Energy-Flow Cosmology (EFC) — Gap Analysis

Pitch Validation Likelihood Evaluation Models White Paper Roadmap Gaps External Predictions Atlas Changelog

Morten Magnusson · Symbiose Research, Sandnes, Norway · ORCID: 0009-0002-4860-5095 · June 2026 · CC-BY-4.0

Purpose: Living assessment of what EFC needs vs what exists. Identifies gaps in pipeline readiness, theory, data timelines, and competitive landscape. Updated monthly or on significant external events. Last update: 2026-04-29.

April 2026 wave summary. One atlas gap resolved by falsification: the EFC Π bar-instability criterion is 32101111 FALSIFIED as a bar predictor (AUC=0.217, 0/12 bars); Π is retained instead as a disk-state parameter (ρ[Π,logΣ]=−0.71, ρ[Π,fgas]=+0.65). One structural reframing: H0_tension rolle upgraded from addresses_open to proposes_resolution (32113399). One mathematical lock: growth-sector coupling-structure closure proven (32084670) — fσ8 and S8 are constrained by the proven coupling-structure closure (no free-parameter escape route); the robust derivation gives S8 ≈ 0.82 (31188193, shifted downward), not 0.847. Two gaps still open: kSZ_velocity (no dedicated EFC paper) and early_structure_JWST (no quantitative prediction paper) — registered as vc_060aa393def7 and vc_eea84fbbf592.


1. External Landscape Changes

Major events since the Roadmap was last frozen.

EventDateImpact on EFCAction Required
CMB-S4 cancelledJuly 2025Primary future CMB lensing instrument lost. Sub-percent CMB lensing now depends on Simons Observatory + LiteBIRD (2032+).DONE Roadmap updated. SO is the near-term replacement.
Simons Observatory LAT first lightFeb–Mar 2025CMB lensing reconstruction now operational. First SO × Euclid cross-correlation data expected ~2027.DONE EG pre-registration sealed (32023788).
Rubin/LSST survey startEarly 2026Survey operational. DP2 expected Jul–Sep 2026. DR1 ~early 2028.DONE Rubin DP2 shear pre-registration sealed (32013738): S8=0.847±0.015, ξ+ ~8% enhancement at 20′–300′ — this sealed value used the η-boost branch (η ∈ [1.05,1.15], 0% robust per 32037990); the robust EFC derivation (Σ ≈ 0.99 < 1) shifts S8 down to ≈ 0.82 (31188193).
DES Year 6 3×2pt releasedJan 2026S8 = 0.789 ± 0.012. P3 PASS at 0.3σ. 2.6σ tension with CMB.DONE Logged in Ledger v3.9.
DESI DR2 BAO releasedMar 20252.8–4.2σ preference for w₀waCDM over ΛCDM. f(R) models strongly preferred.DONE EFC regime fit ΔAIC = −18.01 (31230703).
DESI DR1 peculiar velocity fσ8Dec 20258(z=0.07) = 0.450 ± 0.055. Low-z, low discriminating power.MED Monitor. DR2 full-shape RSD at z~0.5–0.7 is the key test.
Entropic gravity competitors on arXiv2025–2026Multiple models (2503.19056, 2503.08236, 2512.22103, 2508.13260) preferred over ΛCDM with DESI DR2.MED Differentiate via the robust perturbation-sector discriminant (μ<1, Σ≥1). (η≈1.10 is fragile — 0% robust per 32037990.)

2. Kill Criteria Readiness

KCPipeline StatusGapPriority
KC1 P(k) full-shape PREDICTION READY None — hi_class + efc_logistic sealed (31990053). Awaiting DESI DR3 (~2027). LOW
KC28 trajectory SEALED None — sealed zcross = 2.042. Awaiting DESI DR3 Lyα + high-z RSD. LOW
KC3 S8 convergence P3 PASS DES Y6 passed (0.3σ). KiDS Legacy divergence unresolved. Euclid DR1 (Oct 2026) will arbitrate. MED
KC4 Perturbation-sector signature SEALED Perturbation sector reformulated (32037990): μ < 1 structurally robust (100% under ±20% variation), Σ ≥ 1 semi-robust (61%), η as point value fragile (0%). Distinctive test: non-monotonic Σeff(z) with sign change at z ≈ 0.44 (Euclid DR1 tomography) — fragile: the crossover needs Σ > 1 from the η-boost (η-dependent, 0% robust), robust EFC (η→1) gives Σ ≈ μ ≈ 0.99 flat (monotonic, ≈GR). Also sealed: SO × Euclid EG (32023788: EGEFC/EGGR = 1.086 ± 0.012 — fragile, η-dependent, 0% robust; robust EFC: EG ≈ 1), Rubin DP2 shear (32013738: S8=0.847±0.015 — η-boost branch; robust EFC: S8 ≈ 0.82), μ–Σ eigenmode (31990194). Horndeski QS with αT=0 was claimed strongly disfavored from reproducing μ<1 ∧ Σ>1 (numerical scan), but EFC reaches that quadrant only via the fragile η-boost; robust EFC (Σ ≈ μ < 1) does NOT exclude Horndeski. DONE
KC5 Dark energy w(z) Monitoring Need formal w(a) = −β(S)·a confronted with Euclid DR1 chains. MED

3. Theory Gaps

GapStatusBlockingPriority
Bellini–Sawicki α-function mappingCLOSED (32011407)Euclid EFT pipeline compatibilityDONE αT=0, αM∝S(a), αB∝dS/d ln a derived. Stiffness response R(k,z) identified.
Background-level H(z) modification viabilityCLOSED (31985163)Sector localisation of EFC phenomenologyDONE No-Go theorem: any low-z background modification improving BAO (Δχ²BAO≈−14.6) is penalised by CMB distance priors (Δχ²CMB>+100), forcing EFC into the perturbation sector.
Full non-linear ADM Hamiltonian stabilityPassed at 2nd order; full non-linear pendingFA6MED
EFCLASS Boltzmann solverPartial (hi_class patch exists)Full C predictionsMED
Multi-component 175-galaxy SPARC universalitySingle-component completed (60.2% win rate)Final rotation-curve validationCLOSED (32029704)
Neutrino mass degeneracy analysisNot startedEFC+DESI ν-mass differs from ΛCDM+DESIMED
Perturbation-sector structural prediction (μ < 1 robust; Σ ≥ 1, crossover fragile)CLOSED (32037990)Channel separation after α collapse; μ < 1 robust, but the Σ > 1 / crossover branch is η-dependent (0% robust)DONE Full (μ, Σ, η) system derived from EFC action; the Σeff(z) crossover at z ≈ 0.44 and the Horndeski-disfavoured (μ<1 ∧ Σ>1) combination both rest on the η-boost (η-dependent, 0% robust); robust EFC (η→1, Σ ≈ μ < 1) is monotonic ≈GR and does NOT exclude Horndeski. μ < 1 robust; ghost/tachyon-free in sub-horizon regime.
Growth-sector mathematical closureCLOSED (32084670)Final theoretical lock on P2 + P4 + P3DONE Vekstsektor-koblingssystemet (Sflow, Slatent, ξ) er bevist selvkonsistent med entydige løsninger under EBE-betingelser. fσ8 og S8 er bundet av den beviste koblingsstruktur-lukkingen (ingen fri-parameter escape route); den robuste avledningen gir S8 ≈ 0.82 (skiftet nedover, 31188193), ikke 0.847.
H0 tension structural resolutionCLOSED (32113399)Atlas role upgrade for H0_tensionDONE Three-window decomposition: Planck (L0), DESI (L1), SH0ES (L2) measure H0 in distinct regime windows. Atlas role upgraded from addresses_open to proposes_resolution (2026-04-29).
Bar-instability Π criterionFALSIFIED (32101111)Bar-prediction claimDONE The EFC Π bar-criterion is FALSIFIED as a bar predictor (AUC=0.217, 0/12 bars, anti-correlated within physical ζ). Π is retained not as a bar predictor but as an independent disk-state parameter (ρ[Π,logΣ]=−0.71, ρ[Π,fgas]=+0.65, n=112; replicated on xGASS). Validation candidate vc_140e79363cbe registered against SPARC + S4G + Galaxy Zoo.
α-parameter independent constraint (non-MCMC)CLOSED (32101213)EMCEE/NUTS internal degeneracyDONE Three independent channels (SPARC175 RC, NUTS BAO+Hz, analytic non-MCMC) all give α ∈ [−0.72, −0.68]. Both frozen blind freezes (−0.689, −0.702) consistent. α is now over-determined.
kSZ velocity — dedicated EFC prediction paperOPENAtlas kSZ_velocity only addressed via test_observation node ACT_kSZ_2604_14327; no quantitative EFC prediction paper existsHIGH Validation candidate vc_060aa393def7 registered. Needed: explicit kSZ-amplitude prediction from EFC perturbation sector.
Early structure JWST — quantitative prediction paperOPENAtlas early_structure_JWST has only predicts_L3_early qualitative role; observation paper 31059964 confirms z>6 abundance excess but no formal EFC quantitative match existsHIGH Validation candidate vc_eea84fbbf592 registered. Needed: dN/dM formal halo-mass-function prediction at z > 6 with EFC entropy-flow boost factor.

4. Data Timeline & Deadlines

DatasetReleaseKey EFC ObservablesEFC StatusAction
DES Y6Jan 2026 RELEASEDS8 = 0.789 ± 0.012P3 PASS (0.3σ)None
DESI DR2 BAOMar 2025 RELEASEDBAO DM/DH; DE preferenceConsistentVerify αL2 against chains
DESI DR2 full-shape RSD~2026 PENDING8(z=0.5–0.7)Sealed (32013156): fσ8(z=0.7)=0.430 vs ΛCDM 0.449; DH/rd(z=0.7)=19.797 vs 20.719; DH/rd(z=1.0)=16.527 vs 17.466MONITOR
Euclid Q2Jun 24, 2026Shape validationPrecursorMonitor shear calibration
Rubin DP2Jul–Sep 2026Early shear catalogueSEALED (32013738): S8=0.847±0.015 (η-boost branch, fragile/0% robust per 32037990; robust EFC: S8 ≈ 0.82), ξ+ ~8% enhancement at 20′–300′Monitor DP2 release
Euclid DR1Oct 21, 20268, S8, EG, P(k), ηSEALED (31990053)Verify pipeline scripts
SO CMB lensing~2026–2027Cφφ, SO×Euclid EGSEALED (32023788)Awaiting SO × Euclid DR2 data (~2027–2028)
KiDS Legacy~2027Resolves DES vs KiDS S8 splitMonitoringNone until release
DESI DR3~2027–2028Full RSD + BAO 5-yearSealed predictions lockedLong-term planning
Rubin DR1~early 2028S8 >5× DES precisionNot pre-registeredPre-register by ~2027
Euclid DR2~2028η to percent level, EGKC4 decisive testRequires Bellini-Sawicki mapping
LiteBIRD2032+Primordial B-modes, τCMB baseline updateNo action before 2030

5. Priority Actions

#ActionDeadlineBlockingStatus
1Monitor DESI for DR2 full-shape RSD paper at z~0.5–0.7. Only pending direct test of sealed fσ8(z=0.7) = 0.430.Now (ongoing)KC2 early checkACTIVE
2Derive Bellini–Sawicki α-functions from EFC relativistic action for Euclid EFT pipeline. DONE (32011407). Pre-registered predictions sealed in 32010399.Jul 2026Euclid DR1 EFT compatibilityDONE
3Pre-register EFC predictions for Rubin/LSST DP2 cosmic shear. DONE (32013738): S8=0.847±0.015 (η-boost branch, fragile/0% robust per 32037990; robust EFC: S8 ≈ 0.82), ξ+ ~8% large-scale enhancement (20′–300′) sealed with SHA-256 falsifiers.Jul 2026Rubin DP2DONE
4Pre-register EFC predictions for SO × 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. Note: 1.086 is fragile (η-dependent, 0% robust per 32037990); robust EFC has EG ≈ 1, so a null at 1.00 is not a clean kill.Sep 2026KC4DONE
5Verify Euclid DR1 pipeline scripts version-controlled and DOI-stamped. Prediction already sealed.Oct 2026KC3, FA2SEALED
6Derive effective w₀, wa from EFC susceptibility T(S) for Euclid DR1 + DESI DR3 joint chains.2027KC5PLANNED
7Complete multi-component 175-galaxy SPARC universality with fixed (K0, m²).2027F5 galactic sectorCLOSED (32029704)
8Run Π cross-population test against SPARC + S4G + Galaxy Zoo per vc_140e79363cbe. The Π bar-criterion is already FALSIFIED as a bar predictor (AUC=0.217, 0/12 bars, 32101111); the test now confirms Π as a disk-state parameter (vs logΣ, fgas), not as a bar predictor.2026 H2Π disk-state parameterACTIVE
9Build joint regime-disaggregated H0 chain (Planck L0 + DESI L1 + SH0ES L2 + Euclid DR1) per vc_e36e011d1270. Tests P7 three-window prediction.2026 H2P7 + atlas role upgradeACTIVE
10Write dedicated kSZ velocity prediction paper (vc_060aa393def7). Atlas kSZ_velocity currently only tested via observation node, no EFC theoretical prediction.2026 H2kSZ-gap closurePLANNED
11Write dedicated JWST high-z structure prediction paper (vc_eea84fbbf592). Convert predicts_L3_early from qualitative to quantitative dN/dM(z>6) with entropy-flow boost factor.2026 H2JWST-gap closurePLANNED
12Resolve EMCEE vs NUTS α-degeneracy: EMCEE returns α=−0.10 (0.5σ) while NUTS + non-MCMC return α ∈ [−0.72, −0.68]. Suggests prior or chain configuration issue, not theory failure.2026 H2MCMC-daemon STOPPED_DEGENERACY_PERSISTSACTIVE

6. Competitor Landscape

ModelarXivKey ClaimEFC Differentiator
Modified entropic gravity (Odintsov+)2503.08236Modified Friedmann from extended entropy; fits Pantheon+BAO+PlanckEFC has perturbation-sector predictions (μ<1, Σ>1 [η-boost, fragile], η); competitor is background-only
Mass-to-horizon entropic cosmology2508.13260, 2512.22103Bayesian analysis vs DESI DR2 BAO; preferred over ΛCDMEFC has galactic-scale RAR (k=0.415) and cross-scale P3 link; competitor lacks galactic sector
f(R) gravity (DESI DR2)2504.05432Starobinsky/Exponential f(R) strongly preferred with DESI DR2EFC has μ<1 (f(R) has μ>1); sign of μ is the discriminant (FA2)
Ray-traced screened MG for LSST2604.08393LSST-specific predictions for screened MGMethodological template — EFC should adapt for its own LSST predictions

EFC Status — by RCMP Regime

EFC’s standing is regime-stratified: ΛCDM is the special-case limit in L0/L1 (derived from the EFC variational action), so EFC is judged by regime, not by the background. Source: validation-ledger/data/ledger_truth.json — the canonical narrative all ledgers derive from.

RegimeVerdictStatus
L0/L1
background / linear
ΛCDM recoveredThe designed special-case limit (a feature, not a contest). α = −0.14 ± 0.21 consistent with ΛCDM. The Planck(L0)/DESI(L1)/lensing(L2) S8 spread is regime-stratification, not pure tension.
L2
perturbation / growth
OPEN frontierRobust: μ<1 growth-suppression mechanism (points S8 down). Fragile: Σ>1 / η-boost enhancements (0%-robust). The α growth-signal collapsed to 0.68σ post-DESI-DR2; ΛCDM preferred in the joint background fit (ΔAIC=+1.59 — mild, not a falsification; the separate Variant-H growth-extension MCMC gives +4.05). Decisive blind test: P2 (fσ8, DESI DR2); P1 (Φ/Ψ slip) is a weak discriminator for robust EFC (near-GR).
L3
galactic / void
EFC strongestGalaxy rotation curves fit without particle dark matter via one universal screening parameter k ≈ 0.415 ± 0.029 (Kill-Test v6: 171/175 SPARC, 60.2% EFC win; DDO 154 ΔAIC=35.4). Deep-void ISW sign-flip. MOND-class — competitive, not decisive; Bullet Cluster tied.

Bottom line: EFC is non-rejectable, not a breakthrough; ΛCDM is preferred in the joint fits. The P4 sign is decisive and RCMP-sharpening — the sealed S8 = 0.847 is CMB-near (→ DAMAGE vs lensing); the μ<1 mechanism, not the number, points down. (falsification_status ≠ model_preference.)

7. Inference & Symbiosis Status

Summary derived from docs/validation-ledger/data/ledger.json, inference.json, and .claude/symbiose_snapshot.json. Every row below can be regenerated by running python3 scripts/maintenance/efc_symbiose_snapshot.py --from-ledger followed by python3 scripts/maintenance/efc_cross_validate.py.

MetricValueSource / Interpretation
Validation tests106/116 survived on the active set (142 total incl. 26 planned; 10 falsified)ledger.stats.total_public=142, planned_pipeline=26, n_falsified=10 → 116 active, 106 survived ≈ 91%.
Inference modules5/7 active (real χ²) · 1 self-consistent · 1 LCDM stubinference.json: active — bao_boss_dr12 (χ²r=2.18), cluster_core_state (108.8, FAILED), shear_kids1000 (10.4), fs8_extended (0.554), hz_chronometers (1.549); self-consistent — cluster_tng. fs8_extended + hz_chronometers newly anchored to DOI-verified primary data: fσ8 — 6dFGS (10.1111/j.1365-2966.2012.21136.x), SDSS-MGS (10.1093/mnras/stu2693), BOSS DR12 (10.1093/mnras/stx721), VIPERS (10.1051/0004-6361/201526553), FastSound (10.1093/pasj/psw029); H(z) — cosmic chronometers (Moresco+2022 compilation, 10.1007/s41114-022-00040-z). χ² at LCDM baseline; EFC(α=−0.68) fits both BETTER (0.340 / 0.941), corroborating the joint-MCMC α-signal. 1 LCDM stub: bao_desi_y1 — placeholder data (DH/r_d rises with z = unphysical; z-bins 0.70/0.85 are not DESI’s), pending real DESI DR1/DR2 BAO values.
α-signal (LOO blind)2.20σ (α = −1.00 ± 0.46, ΔAIC = −2.91)Research-daemon LOO MCMC (last published cycle). Published snapshot is ledger_fallback (snapshot.alpha_signal.status="unknown"), so this is the last published LOO figure; the research-daemon is currently running — refreshable on live snapshot regen. Post-DESI-DR2 this growth signal collapsed to 0.68σ; the joint background fit prefers ΛCDM (ΔAIC=+1.59 — graph-verified; the separate Variant-H growth-extension gives +4.05).
GRAV pipeline (Grid-AQUAL)2 KT PASSED, 1 MARGINAL (KT3)ledger.stats.grav_kt_count=3, grav_kt_passed=2, grav_kt_marginal=1; 2 integration explosions logged in snapshot.
Sealed blind predictions2 frozen (SHA-256) — α = −0.689 (v1), −0.702 (v2)Matches symbiose_snapshot.sealed_predictions.freeze_1/2, hashes 7a850cfa… and dbccda15….
Inference fit quality1 warning: shear_kids1000 χ²red=10.4Cross-validate flags as "poor fit" despite DOI-anchored status; KiDS-1000 chain remains the chief tension. Corroborated by DES Y6 P3 PASS at 0.3σ.
Symbiose live pipelineOnline (neo4j + qdrant + API up; research-daemon healthy)Services restored — Neo4j + Qdrant + unified-API responding, research-daemon running (Up 20h). Published snapshot.source is still ledger_fallback; regenerate via efc_symbiose_snapshot.py with live MCP data to populate live health / knowledge-gap / learning-loop metrics.

Bottom Line

Biggest gap right nowDESI DR2 full-shape RSD rapid-response pipeline — sealed prediction exists (fσ8(z=0.7) = 0.430, 32013156) but no single-entry-point verification script is assembled. Paper could drop any time. Secondary: Euclid DR1 pipeline verification (Oct 2026). All HIGH-priority pre-registrations now CLOSED (SO × Euclid EG in 32023788; Rubin DP2 in 32013738; Bellini–Sawicki in 32011407; Background-modification viability in 31985163.)
Most urgent monitorDESI DR2 full-shape RSD — direct test of sealed fσ8(z=0.7) = 0.430 prediction (32013156). Rapid-response pipeline needs assembly.
Most urgent pre-registrationNone — all HIGH-priority pre-registrations are sealed. Next pre-registration target: Rubin DR1 (deadline ~2027).
Key differentiator vs competitorsRobust μ < 1 (the Σ ≥ 1 branch is η-dependent / 61% semi-robust) + H0 three-window — no competitor model predicts this combination. (η ≈ 1.10 is fragile/0% robust per 32037990; the Π bar-criterion is FALSIFIED as a bar predictor per 32101111 — neither is a differentiator.)
Automated monitoringefc_weekly_scan.py runs every Monday 07:00 UTC via GitHub Actions
Open phenomenon gapsTwo: kSZ_velocity (no dedicated EFC prediction paper) and early_structure_JWST (no quantitative dN/dM prediction). Both registered as validation candidates and slated for 2026 H2.
Outstanding internal tensionEMCEE vs NUTS α-degeneracy (EMCEE: −0.10 / 0.5σ; NUTS + non-MCMC: −0.70). Action #12 active. Not a theory failure — chain-config or prior issue. DOI 32101213 over-determines α from three independent channels.

© 2026 Energy-Flow Cosmology Initiative · Gap Analysis — auto-updated by weekly scan