set of resonant peaks at multipoles $\ell=4$ and $\ell=6$ that cannot be recovered by any standard inflationary or $\Lambda$CDM model.

10.3.1 Operational Constraints and Falsification Criteria

While this prediction is theoretically absolute, its measurement is subject to practical astrophysical constraints.

• Astrophysical Noise: The primordial B-mode signal is severely contaminated by Galactic foregrounds (dust polarization, synchrotron radiation) and secondary B-modes (gravitational lensing). Successful detection depends critically on the robustness of component separation techniques utilizing LiteBIRD's 15 frequency bands.

The Falsification Bar: The predicted sawtooth signature is a Unique Spectral Necessity of the SBF. An ambiguous result would not immediately invalidate the SBF, as the signal may be obscured by noise. However, if the final, fully-processed LiteBIRD data definitively excludes the presence of the predicted $\ell=4$ and $\ell=6$ peaks at the required amplitude (i.e., ruling out the SBF signal within measurement uncertainty), the core topological-mechanics hypothesis of the Single Bulk Framework would be definitively falsified. 

This is the PRIMARY test. Results by 2035 will settle the framework.

10.1.2 LIGO Gravitational Wave Echoes

(Prediction Retained: Echoes at $\Delta t \approx 2R_s/c$)

Current Observational Status (O3/O4):

Comprehensive searches in LIGO/Virgo O3 and O4 data have yielded no statistically significant evidence for post-merger echoes. While tentative signals were claimed in events like GW150914, subsequent Bayesian analyses indicate these are consistent with instrumental noise (p-values > 0.1).

The SBF Interpretation: The Impedance Gradient Defense

The absence of loud echoes does not necessarily falsify the crystalline core, but it does constrain the sharpness of the phase boundary.

• The Hard Wall Fallacy: Standard echo models assume a step-function discontinuity in impedance (a perfect "hard wall" mirror) at the horizon.

• The Granular Reality: In a physical phase transition (liquid $\to$ crystal), the boundary is rarely a mathematical step function. It is likely a structured gradient or "mushy zone" of intermediate stiffness.

• Mechanism: If the width of this transition layer $\delta r$ is comparable to the gravitational wavelength ($\delta r \sim \lambda_{GW}$), the impedance mismatch is smoothed out. This drastically suppresses the reflection coefficient ($\mathcal{R} \ll 1$), rendering echoes effectively invisible to current detectors ($SNR < 8$) while maintaining the crystalline core structure.

Updated Falsification Criteria (O5 Era):

The upcoming O5 run (2027) will increase sensitivity by factor $\sim 2$.

• Soft Falsification: If O5 detects no echoes, the "Hard Wall" limit is ruled out.

• Hard Falsification: If SBF is correct, the impedance gradient cannot be infinite. We predict that with $SNR > 100$ (expected in 3G detectors like Cosmic Explorer), even "soft" boundaries must produce detectable residuals. A null result at $3G$ sensitivity would definitively falsify the material core hypothesis.

10.1.3 Fourth Generation Exclusion

Prediction: No stable lepton with M > M_τ can exist (N = 7 forbidden).

Current Status: LHC has excluded 4th generation up to ~1 TeV.

Falsification: If 4th generation lepton is discovered at any mass, knot topology model fails.

Confidence: High (this is unlikely to falsify SBF given current limits).

10.2 Tier 2: Medium-Term Tests (2025-2040)

10.2.1 Entanglement Gravitational Mass

Timeline: 2030-2040 (technology development needed)

Prediction:

Flux tube connecting entangled particles has mass: $$M_{tube} \approx \frac{\hbar}{c^2} \cdot \frac{d}{L_P}$$

For d = 1000 km (satellite entanglement): $$M_{tube} \approx 10^{-18} \text{ kg}$$

Detection Strategy:

• Entangle macroscopic masses (10⁻¹⁰ kg optomechanical resonators)

• Separate by km-scale distances (satellite links)

• Measure gravitational strain with precision gravimeters

Sensitivity Required: ~10⁻¹² g (near current limits)

Falsification:

If experiments achieve required sensitivity and find no gravitational signature (null to within 10× prediction), flux tubes are not physical.

10.2.2 Neutrino Mass Sum

Prediction: $$\Sigma m_\nu < 0.12 \text{ eV}$$

(from void network scaling, Section 4.4)

Current Limits:

• Planck + BAO: Σm_ν < 0.12 eV

• KATRIN direct: m_ν < 0.8 eV

Future:

• KATRIN Phase 2: ~0.2 eV sensitivity (2025-2027)

• Project 8: ~0.04 eV sensitivity (2030+)

Falsification: If Σm_ν > 0.12 eV confirmed, void network mass scale is wrong.

10.2.3 Galactic Breathing Modes

Prediction (negative): Dark matter halos should NOT show oscillations (breathing modes).

Reason: Plastic deformations (ghost dents) don't oscillate - they're permanent unless re-stressed.

Test: Long-term monitoring of galaxy mergers, intracluster gas dynamics.

Falsification: If breathing modes are observed, the plastic vacuum model fails.

10.3 Tier 3: Long-Term Tests (2040+)

10.3.1 Generalized Uncertainty Principle (GUP)

Prediction:

At energies E > 1 TeV, pixelation effects become measurable: $$\Delta x \cdot \Delta p \geq \frac{\hbar}{2}\left[1 + \beta\left(\frac{\Delta p}{m_P c}\right)^2\right]$$

where β ~ (L_P/λ_C)² (lattice spacing / Compton wavelength).

Test: Future colliders (FCC at 100 TeV) or precision interferometry.

Falsification: If no GUP deviations are observed up to Planck energy, the discrete lattice model is wrong.

10.3.2 W/Z Boson Substructure

Prediction:

W and Z bosons are transition states (Section 7.3), not fundamental. At E > 10 TeV, they should show:

• Anomalous form factors (deviation from point-like)

• Internal excitations (resonances)

Test: Future Circular Collider (FCC-hh) at 100 TeV.

Falsification: If W/Z remain point-like at all accessible energies, they may be truly fundamental.

10.3.3 The Planck Magnetic Yield Limit ($B_{max}$)

Prediction:

Unlike standard electrodynamics, which allows for arbitrarily high field strengths, SBF predicts a hard upper limit imposed by the mechanical yield stress of the vacuum lattice.

The magnetic energy density $U_B = B^2 / (2\mu_0)$ corresponds to physical shear stress. When this stress exceeds the vacuum's Mohr-Coulomb yield point ($\tau_{yield} \approx F_P/L_P^2$), the lattice undergoes plastic flow (liquefaction).

$$B_{max} \approx \sqrt{2\mu_0 \tau_{yield}} \approx 10^{53} \text{ T}$$

Observable Consequence:

Fields exceeding $B_{max}$ are physically impossible; they would result in the local "melting" of spacetime into a non-transmissive fluid state.

• Consistency Check: The strongest known magnetic fields in the universe (Magnetars) reach $\approx 10^{11}$ T. This is safely 42 orders of magnitude below the yield limit, explaining why vacuum breakdown is not routinely observed.

• Falsification: If primordial cosmology or high-energy collisions reveal stable field configurations exceeding $10^{53}$ T without vacuum decay, the granular yield model is falsified.