HELIX‑D RFC (Successor Hypothesis)
HELIX‑C (Yukawa, κ=5, λ=8 kpc) failed on NGC 3198 under frozen constants.
The governance engine is untouched; the physics layer moves forward.
HELIX‑D defines a new stability‑field operator D, frozen before any plot, and subjected to the same falsifier: one operator, one set of constants, one galaxy. No retuning. No second chances.
This is the continuation of the stability‑physics program:
a new mapping, a new test, and a clean public verdict.
RFC: HELIX‑D — Successor Stability Mapping Successor to HELIX‑C. Purpose: Define a new stability‑field hypothesis sourced only by baryonic matter, with all constants frozen before any comparison to rotation‑curve data. Engine note: The governance engine (Slice 37–38) is unchanged; it never computed I. HELIX‑D is a physics‑layer RFC only.
1. Field Definition HELIX‑D defines a stability field I(x,t) sourced only by baryonic mass‑energy. I is not a particle species and not a fit parameter. Units: I → J/m³ rho_I = I / c² → kg/m³
2. Source Operator (new D) HELIX‑D replaces the HELIX‑C Helmholtz operator with a new differential operator D. One operator must be chosen and frozen before any plot.
Candidate forms: A) Modified Poisson ∇² rho_I = −α rho_b
B) Nonlinear Helmholtz ∇² rho_I − rho_I/λ² = −κ rho_b (1 + β rho_I/rho_b)
C) Diffusion‑driven (steady state) 0 = D ∇² rho_I − γ rho_I + S(rho_b)
D) Custom operator D[rho_I] = S(rho_b)
RFC rule: Only one operator is allowed. No retuning after seeing data.
3. Gravitational Coupling ∇² Φ = 4πG (rho_b + rho_I) v²(R) = R (∂Φ/∂R) No additional force‑law terms permitted.
4. Ceiling Condition |∂I/∂t| ≤ C_max Steady disks: ∂I/∂t = 0. Ceiling activates only for time‑dependent systems (mergers, bars, satellites).
5. Frozen Constants All constants must be declared before any solve: • Operator choice D • Coupling constants (α, κ, λ, β, D, γ, etc.) • Vertical scale height z_d • Numerical grid parameters No retuning after seeing v_obs.
6. Falsifier HELIX‑D is false if: • Frozen constants fail for a galaxy within published baryonic uncertainties • Mismatch occurs at ≥2 independent radii • A second galaxy fails under the same constants • Cluster lensing requires mass not aligned with baryons in a way D cannot produce No retuning permitted.
7. First Test Galaxy NGC 3198 is the required first test. Procedure: • Load published baryonic model (stars + HI) • Convert Σ_b(R) → rho_b(R,z) using frozen z_d • Solve source equation for rho_I • Solve Poisson for Φ • Compute v_HELIX(R) • Compare to v_obs • Apply falsifier
8. Second Galaxy Repeat with the same constants. If both fail, HELIX‑D is false.
9. Engine Note HELIX‑D physics is not implemented in
helix.py. This RFC defines the theory to be added. Governance engine remains separate.
10. Summary HELIX‑D is the successor hypothesis. It replaces the HELIX‑C operator with a new D, freezes constants before data, and subjects the mapping to the same public falsification rules. This is the scientific continuation of the HELIX stability program.
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