Energy-Flow Cosmology (EFC) — Stage-IV Data Roadmap
Morten Magnusson · Symbiose Research, Sandnes, Norway ·
ORCID: 0009-0002-4860-5095 ·
April 2026 · CC-BY-4.0
What is Energy-Flow Cosmology? A 60-second version.
Today's standard picture of the universe says 95% of it is made
of two invisible ingredients — dark matter and
dark energy — neither ever detected in a laboratory.
EFC proposes a simpler alternative: gravity adjusts itself where
disorder (entropy) is still building up, and behaves like ordinary Einstein
gravity everywhere else. One mechanism, two numbers, no invisible
particles required.
The difference is ontological, not parametric. ΛCDM treats
spacetime as a fixed stage with dark matter + dark energy as ingredients. EFC
treats energy and entropy as primary — spacetime, gravity, and time
itself (an index over irreversible Grid transitions) emerge from them. The
"dark" sector is not a set of missing particles; it is a consequence of how
a single-regime observer reads cross-regime physics. See the
Pitch for the full
side-by-side.
This roadmap lists the next-generation surveys that will decide whether EFC
survives or falls. Each row is a kill criterion frozen before the
relevant data arrives, so no result can be back-fitted.
Ledger for the
121 tests registered (103 active, 93 survived, 10 falsified, 18 in pipeline).
One sentence: This roadmap maps every major Stage-IV data release (2026–2031+) to the specific EFC prediction, observable, regime, and kill criterion it will test — so that no result arrives without a pre-registered expectation.
0. Purpose and Governance
The Ledger documents what has been tested.
The White Paper documents what EFC predicts.
This roadmap documents when and how those predictions will be confronted with data.
The Background No-Go Theorem establishes why all predictions are in the perturbation sector, not the background.
Governance rule: All entries in this roadmap are frozen at the time of publication.
No post-hoc addition of tests after data release is permitted.
New tests may be added to future versions of this roadmap before the relevant data becomes public.
Additions are versioned and timestamped.
0.1 Notation and Conventions
| Symbol |
Definition |
Domain |
| μ(k,z) |
Effective gravitational coupling (Poisson equation modifier). μ = 1 is GR. EFC perturbation sector: μ ≈ 0.94. |
Perturbations (L1–L2) |
| Σ(k,z) |
Lensing potential modifier. Σ = 1 is GR. EFC: Σ ≈ 1.05. |
Lensing (L1–L2) |
| η |
Gravitational slip: η ≡ Φ/Ψ. η = 1 is GR. EFC: η ≈ 1.10. |
Perturbations (L1) |
| β |
Entropy-gradient coupling strength. β ≈ 0.16 from SPARC (galactic); βcosm ≈ 1.0 (cosmological). |
All regimes |
| S(a) |
Entropy field, S ∈ [0, 1]. Fundamental scalar in EFC. |
All regimes |
| T(a) |
Regime transition function. Controls when background coupling activates. |
Background (L0–L2) |
| αL2 |
Integrated growth-sector coupling amplitude. Sealed: α = −0.689 (v1), −0.702 (v2). |
Growth (L1–L2) |
| Θ(ρ) |
Density saturation function. Θ → 0 at high density (Solar System); Θ → 1 at low density (cosmological). |
Screening (L2–L3) |
| k |
SPARC screening exponent: k = 0.415 ± 0.029 (174 galaxies). |
Galactic (L2) |
| ξ, ηreg |
Regime coordinates: ξ ≡ |∇Φ|/a₀ (gradient); ηreg ≡ μΛΦ/|∇²Φ| (screening). See Ledger. |
All regimes |
| L0–L3 |
Regime levels: L0 = early-universe linear; L1 = late-time linear; L2 = non-linear; L3 = strong-field. |
Classification |
Statistical conventions
All significance levels (σ) in this document are frequentist,
computed as √Δχ² for nested models or as the equivalent Gaussian significance
of a p-value for non-nested comparisons. Unless stated otherwise, tests are
two-sided except where a directional prediction is specified
(e.g., μ < 1, α < 0), in which case one-sided significance is reported and
explicitly marked. Model comparison uses Δχ² and ΔAIC as primary metrics;
Bayesian evidence ratios (ln B) are reported where available but are not used
as primary decision criteria due to prior sensitivity.
1. Survey Timeline Overview
| Survey / Instrument |
Data Release |
Expected Date |
Key Content for EFC |
| DESI |
DR2 (cosmology chains) |
2025 Oct (released) |
BAO (14M galaxies+QSOs, 3 yr); w₀waCDM constraints |
| DESI |
DR2 (full spectra + redshifts) |
2026 H2 |
Full-shape P(k); RSD fσ8 multi-epoch; Lyα forest |
| Euclid |
Q2 (Quick Release 2) |
2026 Jun 24 |
Galactic bulge survey; calibration; cross-match with Roman precursor |
| Euclid |
DR1 |
2026 Oct 21 |
~2100 deg² weak lensing; photometric redshifts; cosmic shear; galaxy clustering; first dark energy constraints |
| Rubin/LSST |
DP2 (Data Preview 2) |
2026 Jul–Sep |
LSSTCam commissioning data; deep drilling fields; transient alerts |
| Rubin/LSST |
Alert stream (live) |
2026 Feb (active) |
Real-time transients; void identification precursors |
| Planck + ACT DR6 + SPT-3G |
CMB lensing 2026 baseline |
2026 (available) |
S8CMB = 0.836 ± 0.012 (Qu et al. 2026, SNR = 61) |
| JWST |
Cycle 4 observations |
2026 (ongoing) |
Cluster κ maps (Bullet, Abell 2146); high-z galaxy abundances; void lensing |
| DESI |
DR3 (full 5-year) |
~2027–2028 |
Full-shape + RSD joint; neutrino mass; fσ8 trajectory z = 0.02–1.5 |
| Euclid |
DR2 |
~2028 |
First 3 years; ~7000 deg²; tomographic cosmic shear; galaxy clustering; gravitational slip η; EG statistic |
| Rubin/LSST |
DR1 |
~2028 Jun |
First full year; 18000 deg² southern sky; shear catalogue; void catalogues; cluster abundance N(M,z) |
| Roman |
Early observations |
~2027–2028 |
High-z SNe Ia; complementary weak lensing; BAO independent check |
| KiDS |
Legacy (final) |
~2027 |
Resolves DES vs KiDS S8 bifurcation; definitive Stage-III reference |
| SPT-3G / ACT DR7 |
Next-gen CMB lensing |
~2027–2028 |
Improved Cℓφφ; AL degeneracy resolution; independent η constraint |
| Euclid |
DR3 (final) |
~2030–2031 |
Full 14000 deg²; definitive w₀, wa; μ–Σ joint; η to 1% precision |
| Rubin/LSST |
DR2–DR5 |
2029–2034 |
Cumulative depth; small-scale non-linear structure; void ISW stacking |
| DESI |
Final legacy |
~2029 |
40M redshifts; definitive RSD trajectory; BAO anisotropic split |
CMB-S4 → Simons Observatory |
SO science data / LiteBIRD (2032+) |
SO: ~2026–2028; LiteBIRD: 2032+ |
CMB-S4 cancelled July 2025. SO LAT operational (first light Feb 2025): CMB lensing, E/B polarisation, ISW. LiteBIRD: primordial B-modes, full-sky τ. |
| Einstein Telescope |
Design / early |
2030s |
Standard sirens: propagation-sector test (GW vs EM distances) |
| SKA |
Early science |
~2029–2030 |
HI intensity mapping; independent BAO; cosmic dipole test |
2. Prediction × Data Matrix
Each row maps a specific EFC prediction to the dataset that will test it, the observable, the quantitative pass/fail criterion, and the pipeline readiness status.
2.1 Kill Criteria (KC1–KC5) — Stage-IV Falsification Tests
Thresholds frozen before data release. No post-hoc adjustment permissible.
Defined in White Paper.
| KC |
Criterion |
Trigger |
Primary Dataset |
Expected Date |
Pipeline Status |
| KC1 |
Growth suppression absent |
|αL2| < 0.1 at 3σ |
DESI DR3 full-shape + RSD |
~2027–2028 |
PIPELINE NEEDED Full-shape likelihood |
| KC2 |
Wrong fσ8 trajectory |
|zcross − 2.042| > 3σ |
DESI DR3 RSD multi-epoch |
~2027–2028 |
SEALED Freeze v1 hash: 7a850cfa... |
| KC3 |
S8 converges to ΛCDM |
S8 = S8,ΛCDM ± 0.005 |
Euclid DR1 cosmic shear + CMB lensing 2026 |
2026 Oct |
P3 PASS on DES Y6 (0.3σ); Euclid will arbitrate |
| KC4 |
Perturbation-sector signature absent |
μ > 1 detected OR Σeff(z) monotonic OR EGobs/EGGR = 1.00 ± 0.01 (all at >3σ) |
Euclid DR1 tomographic shear; SO × Euclid DR2 EG |
2026 Oct (DR1) — 2028 (DR2) |
SEALED Perturbation sector (32037990: μ < 1 structurally robust, Σeff(z) crossover at z ≈ 0.44), EG pre-registration (32023788), Rubin DP2 cosmic shear (32013738), μ–Σ eigenmode (31990194) |
| KC5 |
No dynamical dark energy |
|w₀ + 1| < 0.02 (Euclid) |
Euclid DR1/DR2 + DESI DR3 joint |
2026–2028 |
DESI DR2 shows 2.3σ preference for w₀waCDM; monitoring |
2.2 Sealed Blind Predictions
| Prediction | Value | Hash | Test Dataset | Expected Date |
|---|
| SEALED v1 αL2 | −0.689 | 7a850cfa... | DESI DR3 fσ8 + BAO joint | ~2027–2028 |
| SEALED v1 fσ8 crossover | z = 2.042 | 7a850cfa... | DESI DR3 Lyα + high-z RSD | ~2027–2028 |
| SEALED v2 αL2 | −0.702 | dbccda15... | DESI DR3 fσ8 + BAO joint | ~2027–2028 |
| SEALED v1 DH/rd(z=1.0) | EFC: 16.527 vs ΛCDM: 17.466 (3.1σ) | 7a850cfa... | DESI DR3 BAO anisotropic | ~2027–2028 |
| SEALED v1 DH/rd(z=0.7) | EFC: 19.797 vs ΛCDM: 20.719 (2.3σ) | 7a850cfa... | DESI DR3 BAO anisotropic | ~2027–2028 |
| SEALED v1 fσ8(z=0.7) | EFC: 0.430 vs ΛCDM: 0.449 (2.0σ) | 7a850cfa... | DESI DR3 RSD | ~2027–2028 |
| ↑ Formal DOI publication of all three sealed predictions: 32013156 (Magnusson 2026, NUTS sampler, T1 pre-registered) |
2.3 Action-Level Falsification Conditions (FA1–FA6)
Defined in the EFC Relativistic Action (31876324).
These govern the perturbation sector and supersede phenomenological F7.
| FA | Condition | Primary Dataset | Expected Date | Notes |
|---|
| FA1 | cT ≠ c at any redshift | LIGO/Virgo/KAGRA O5; Einstein Telescope | 2027+ / 2030s | Currently PASS (GW170817) |
| FA2 | μ > 1 in linear cosmological regime | Euclid DR1/DR2 tomographic growth | 2026–2028 | EFC predicts μ ≈ 0.94 in survival valley |
| FA3 | Σ < 1 in perturbation sector | Euclid DR2 cosmic shear Cℓ | ~2028 | EFC predicts Σ ≈ 1.05 |
| FA4 | η = 1 to sub-percent precision | Euclid DR2/DR3 (EG + lensing×RSD) | 2028–2031 | EFC predicts η ≈ 1.10 |
| FA5 | No GR screening in high-density | Solar System (Cassini, LLR) — already constrained | Ongoing | Currently PASS; future: LISA Pathfinder legacy |
| FA6 | Ghost / tachyon instability detected | Theoretical / numerical (ADM Hamiltonian) | N/A | Currently PASS at 2nd order; full non-linear pending |
2.4 Standing Falsification Conditions (F1–F6)
| F | Condition | Primary Dataset | Expected Date | EFC Prediction |
|---|
| F1 | AISW = 1.00 ± 0.02 (tracer-independent) | DESI DR2/DR3 × Planck CℓTg | 2026–2028 | EFC: AISW ≈ 0.89 ± 0.03 |
| F2 | No RSD deviation from ΛCDM across z = 0.02–1.5 | DESI DR3 multi-epoch RSD | ~2027–2028 | EFC: monotonic suppression via β·T(a) |
| F3 | Cluster lensing asymmetry absent (Asig = 0) | JWST κ maps (Bullet, Abell 2146) | 2026–2027 | EFC: directional residual from entropy coupling |
| F4 | Full-shape P(k) inconsistent with background-only growth | DESI DR3 full-shape likelihood | ~2027–2028 | EFC: background channel primary; scale-dependent if μ(k,z) active |
| F5 | Graph-AQUAL fails rotation curve diversity | SPARC + MaNGA joint likelihood (ongoing) | Incremental | EFC: regime-dependent EBE with k = 0.415 |
| F6 | Λ-locked screening produces growth instability | Numerical (N-body + Λ-lock) | Incremental | EFC: stable under Λ-lock (CGS pass) |
2.5 Specific Observational Predictions (Awaiting Data)
| Prediction | EFC Value / Expectation | Primary Dataset | Expected Date | Regime | Reference |
|---|
| Void ISW sign-flip | Cold→hot for δ ≲ −0.8; turnover near δ ≈ −0.7 | Rubin DR1 void catalogue × Planck/ACT CMB | ~2028 | L1–L2 | 31942677 |
| Cosmic dipole excess | ~2% entropy gradient → directional Geff | Rubin DR1 + SKA early science number counts | 2028–2030 | L1 | 31942731 |
| Regime transition μ<1 ↔ μ>1 | Cluster-scale μ ≈ 1.1, Σ ≈ 1.2; no μ>1 in linear | Euclid DR2 cluster lensing + Rubin DR1 | ~2028 | L2–L3 | 31941543 |
| Dynamical dark energy w(a) ≠ −1 | w(a) = −β(S)·a; KC5 test | Euclid DR1/DR2 + DESI DR2/DR3 BAO joint | 2026–2028 | L1–L2 | WP Part 4 |
| Cross-scale amplification βcosm/βgal ≈ 6.25 | Susceptibility T(S) links SPARC → cosmic shear | Euclid DR2 tomographic shear × SPARC Phase 3 | ~2028 | L2 | WP Part 4 |
| AL degeneracy resolution | Physical Σ>1 distinguishable from phenomenological AL>1 | Euclid DR2 galaxy lensing + CMB lensing + fσ8 | ~2028 | L0–L1 | 31368433 |
| Lensing-to-CMB S8 ratio (P3 replication) | 0.95 ± 0.03 (pre-registered); DES Y6 PASS at 0.3σ | Euclid DR1 cosmic shear / CMB lensing 2026 | 2026 Oct | L1–L2 | 31951992 |
| Standard sirens (GW vs EM distance) | Propagation-sector β-split test | Einstein Telescope / LISA | 2030s | PROP | 31305421 |
| SMBH thermostat: AGN decline drives S(z) sigmoid | S(z) transition at z ~ 1 tracks AGN luminosity density | JWST + eROSITA AGN catalogue | 2027–2029 | L2 | 31942734 |
| Cluster abundance N(M,z) | Mass function evolution discriminates EFC vs ΛCDM | eROSITA + Euclid DR2 + Rubin DR1 | ~2028 | L2–L3 | Method defined |
| EG(k,z) scale-localised bump | ~7% excess at kc = 0.05 h/Mpc from band-pass stiffness R(k,a); testable at 2.5–3.5σ | DESI DR3 × Planck lensing (EG estimator) | ~2027–2028 | L1–L2 | 31985313 |
| Lensing crossover Σeff(z) | Sign-changing tomographic response: Σeff > 1 at z < 0.4 (+2.6% at z=0.10), crossover at z ≈ 0.44, Σeff < 1 at z > 0.5 (−1.5% at z=1.21). Non-monotonic, distinctive within MG model class. | Euclid DR1 tomographic cosmic shear (6 bins over 0.2–1.4) | 2026 Oct | L1–L2 | 32037990 |
| Structural signature μ < 1 ∧ Σ ≥ 1 | Growth suppression (μ < 1) with lensing enhancement (Σ ≥ 1), strongly disfavored in standard QS Horndeski with αT=0 (numerical scan, 135k points). Enabled by λ-constraint anisotropic stress. | Euclid DR1 μ–Σ tomography; SO × Euclid EG | 2026–2028 | L1–L2 | 32037990 |
3. Statistical Evaluation Framework
3.1 Likelihood and Model Comparison
| Element | Specification |
|---|
| Likelihood form | Gaussian likelihood assumed for all Stage-IV probes unless survey documentation specifies otherwise. For cosmic shear: L ∝ exp(−½ ΔdT C−1 Δd) where d is the data vector and C the covariance. |
| Data vectors | Probe-specific: shear Cℓ (Euclid); P(k) multipoles + BAO (DESI); fσ8(z) (RSD compilation); CMB lensing Cℓφφ (Planck/ACT/SPT). Each data vector is defined by the survey collaboration. |
| Covariance | Survey-provided covariance matrices are used in all cases. EFC does not introduce independent covariance estimates. Where survey covariance is unavailable, Fisher matrix projections from official survey specifications are used and explicitly flagged. |
| Model comparison | Primary: Δχ² between EFC and ΛCDM. Secondary: ΔAIC = Δχ² + 2Δk. Bayesian evidence (ln B) reported where available but not used as primary criterion. |
| Parameter handling | EFC parameters (β, T(a), zt) are frozen in the Global Parameter Registry (Ledger). Standard cosmological parameters (Ωm, H₀, σ8, ns) are marginalised over with Planck 2018 + BAO priors unless stated otherwise. No probe-specific re-tuning is permitted. |
| Threshold interpretation | Kill criteria (KC) are evaluated as: if the best-fit EFC parameter falls within the stated null range at the stated confidence level, the sector is falsified. The confidence level is determined by the posterior width from the survey likelihood, not by an EFC-internal estimate. |
3.2 Specific Threshold Definitions
| Criterion | Observable | Null hypothesis (ΛCDM) | EFC prediction | Evaluation method |
|---|
| KC1 | αL2 | α = 0 | α ≈ −0.7 | Posterior from DESI DR3 fσ8 + BAO joint likelihood; falsified if 99.7% CI includes zero |
| KC2 | zcross | No crossover | z = 2.042 | Profile likelihood on fσ8(z) trajectory; falsified if |zcross − 2.042| > 3σsurvey |
| KC3 | S8 ratio | S8lens/S8CMB = 1 | 0.95 ± 0.03 | Ratio of Euclid DR1 S8 to CMB lensing 2026 baseline; falsified if ratio = 1.000 ± 0.005 |
| KC4 | η − 1 | η = 1 | η ≈ 1.10 | EG statistic from Euclid DR2 lensing×RSD; falsified if |η − 1| < 0.01 at 3σ |
| KC5 | w₀ + 1 | w₀ = −1 | w₀ ≠ −1 | Euclid + DESI BAO joint posterior; falsified if |w₀ + 1| < 0.02 at 3σ |
4. Systematics Control
The governing principle is: EFC uses survey-provided systematics budgets and does not
introduce its own nuisance parameters beyond those in the Global Parameter Registry.
| Observable | Dominant Systematics | Handling | Reference |
|---|
| S8 (cosmic shear) | Intrinsic alignments (IA); shear calibration bias (m); photometric redshift errors (Δz) | Marginalised using survey-provided IA model (NLA or TATT) and m/Δz priors from Euclid calibration pipeline. EFC Case A test verified: not IA compensation (IA=0 gives 63% persistence); not just amplitude (Δ=41 residual after As tuning). | 31271917 |
| fσ8 (RSD) | Galaxy bias model; fibre collisions; RSD modelling | Uses DESI/BOSS official pipeline. MVP-G1 LOO robustness demonstrated: signal stable across all 7 folds (spread = 0.23 in α). | 31332730 |
| CMB lensing | Beam systematics; foreground residuals; noise bias | Baseline fixed by Planck/ACT/SPT collaboration. EFC does not modify the reconstruction pipeline. | Qu et al. 2026 |
| BAO | Reconstruction method; template fitting; fiducial cosmology | Uses survey-provided consensus measurements with full covariance. BAO covariance-aware test passed (Δχ² = −3.0). | 31314922 |
| P(k) full-shape | Baryonic feedback; non-linear modelling; shot noise | Scale cuts applied following survey specifications (kmax ≈ 0.20–0.25 h/Mpc). See §6 for degeneracy. | Method defined |
| ISW | Tracer bias; foreground contamination | EFC prediction (AISW ≈ 0.89) is tracer-independent by construction. | 31329082 |
| Void ISW stacking | Void finder algorithm; aperture photometry | Depth-binned protocol pre-specified. Sign-flip is qualitative (cold→hot for δ ≲ −0.8). | 31942677 |
| Cluster κ maps | PSF modelling; source redshift distribution | Pre-registered directional residual estimator (Asig) insensitive to azimuthally symmetric systematics. | Methodology locked (2026) |
| Solar System (PPN) | Spacecraft systematics; ephemeris model | Cassini/LLR constraints taken as published. Density Saturation ensures Θ(ρ) → 0 at solar densities. | 31244827 |
5. Blinding and Analysis Protocol
5.1 Prediction Integrity
| Element | Implementation |
|---|
| Sealed predictions | Two cryptographic freezes (SHA-256) deposited before data release. Hash 7a850cfa... (2026-02-18) and dbccda15... (2026-02-21). Full parameter sets recoverable from hash verification. |
| Kill criteria frozen | KC1–KC5 thresholds defined in White Paper and deposited via Figshare DOI (31970904) before any Stage-IV data release. |
| Parameter freeze | Global Parameter Registry (Ledger) governs all shared parameters. No parameter may be modified between prediction deposit and analysis completion. |
5.2 Analysis Execution
| Element | Implementation |
|---|
| Pipeline versioning | All analysis code maintained in github.com/supertedai/EFC. Git commit hash recorded at analysis time. No code modifications after data unblinding. |
| Survey pipelines | Official pipeline version used without modification. Version and configuration documented. |
| No post-hoc tuning | After unblinding, prohibited: (i) modifying EFC parameters, (ii) changing scale cuts, (iii) switching likelihood forms, (iv) adding/removing probes. If necessary, restart as exploratory analysis (clearly labeled). |
| Reporting obligation | All results — including failures — reported in the Ledger within one revision cycle. Suppression prohibited under Core Lock v1.0. |
6. Degeneracy and Discriminant Structure
The key discriminant is that EFC predicts a specific combination of μ < 1, Σ > 1, and η ≈ 1.10 simultaneously — a pattern rare or absent in competing models.
6.1 What Can Mimic EFC
| Competing Effect | Mimics Which EFC Signal | Where It Fails | Discriminating Observable |
|---|
| Massive neutrinos | Growth suppression (lower σ8/S8) | η = 1 exactly; scale-dependent; no galactic RAR | η via EG (KC4); scale-dependence of fσ8(k); SPARC |
| Baryonic feedback | P(k) suppression; lower S8 | Confined to k > 0.5 h/Mpc; no ISW; η = 1 | Scale cuts; ISW (F1); gravitational slip (KC4) |
| f(R) gravity | μ ≠ 1; modified growth | μ > 1 (wrong sign); Σ = μ; different screening | Sign of μ (FA2); μ vs Σ (Euclid DR2) |
| Horndeski / EFT of DE | General μ(k,z), Σ(k,z) | Standard QS Horndeski with αT=0: μ < 1 ∧ Σ > 1 strongly disfavored (numerical scan, 135k points finds max Σ=0.989 when μ<0.99; see 32037990). EFC’s λ-constraint mechanism is structurally distinct. | Joint μ–Σ (Euclid DR1/DR2); tomographic Σeff(z) sign change |
| w₀waCDM | Modified expansion; BAO shifts | μ = Σ = η = 1 in perturbations | Perturbation-sector: fσ8, EG, void ISW |
| Phenomenological AL > 1 | Enhanced CMB lensing | No perturbation-sector origin; no additional predictions | Galaxy lensing + fσ8 joint; see 31368433 |
6.2 The EFC Discriminant Signature
| Property | EFC | Massive ν | f(R) | Horndeski (QS, αT=0) | w₀waCDM |
|---|
| μ < 1 (structural) | ✓ Robust (100%) | — | ✗ (μ > 1) | ✗ Disfavored by scan | — |
| Σ ≥ 1 (with μ < 1) | ✓ Semi-robust (61%) | — | ✗ (Σ ≈ μ) | ✗ Disfavored by scan | — |
| Σeff(z) sign change at z≈0.44 | ✓ Non-monotonic | ✗ | ✗ | Distinctive within class | ✗ |
| Void ISW sign-flip | ✓ | ✗ | ✗ | ✗ | ✗ |
| Galactic RAR | ✓ (k = 0.415) | ✗ | Partial | ✗ | ✗ |
Bottom line: The structural signature μ < 1 ∧ Σ ≥ 1 combined with a non-monotonic Σeff(z) crossover at z ≈ 0.44 (32037990) is the most distinctive observational test within the current MG model class. Euclid DR1 tomographic cosmic shear (October 2026) is the decisive instrument: percent-level sensitivity over 0.2 < z < 1.4 is exactly the regime where the predicted crossover lives. Earlier framing emphasised η ≈ 1.10 as a point prediction; structural analysis shows that value is fragile at ±20% parameter variation (0% robustness) while the μ < 1 signature survives.
7. Failure Response Protocol
| Level | Conditions | Consequence if Triggered | Scope of Revision |
|---|
| Kill Criterion (KC) | KC1–KC5 | Hard falsification of the specified sector. Formally abandoned. Documented in Ledger within one revision cycle. | Sector-specific: KC1 kills growth; KC3 kills S8 channel; etc. |
| Action-Level (FA) | FA1–FA6 | Theory-level rejection of the Relativistic Action. Must be revised or replaced. | Perturbation sector only. Galactic sector unaffected. |
| Standing Falsification (F) | F1–F6 | Tension / revision trigger. Framework may survive if other channels compensate. | Channel-specific. |
7.1 Compound Failure Rules
| Scenario | Interpretation |
|---|
| 1 KC triggered, others pass | Sector falsified. Remaining framework viable but reduced. Documented as partial falsification. |
| 2+ KC triggered | Framework-level crisis. Perturbation sector abandoned if growth + lensing + slip all fail. |
| KC passes but FA fails | Empirical signal survives but derivation wrong. Action must be revised. |
| All KC pass, all FA pass | Confirmation ladder advances. Survival, not proof. |
| Sealed prediction within 1σ | Strong support. Reported as pre-registered confirmation. |
| Sealed prediction within 2σ | Consistent. No action required. |
| Sealed prediction beyond 3σ | Prediction falsified. Documented. Exploratory re-estimation permitted (clearly labeled). |
Governance commitment: The failure response protocol is frozen at publication. No reclassification of KC → F or FA → F post-data. Historical falsifications (Ledger) demonstrate EFC has already applied this protocol to itself.
8. Mapping to Standard Parameterisations
| Standard Framework | EFC Mapping | Notes |
|---|
| μ(k,z), Σ(k,z) | At linear scales μ ≈ 0.94, Σ ≈ 1.05, η ≈ 1.10. Scale dependence via stiffness response R ∝ k−4. | Directly comparable to Euclid MG pipeline. See 31876324. |
| w₀waCDM | EFC: w(a) = −β(S)·a. Not a free fit — derived from susceptibility T(S). Effective w₀, wa extractable by Taylor expansion. | See WP Part 4. |
| EFT of DE (α-functions) | DERIVED (32011407). αT = 0; αM ∝ S(a); αB ∝ dS/d ln a. Stiffness response R(k,z) beyond standard Horndeski. | DONE. Predictions sealed in 32010399. |
| Σmν | EFC growth suppression partially degenerates with neutrino mass. EFC’s η ≠ 1 breaks the degeneracy. | Neutrino mass constraints from EFC+DESI will differ from ΛCDM+DESI. |
9. Critical Path: What Must Be Ready Before Data Arrives
| Priority | Item | Required For | Deadline | Status |
|---|
| 1 | Euclid DR1 S8 extraction pipeline | KC3; P3 replication | 2026 Oct | PREDICTION READY hi_class + efc_logistic; benchmark frozen (31990053, SHA-256 sealed 2026-04-12) |
| 2 | ISW cross-correlation (AISW) | F1 | 2026 H2 | PREDICTION READY ClTT(ℓ=30): +1.88% at benchmark |
| 3 | EG estimator implementation | KC4; FA4 | ~2028 | PREDICTION READY EG(ℓ=66): −3.98% from Clφφ/P(k) ratio |
| 4 | Full-shape P(k) likelihood with EFC growth | KC1; F4 | ~2027 | PREDICTION READY P(kc,z=0.5): +2.09% via hi_class Boltzmann |
| 5 | Void catalogue + ISW stacking | Void ISW sign-flip | ~2028 | METHOD DEFINED |
| 6 | Cluster shock-front κ analysis | F3 | 2026–2027 | PRE-REGISTERED |
| 7 | EFCLASS Boltzmann solver | Full Cℓ; ADM Hamiltonian | ~2028 | PLANNED |
| 8 | BAO anisotropic split | Sealed DH/rd | ~2027 | PREDICTION READY |
10. Confirmation Ladder (Updated)
| Level | Threshold | Channels Required | Survey(s) | Timeline | Status |
|---|
| Hint (current) | 2.20σ single-channel | fσ8 LOO (7/7) | DESI DR1 + BOSS | 2026 | ACHIEVED |
| Suggestive | 3σ joint | fσ8 + S8 | + Euclid DR1 + DES Y6 | 2027 | AWAITING Euclid DR1 |
| Evidence | 3.5σ | μ–Σ + fσ8 | + Euclid DR2 | 2028 | Requires KC4 + EG pipeline |
| Detection | 5σ | All channels locked | Euclid DR3 + Rubin + DESI final | 2030+ | Requires all KC1–KC5 not triggered |
11. Cross-Domain Predictions (Non-Cosmological)
| Prediction | Domain | Criterion | Dataset | Reference |
|---|
| P4** — η = Ceff/Dratioγ | Neuroscience (Track 2) | |r| > 0.40 on n ≥ 20 subjects | HCP structural connectome + multiscale entropy | 31940547 |
| P5 — Optimal βKL from resting-state fMRI | AI Alignment (Track 3) | Calibrate RLHF temperature without grid search | HCP fMRI + RLHF training runs | 31940547 |
| P2 — Grokking phase transition | AI Alignment (Track 3) | Δtgrok ~ (Hmem − Hgen)/Teff; falsified if r < 0.3 | Modular arithmetic datasets | 31940535 |
| Centrifugal gradient (P1, Track 2) | Neuroscience | Core-to-periphery entropy production gradient | HCP connectome + resting-state fMRI | 31940505 |
12. Gap Analysis (April 2026)
Living assessment of what the project needs vs what exists. Updated monthly or on significant external events. Last update: 2026-04-17.
12.1 External Landscape Changes Since Last Roadmap Version
| Event | Date | Impact on EFC | Action Required |
|---|
| CMB-S4 cancelled | July 2025 | Primary future CMB lensing instrument lost. Sub-percent CMB lensing now depends on Simons Observatory + LiteBIRD (2032+). | Update all CMB-S4 references in roadmap. Simons Observatory is the effective near-term replacement. |
| Simons Observatory LAT first light | Feb–Mar 2025 | CMB lensing reconstruction capability now operational. First SO × Euclid cross-correlation data expected ~2027. | DONE — EG pre-registration sealed (32023788): EGEFC/EGGR = 1.086 ± 0.012. |
| Rubin/LSST first photons | Apr 2025 | Survey now operational. DP2 expected Jul–Sep 2026. DR1 ~early 2028. | DONE — Rubin DP2 cosmic shear sealed (32013738): S8 = 0.847 ± 0.015, ξ+ ~8% enhancement. |
| DES Year 6 3×2pt released | Jan 2026 | S8 = 0.789 ± 0.012. P3 PASS at 0.3σ. 2.6σ tension with CMB. | Completed. Result logged in Ledger v3.9. |
| DESI DR2 BAO released | Mar 2025 | 2.8–4.2σ preference for w₀waCDM over ΛCDM. f(R) models strongly preferred. | Verify αL2 against DR2 chains. EFC regime fit shows ΔAIC = −18.01 (31230703). |
| DESI DR1 peculiar velocity fσ8 | Dec 2025 | fσ8(z=0.07) = 0.450 ± 0.055. Low-z, low discriminating power for EFC. | Monitor. DR2 full-shape RSD at z~0.5–0.7 is the key pending test. |
| Entropic gravity competitors | 2025–2026 | Multiple arXiv papers (2503.19056, 2503.08236, 2512.22103, 2508.13260) show entropic cosmology models statistically preferred over ΛCDM with DESI DR2. Competitive landscape intensifying. | Differentiate EFC via the perturbation-sector discriminant signature (μ<1, Σ>1, η≈1.10) which competitors lack. |
12.2 Kill Criteria Readiness
| KC | Pipeline Status | Gap | Priority |
|---|
| KC1 P(k) full-shape | PREDICTION READY | None — hi_class + efc_logistic sealed (31990053). Awaiting DESI DR3 (~2027). | Low (pipeline complete) |
| KC2 fσ8 trajectory | SEALED | None — sealed prediction zcross = 2.042. Awaiting DESI DR3 Lyα + high-z RSD. | Low (prediction locked) |
| KC3 S8 convergence | P3 PASS | DES Y6 passed (0.3σ). KiDS Legacy divergence unresolved. Euclid DR1 (Oct 2026) will arbitrate. | Medium (Euclid pipeline ready, need to monitor KiDS Legacy release ~2027) |
| KC4 Gravitational slip η | SEALED | All KC4 channels pre-registered: SO × Euclid EG (32023788: EGEFC/EGGR = 1.086 ± 0.012, kill at 1.00 ± 0.01 >3σ), Rubin DP2 cosmic shear (32013738), μ–Σ eigenmode (31990194). | DONE |
| KC5 Dark energy w(z) | Monitoring | DESI DR2 shows 2.3σ for w₀waCDM. EFC consistent. Gap: need formal w(a) = −β(S)·a prediction confronted with Euclid DR1 chains. | Medium — derive effective w₀, wa from EFC susceptibility |
12.3 Theory Gaps
| Gap | Status | Blocking | Priority |
|---|
| Bellini–Sawicki α-function mapping | CLOSED (32011407) | Euclid EFT pipeline compatibility | DONE — αT=0, αM∝S(a), αB∝dS/d ln a |
| Full non-linear ADM Hamiltonian stability | Passed at 2nd order; full non-linear pending | FA6 | Medium |
| EFCLASS Boltzmann solver | Partial (hi_class patch exists) | Full Cℓ predictions | Medium — hi_class efc_logistic covers the key regime |
| Multi-component 175-galaxy SPARC universality | CLOSED (32029704) | Final rotation-curve validation | DONE |
12.4 Priority Actions
- IMMEDIATE (Apr–Jun 2026): Monitor DESI for release of DR2 full-shape RSD paper at z~0.5–0.7. This is the only currently pending direct test of the sealed prediction fσ8(z=0.7) = 0.430. Bellini–Sawicki α-functions: DONE (32011407). Pre-registered predictions sealed (32010399).
- BY JULY 2026:
Pre-register EFC predictions for Rubin/LSST DP2 cosmic shear. DONE (32013738): S8 = 0.847 ± 0.015, ξ+ ~8% large-scale enhancement (20′–300′), SHA-256 sealed.
- BY SEPTEMBER 2026:
Pre-register EFC predictions for Simons Observatory × Euclid EG cross-correlation. DONE (32023788): EGEFC/EGGR = 1.086 ± 0.012 at kc ≈ 0.05 h Mpc−1, zeff ≈ 0.5. Pass window [1.03, 1.14], kill at 1.00 ± 0.01 (>3σ). Sealed 15 Apr 2026.
- BEFORE OCTOBER 2026: Euclid DR1 pre-registration is sealed (31990053). Verify pipeline scripts and Boltzmann outputs are version-controlled and DOI-stamped.
- 2027: Derive effective w₀, wa from EFC susceptibility T(S) for confrontation with Euclid DR1 + DESI DR3 joint chains.
12.5 Competitor Landscape
| Model | arXiv | Key Claim | EFC Differentiator |
|---|
| Modified entropic gravity (Odintsov+) | 2503.08236 | Modified Friedmann from extended entropy; fits Pantheon+BAO+Planck | EFC has perturbation-sector predictions (μ<1, Σ>1, η); competitor is background-only |
| Mass-to-horizon entropic cosmology | 2508.13260, 2512.22103 | Bayesian analysis vs DESI DR2 BAO; preferred over ΛCDM | EFC has galactic-scale RAR (k=0.415) and cross-scale P3 link; competitor lacks galactic sector |
| f(R) gravity (DESI DR2) | 2504.05432 | Starobinsky/Exponential f(R) strongly preferred with DESI DR2 | EFC has μ<1 (f(R) has μ>1); sign of μ is the discriminant (FA2) |
| Ray-traced screened MG for LSST | 2604.08393 | LSST weak-lensing predictions for screened MG | Methodological template — EFC should adapt for its own LSST predictions |
Bottom Line
| Purpose | Map every Stage-IV data release to a specific, pre-registered EFC test |
| Next critical date | 2026 Oct 21 — Euclid DR1: tests KC3, KC5, FA2, P3 replication |
| Sealed predictions | 2 cryptographic freezes; 6 quantitative values; testable by DESI DR3 (~2027–2028) |
| Kill criteria | 5 (KC1–KC5) + 6 action-level (FA1–FA6) + 6 standing (F1–F6) = 17 falsification conditions |
| Pipeline gaps | 1 item before data arrival (void stacking); EG, full-shape P(k), and S8 pipelines now complete via hi_class efc_logistic (2026-04-12) |
| Statistical framework | Survey-provided likelihoods/covariance; Δχ² / ΔAIC primary; no EFC nuisance parameters |
| Key discriminant | η ≈ 1.10 — rules out massive neutrinos, f(R), w₀waCDM if confirmed |
| Failure protocol | KC = hard kill; FA = action revision; F = tension. No reclassification post-data. |
| Governance | Frozen at publication; versioned updates only before data release |
Resources
© 2026 Energy-Flow Cosmology Initiative · Stage-IV Data Roadmap (v1.1 – April 2026)