D.R.E.A.M. — Testable Predictions

S2 — Retention Law Confirmed

Claim. Interference-grade information decays with probe scale as a stretched exponential with kernel invariants \(\lambda_q\) and \(D_{\mathrm{eff}}\):

Why this rating. The live inter-domain demonstrator shows collapse across disparate datasets after rescaling by \(\lambda_q\); the standard transform is linear over a stable window, exposing a common \(\lambda_q\) and consistent slopes \(D_{\mathrm{eff}}\) for both HF-power and structural-correlation channels. (See Retention page.)

How to test (any instrument)

• Define a monotone smoother tied to resolution; compute \(R_{\mathrm{HF}}(\lambda)\) and/or \(R_{\mathrm{corr}^2}(\lambda)\).
• Fit \(y=\ln(-\ln R)\) vs \(\ln\lambda\); extract \(\widehat{D}_{\mathrm{eff}},\,\widehat{\lambda}_q\). Report CI + λ-window.
• Show cross-context collapse after rescaling by \(\widehat{\lambda}_q\).

Falsification. Persistent curvature in \(y(\lambda)\) after calibration; irreconcilable \(D_{\mathrm{eff}}\) across the two channels in the same context; failure of collapse under \(\lambda/\lambda_q\).

S3 — Cosmology & Fractal Spectrum Partially confirmed (strong support to S2)

Claim. The effective spectral exponent \(D_{\mathrm{eff}}\) governs retained-mode counts and the density of states; structure exhibits bounded fractality below the coherence cliff and flows toward homogeneity above it.

Why this rating. Survey-style trends (multiscale analyses, web-to-homogeneity behavior) and spectrum-page diagnostics align with S2’s prediction of bounded fractality and the flow to \(D\!\to\!3\) on large scales. We treat this as strong support for S2 but keep the rating “partial” pending harmonized, pre-registered pipelines across DESI/Euclid/LSST.

Program

• Exponents: fit \(D_{\mathrm{eff}}\) from retained-mode counting / spectral slopes across band-limited layers.
• Flow check: verify approach to homogeneity (counts \(\sim r^3\), correlation decay) above the cliff.
• Cross-checks: compare cosmology-inferred \(D_{\mathrm{eff}}\) to lab-inferred from S2 fits (same transform).

Falsification. Stable inconsistency between cosmology-inferred and lab-inferred \(D_{\mathrm{eff}}\); absence of homogeneity flow at large scales after systematics.

S5 — Strong Lensing Invariants Partially confirmed (early)

Claim. Under angular smoothing \( \lambda \), two retention channels behave as S2 predicts with a shared \(\lambda_q\): rapid HF-power loss vs. slower structural-correlation decay; the ring/arc skeleton (critical-set connectivity/parity) persists on CPI ridges as HF texture collapses.

Status. Early analyses show the two-channel split and approximate log-linear fingerprints consistent with a common \(\lambda_q\); broader, harmonized reductions are in flight.

Program

• VIS/NIR/mm cross-band λ-grid; fit both channels; show common \(\widehat{\lambda}_q\) and slopes.
• Summarize critical-set topology vs. \(\lambda\); map CPI ridges and their persistence.

Falsification. Divergent \(\widehat{\lambda}_q\) across bands for the same lens; lack of two-channel split; no CPI persistence signature.

S4 — Vacuum-Energy Modulation Open

Claim. Geometry-dependent variations of vacuum energy at \(\sim 10^{-8}\,\mathrm{eV}^4\) scale.

Program

• Fast-switch Casimir geometries; differential readout.
• Precision atomic spectroscopy vs. engineered mode densities.
• Optomechanics in tailored cavities.

Falsification. Null modulation \(\lesssim 10^{-10}\,\mathrm{eV}^4\) across ≥3 distinct setups.