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RCFM Implementation TODO List

Radial-Cyclic Field Model - Complete Task Checklist

Author: MiniMax Agent Generated: 2026-03-28 Based On: RCFM_Deep_Analysis_Report.md + Unified Implementation Plan Goal: Publication-ready scientific codebase

Overview

This TODO consolidates all implementation tasks derived from the deep analysis into a single actionable checklist. The RCFM project is currently at prototype stage (~40% complete) with critical bugs that must be fixed before publication.

PHASE 1: Critical Bug Fixes

[BUG-FIX-1] Raychaudhuri Equation Sign Error ⚠️ CRITICAL

  • File: src/rcfm/core/solver.py
  • Line: 72-73
  • Issue: Sign of pressure term reversed in Raychaudhuri equation
  • Current (WRONG): 
    dH_dr = sqrt_A * (4 * np.pi * self.G / 3 * (rho_eff + 3 * p_eff) - H**2)
  • Fixed (CORRECT): 
    dH_dr = sqrt_A * (-(4 * np.pi * self.G / 3) * (rho_eff + 3 * p_eff) - H**2)
  • Verification: Compare against ΛCDM limit using CAMB/CLASS
  • Impact: Wrong acceleration/deceleration evolution

[BUG-FIX-2] EMT Effective Pressure Formula Mismatch

  • File: src/rcfm/core/fluids.py
  • Line: 140
  • Issue: Uses Lambda_RCFM(0) instead of H variable, factor of 3 mismatch
  • Current (WRONG): 
    p_eff = p_A - beta * self.params.Gamma_drag * rho_A * rho_B * (rho_A - rho_B) / (3 * self.params.Lambda_RCFM(0))
  • Fix: Replace Lambda_RCFM(0) with H and verify factor of 3
  • Verification: Test energy conservation ∇_μ T^{μν} = 0

[BUG-FIX-3] G_eff Formula Incorrect in GW Mass Term

  • File: src/rcfm/core/gravitational_waves.py
  • Line: 80
  • Issue: Wrong formula for effective gravitational constant
  • Current (WRONG): 
    G_eff = self.G * (1 + self.params.Lambda_RCFM(z))
  • Fixed (CORRECT - per paper eq. 523-525): 
    a = 1.0 / (1 + z)
G_eff = self.G * (1 + self.params.beta * self.params.rho_B0 * (self.params.Rmax / a)**3)
  • Impact: Wrong GW cutoff frequency

[BUG-FIX-4] Scale Factor Division by Zero

  • File: src/rcfm/core/metric.py
  • Lines: 54-56
  • Issue: a(r) = a0 * (r/r0)^2 → 0 at r → 0 causes division by zero in H = a'/a
  • Fix Options:
    • Option A: Enforce r_min > 0 in solver initialization
    • Option B: Regularize scale factor near singularity: a = max(a0 * (r/r0)**2, eps)
    • Option C: Use analytical formula for H near r=0
  • Impact: NaN/Inf at r → 0

[BUG-FIX-5] Hubble Derivative Logic Error

  • File: src/rcfm/core/metric.py
  • Line: 162
  • Issue: else: if r > 0 is unreachable logic error
  • Current (WRONG): 
    else:
    da_dr = 2 * a / r if r > 0 else 0  # Logic error!
  • Fixed (ANALYTICAL): 
    # For a(r) = a0 * (r/r0)^2, analytical derivative is:
# da/dr = 2 * a0 * r / r0^2
r0 = self.params.Rmax
a0 = 1.0  # or self.params.a0
da_dr = 2 * a0 * r / (r0**2)
  • Impact: Unreachable else branch, potential division by zero

[BUG-FIX-6] Hardcoded CMB Peak Positions

  • File: src/rcfm/core/cmb_spectrum.py
  • Line: 191
  • Issue: Peak positions [220, 540, 810, ...] are ΛCDM values hardcoded
  • Fix Required:
    • Calculate acoustic peaks from sound horizon rs and angular diameter distance DA
    • Implement acoustic oscillation integral
    • Formula: ℓ_n ≈ n * π * DA / rs
    • Remove hardcoded peak array
  • Impact: CMB predictions not derived from RCFM physics

[BUG-FIX-7] No Solution Success Checks

  • File: src/rcfm/core/solver.py
  • Lines: 134-143
  • Issue: solution.success returned but never checked by calling code
  • Fix Required:
    • Add validation in BackgroundSolver.solve() method
    • Add validation in all calling code (CLI, likelihood, etc.)
    • Raise RuntimeError or return error code on failure
    • Add test for failed integration scenario
  • Impact: Silent failures propagate through pipeline

PHASE 2: Missing Implementations

[IMPL-1] Christoffel Symbols (Placeholder → Real)

  • File: src/rcfm/core/metric.py
  • Line: 234
  • Status: Returns zeros (placeholder)
  • Required:
    • Calculate actual Christoffel symbols for 4-ball metric
    • Formula for metric ds² = -A(r)dr² + a(r)²dΩ₃²
    • Implement: Γ^μ_νρ = (1/2) g^μσ (∂_ν g_σρ + ∂_ρ g_σν - ∂_σ g_νρ)
    • Verify: Newtonian limit yields ∇²Φ = 4πGρ
  • Tests: test_christoffel_newtonian_limit()

[IMPL-2] Tight-Coupling Boltzmann Hierarchy

  • Status: NOT IMPLEMENTED
  • Required for: CMB photon-baryon fluid evolution, Silk damping
  • Components:
    • Photon distribution function
    • Boltzmann equation for photons
    • Thomson scattering term
    • Baryon momentum equation
    • Tight-coupling expansion (ε << 1)
  • Tests: test_tight_coupling_approximation()

[IMPL-3] Actual Planck Data Loading

  • File: src/rcfm/core/cmb_spectrum.py
  • Status: Uses fake Gaussian peaks
  • Required:
    • Parse COM_PowerSpect_CMB-TT-full_R3.01.txt
    • Parse COM_PowerSpect_CMB-TE-full_R3.01.txt
    • Parse COM_PowerSpect_CMB-EE-full_R3.01.txt
    • Load covariance matrices
    • Implement proper likelihood with cosmic variance
    • Replace _load_planck_data() placeholder
  • Data Files: Already in Data/raw/planck_2018/

[IMPL-4] Primordial Spectrum from Singularity

  • File: src/rcfm/core/perturbations.py
  • Status: n_s = 0.965 hardcoded
  • Required:
    • Derive n_s from a ∝ r² boundary condition via Bogoliubov transformation
    • Implement quantum mode function near singularity
    • Match to Bunch-Davies vacuum
    • Extract power spectrum P(k) ∝ k^(n_s - 1)
    • Verify n_s ≈ 0.965 emerges naturally
  • Paper Reference: Section 10, Lines 699-706

[IMPL-5] Ginzburg-Landau Condensate

  • Status: NOT IMPLEMENTED
  • Required for: Critical density ρc determination
  • Components:
    • Define order parameter φ (gauge condensate)
    • Free energy functional F[φ]
    • Phase transition at ρ = ρc where ⟨φ⟩ → 0
    • Calculate ρc from coupling constants
    • Integrate with fluids.py for Phase B identification
  • Paper Reference: Section 4.6, Lines 527-546
  • Tests: test_phase_transition_critical_density()

[IMPL-6] Bogoliubov Transformation (Entropy)

  • Status: NOT IMPLEMENTED
  • Required for: Thermodynamic entropy reset verification
  • Components:
    • Bogoliubov coefficients α_k, β_k
    • S-matrix for singularity passage
    • Entropy calculation: S_out = Σ_k [...]
    • Verify entropy reset to zero
    • Connection to Page's theorem analogy
  • Paper Reference: Section 13, Lines 774-794
  • Tests: test_entropy_reset()

[IMPL-7] DESI/Pantheon+ Data Loading

  • Status: NOT USED (data downloaded but unused)
  • Required:
    • Parse DESI BAO chains from Data/raw/desi_2024/
    • Parse Pantheon+ CSV files from Data/raw/pantheon_plus/
    • Parse GW170817 posterior samples
    • Implement proper likelihood comparison
  • Current Issue: Likelihood code just uses penalty on Λ

[IMPL-8] Production MCMC Sampler

  • File: src/rcfm/core/likelihood.py
  • Status: Toy Metropolis-Hastings implementation
  • Required:
    • Replace with emcee or PyMC3
    • Implement adaptive proposal distribution
    • Add convergence diagnostics (Gelman-Rubin, R̂)
    • Calculate effective sample size (ESS)
    • Proper posterior output packaging
  • Parameters to sample: β, ρ_B0, H0 (if not fixed)

[IMPL-9] Comprehensive Test Suite

  • Status: ZERO unit tests
  • Create tests/ directory structure: 
    tests/
├── __init__.py
├── conftest.py              # pytest fixtures
├── test_constants.py
├── test_metric.py
├── test_fluids.py
├── test_solver.py
├── test_perturbations.py
├── test_cmb.py
├── test_matter_power.py
├── test_gravitational_waves.py
├── test_likelihood.py
└── test_integration.py
  • Critical tests to implement:
    • test_lcdm_limit() - β=0 reproduces ΛCDM
    • test_energy_conservation() - ∇_μ T^{μν} = 0
    • test_exact_solution() - a ∝ r² satisfies ODEs
    • test_newtonian_limit() - ∇²Φ = 4πGρ
    • test_convergence() - solution converges with finer grid
    • test_gw_speed() - c_T = 1 constraint satisfied
    • test_scale_factor_analytic() - analytical H matches numerical

[IMPL-10] Ricci Tensor Calculations

  • File: src/rcfm/core/metric.py
  • Status: Uses approximate derivatives
  • Required:
    • Calculate accurate Riemann tensor components
    • Contract to Ricci tensor R_μν
    • Scalar curvature R
    • Verify Einstein equations: G_μν = 8πT_μν
  • Tests: test_einstein_equations()

[IMPL-11] Reionization Implementation

  • Status: NOT IMPLEMENTED
  • Required for: CMB optical depth τ
  • Components:
    • Optical depth integral τ(z) = ∫ n_e σ_T dz
    • Thomson scattering coefficient
    • Reionization redshift z_re ~ 7-8
    • Impact on CMB E-mode polarization
  • Tests: test_reionization_optical_depth()

[IMPL-12] Silk Damping

  • Status: NOT IMPLEMENTED
  • Required for: CMB damping tail at high ℓ
  • Components:
    • Photon diffusion length
    • Damping factor exp(-k²/k_D²)
    • Integration with CMB spectrum code
  • Tests: test_silk_damping()

PHASE 3: File-Level Tasks

src/rcfm/__init__.py

  • [INIT-1] Add package metadata (version, author, license)
  • [INIT-2] Export public API (RCFMParameters, BackgroundSolver, etc.)

src/rcfm/cli.py

  • [CLI-1] Implement CLI entry point with argparse
  • [CLI-2] Add model execution commands (run, plot, analyze)
  • [CLI-3] Add validation and debugging commands

src/rcfm/core/constants.py

  • [CONST-1] Document all physical constants with references
  • [CONST-2] Add unit conversion utilities (SI ↔ natural units)

src/rcfm/core/metric.py

  • [METRIC-1] Complete implementation (bug fixes + IMPL-1, IMPL-10)
  • [METRIC-2] Add curvature tensor validation
  • [IMPL-1] Christoffel symbols
  • [IMPL-10] Ricci tensor

src/rcfm/core/fluids.py

  • [FLUID-1] Verify EMT implementation (BUG-FIX-2)
  • [FLUID-2] Implement drag terms with disable flag
  • [IMPL-5] Ginzburg-Landau condensate

src/rcfm/core/solver.py

  • [SOLVER-1] Fix solution success checks (BUG-FIX-7)
  • [SOLVER-2] Add input validation
  • [SOLVER-3] Improve error handling and reporting
  • [BUG-FIX-1] Raychaudhuri sign error

src/rcfm/core/perturbations.py

  • [PERT-1] Implement Boltzmann hierarchy (IMPL-2)
  • [PERT-2] Derive n_s from boundary condition (IMPL-4)
  • [PERT-3] Add gauge diagnostics
  • [IMPL-6] Bogoliubov transformation

src/rcfm/core/cmb_spectrum.py

  • [CMB-1] Implement CMB from first principles
  • [CMB-2] Add acoustic peak calculation
  • [BUG-FIX-6] Remove hardcoded peaks
  • [IMPL-3] Load actual Planck data
  • [IMPL-11] Reionization
  • [IMPL-12] Silk damping

src/rcfm/core/matter_power.py

  • [MP-1] Implement with RCFM transfer function
  • [MP-2] Add spectral residual reporting

src/rcfm/core/gravitational_waves.py

  • [GW-1] Full tensor sector implementation
  • [GW-2] Stochastic background + cutoff diagnostics
  • [BUG-FIX-3] Fix G_eff formula

src/rcfm/core/likelihood.py

  • [LIK-1] Strict likelihood interface
  • [LIK-2] Add priors and nuisance handling
  • [LIK-3] Posterior output packaging
  • [IMPL-7] Load DESI/Pantheon+ data
  • [IMPL-8] Production MCMC

src/rcfm/viz/plotting.py

  • [VIZ-1] Reproducible plotting layer
  • [VIZ-2] Add provenance overlays
  • [VIZ-3] Residual plot templates

PHASE 4: Global Audits

[G-1] Repository-wide Audit

  • Inventory all src/rcfm/* files and import graph
  • Record every public function, class, CLI entry point
  • Identify dead code, duplicated math, untested branches
  • Establish execution path: CLI → core → plotting → outputs
  • Map all 7 bugs to specific files/lines

[G-2] Scientific Assumptions Audit

  • Identify every model-defining assumption
  • Separate "derived from equations" vs "chosen modeling ansatz"
  • Flag manuscript claims stronger than code evidence
  • Map all 7 theoretical gaps to sections
  • Map all 12 missing implementations

[G-3] Units and Dimension Audit

  • Verify dimensional consistency at solver boundary
  • Establish units policy (internal natural units, SI at boundaries)
  • Add explicit conversion helpers
  • Flag unit-related bugs

[G-4] Reproducibility Baseline

  • Define clean-room rebuild procedure
  • Fix random seeds
  • Ensure outputs regenerable from source + data
  • Create requirements.txt or environment.yml
  • Add [IMPL-9] test suite

[G-5] Scientific Baseline Comparisons

  • Build comparison harnesses vs ΛCDM baseline (CAMB/CLASS)
  • Define residual metrics and acceptance thresholds
  • Store baseline outputs for regression comparison
  • Verify BUG-FIX-6 produces correct CMB predictions

PHASE 5: Documentation

Paper Updates

  • Update to v1.4 with numerical results
  • Add figures: H(z), C_ℓ, P(k), posteriors
  • Revise theoretical sections with complete derivations
  • Add appendix with numerical methods
  • Finalize bibliography

Code Documentation

  • Add mathematical equation references to docstrings
  • Document all public APIs
  • Add examples to docstrings
  • Create API reference guide
  • Document test coverage

README Updates

  • Add Python environment setup instructions
  • Add example usage scripts
  • Document expected outputs
  • Add computational requirements
  • Add contribution guidelines

Acceptance Criteria

For Publication Readiness

  • All 7 bugs fixed
  • All 7 theoretical gaps addressed
  • All 12 missing implementations completed
  • Test suite > 80% coverage on core modules
  • Baseline comparison shows < 0.1% deviation from ΛCDM limit
  • All figures reproducible
  • Documentation complete
  • Code versioned and archived

Estimated Timeline

Phase Duration Focus
Phase 1 2-4 weeks Bug fixes
Phase 2 4-8 weeks Missing derivations
Phase 3 6-10 weeks Numerical implementations
Phase 4 3-5 weeks Data integration
Phase 5 4-6 weeks Testing & validation
Phase 6 2-4 weeks Parameter estimation
Phase 7 4-6 weeks Publication prep
Total 25-43 weeks ~6-10 months

Risk Register

Risk Impact Probability Mitigation
Theoretical gaps prove insurmountable High Medium Focus on verifiable ΛCDM predictions
Numerical instabilities near singularity High High Regularization + adaptive step size
Data parsing complexity underestimated Medium Medium Allocate buffer time
MCMC convergence issues Medium Low Use established samplers (emcee)
Reviewer challenges model assumptions High High Strengthen theoretical justification

Last Updated: 2026-03-28 Status: Phase 1 - Bug Fixing: 0/7 complete