Evidence & Predictions
What the model predicted, what Stage 3 testing returned, and what that rules out. For the derivations behind these numbers, see the Framework page.
Predictions and the Stage 3 verdict
| Observable | ΛCDM says | We predicted | Data shows | Stage 3 verdict |
|---|---|---|---|---|
| σ₈ (clustering amplitude) | 0.811 | ≈ 0.76 ± 0.03 | 0.76–0.79 | Alone only reachable alone |
| S₈ (weak lensing) | 0.83 | ≈ 0.78 ± 0.03 | 0.76–0.79 | Alone only reachable alone |
| Lyman-α k-cutoff | none | k_c ≈ 0.75 h/Mpc | suppression observed | Alone only reachable alone |
| S₈ AND Lyman-α together | — | both from one T(k) | both confirmed | Failed mutually exclusive |
| G_eff during leakage | G_N | ≈ 0.75 G_N | unconstrained | Not decisive not independently probed |
| CMB acoustic peaks | fit | unchanged | Planck fit | Preserved preserved |
| Damping-tail suppression | 0% | 1–3% | pending CMB-S4 | Not decisive moot given exclusion |
Rows 1–3 were the v1.8.3 successes. Row 4 is what Stage 3 added, and it is the row that decides the model.
Predictions by Confidence Tier
- • The 5D Einstein–Gauss-Bonnet solution is valid (residual < 6×10⁻⁶).
- • Holographic entanglement entropy uniquely fixes T(k).
- • The k^(−1/2) scaling follows from geometry, not from fitting.
Checked numerically and reproducible from the published code. This part of the work stands.
- • CAMB pipeline validated against ΛCDM baselines before use.
- • Constraints imposed jointly rather than one at a time.
- • Full data files and scripts published for replication.
The methodology is the durable output of Stage 3, independent of the verdict it returned.
- • A monotonic power-law T(k) satisfying both S₈ and Lyman-α.
- • σ₈ = 0.76 ± 0.03 alongside the Lyman-α cutoff depth.
- • The mechanism as a joint explanation of both tensions.
Excluded by direct CAMB testing. The two constraints sit about a decade apart in wavenumber and cannot be met by one monotonic function.
Falsification Criteria
Triggered (v1.9.0): the joint constraint at k ≈ 0.5–5 h/Mpc failed under direct CAMB testing. The criteria below were published in advance and are kept here unchanged.
- ◇ Precise linear P(k) at k ≈ 0.5–1 h/Mpc shows standard ΛCDM with no cutoff.
- ◇ σ₈ measured higher than ΛCDM (wrong sign of the effect).
- ◇ Lyman-α forest shows no small-scale suppression.
- ◇ Growth rate f(z) matches ΛCDM exactly.
- ◇ CMB damping-tail suppression > 5% (too large).
- ◇ PIXIE-class spectral-distortion measurement rules out any H(z) deviation near z ≈ 50,000.
Publishing these in advance is what made the negative result meaningful rather than negotiable.
Validation Roadmap — where each stage landed
- 1CompletedCompleteStage 1: Boltzmann code validation
CAMB/CLASS patched with the modified G_eff(z) and validated against ΛCDM baselines. Pipeline sound.
- 2CompletedCompleteStage 2: Alternative-model comparison
Compared against Warm and Fuzzy Dark Matter and other small-scale suppressors; the same wavenumber-gap constraint applies to any monotonic suppressor.
- 3Completed — negative resultCompleteStage 3: First-principles 5D derivation and test
Brick 4 derived holographically rather than fitted, then tested. Derivation succeeded; the joint observational test failed. This is the falsification.
- 4OngoingActiveStage 4: Resurrection-path investigation
Paths A, B, and C under consideration, with Path C (partially-coupled dark matter) receiving the current effort. Speculative, not yet derived.
Observations that still matter (2027–2029)
These surveys no longer test this mechanism — they test whatever replaces it, and they will sharpen the constraint that excluded it.
- • CMB-S4: damping-tail precision at the percent level.
- • Euclid: weak-lensing S₈ to 1% precision.
- • DESI Lyman-α: cutoff shape extraction from the forest.
- • Roman: high-z galaxy-cluster growth history.