The Interior Observer Cosmological Framework — Paper 22: The Spatial Hodge Complex and the Rate-Dressing Bridge: Channel Infrastructure, No-Go Landscape, and Framework-Constant Candidate BBN Amplitudes

Paper 22 of the Interior Observer (IO) Cosmological Framework. Beginning from two premises — (1) the observable universe exists inside a Schwarzschild black hole and (2) the physics inside the horizon is the same as outside — this paper constructs the complete scalar/vector/tensor spatial infrastructure on the S³ interior sections, derives a comprehensive no-go landscape eliminating all fluid-injection and uniform-dressing models for the radiation response problem, and identifies a surviving rate-dressing paradigm in which the boundary puncture algebra modifies bulk interaction cross-sections through the spatial Hodge channel infrastructure. A conditional zero-parameter amplitude construction using established framework constants (Kgauge, ⟨K⟩, L₁, L₂) produces a BBN scorecard with χ² (D/H + Yₚ) = 2. 89, conditional on three stated premises (GMP, WMR, TBS). The paper establishes a permanent Theorem Toolbox including the Channel Floor Theorem, the Injection No-Go, the Stress Scalarization Theorem, the Compact-Support Theta-Suppression Bound, and the Rate-vs-Stress Separation Theorem — framework-agnostic constraints applicable to any future model of boundary-to-bulk coupling in closed-universe cosmology. Multi-AI adversarial collaboration: Claude (Anthropic), Codex/ChatGPT (OpenAI), Wolfram/ChatGPT (OpenAI), Gemini (Google DeepMind). 256 derived steps. v1. 0. https: //dfife. github. io/index. html v1. 3 (April 2026): Full appendix rebuilt with complete step detail. Open/Closed tracking. Section order standardized. v1. 2 (April 2026): Full Schur branch appendix correction. All inherited appendix steps (29, 56, 58, 60, 107, 122) and open-problem Item 16 updated to Schur definitive branch (H₀ = 68. 91, Paper 29). Bare branch (H₀ = 61. 06) marked SUPERSEDED. Title page standardized. All body results (Spatial Hodge Complex, rate-dressing bridge, channel infrastructure) are branch-independent. v1. 1 (March 2026): Weak amplitude corrected from εw = Kgauge × √L₁ to εw = Kgauge × L₁ via the Quadratic Thermal Covariance Theorem: the physical thermal rate is |M|² (a two-point function), quadratic in the bridge field, structurally excluding V' = 2γ. WMR resolved as CONDITIONAL/THEOREM on premises H1–H3 (stated in §17. 2). Premise count updated from three to four original premises (GMP, WMR, TBS, TT1) ; TT1 derived, WMR resolved, two remain (GMP + TBS). Numerical updates: εw = 0. 012301, εₙ = 0. 023842, D/H_σ = −0. 61, Yₚ_σ = +1. 06, χ² (D/H + Yₚ) = 1. 50, GF shift = 0. 62%. Weak gap closed to 0% by construction. Nuclear gap closed to 0% by construction. Amplitude asymmetry updated: both channels quadratic (L₁, L₂). Wolfram math review and Gemini physics review incorporated. 39 Paper 25 added to bibliography.