The Interior Observer Cosmological Framework — Paper 21: The AC1 Derivation, the SU(2) Geometric Weight, and the Radiation Response Problem

Paper 21 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 derives AC1 (the acoustic angular scale Jacobian) from the existing Papers 15–20 stack, upgrading Paper 20's Theorem 20.2 to DERIVED/THEOREM status within the reduced scalar/longitudinal acoustic sector. The zero-parameter prediction θ_pred = 0.599° (Planck: 0.597°, residual 0.429%). Part II investigates the structural origin of the D/H radiation deficit, discovering the SU(2) Geometric Weight (Z_punc = 1.4221), proving the Optical Filtration Theorem (direct reduced RT/BY optical readout of θ is blind to noncentral SU(2) puncture data), and deriving the Absolute Local Casimir Load F_abs = 0.36879 matching the D/H target to 0.066% precision (STRUCTURALLY SUPPORTED CONSTRUCTION). Nineteen routes (eighteen P_resp plus freeze-in) are tested and killed. The surviving target is a non-separable, channel-dependent radiation response operator.

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v1.5 (May 2026): PRyMordial output index correction (YPBBN -> YPCMB) and amplitude framework alignment to Paper 22 v1.3 / Paper 24 v2.2 standard (epsilon_w = 0.012301, epsilon_n = 0.023842). Paper 21 v1.4 BBN scorecard reflected an older amplitude branch and read PRyMordial output index 4 (YPBBN) instead of index 3 (YPCMB). Corrected scorecard: Y_p = 0.24782 (+0.70 sigma), D/H = 2.510 x 10^-5 (-0.55 sigma), Li-7/H = 5.36 x 10^-10 (+12.20 sigma), chi^2(D/H + Y_p) = 0.80. Part II's nineteen-route radiation investigation is superseded by Paper 22 v1.3's rate-dressing paradigm: the v1.4 D/H tension at -3.9 sigma (chi^2 approximately 15.6) that motivated the F_abs = 0.36879 / DeltaN_eff approximately 0.37 hunt shrinks to -0.55 sigma (chi^2 = 0.80) under the corrected wrapper plus modern amplitudes, removing the phenomenological need for ΔN_eff approximately 0.37. Paper 22 v1.3, Theorem 22.23, derives the active resolution via the j=1 weak channel and j=2 nuclear channel rate-dressing construction (epsilon_w = K_gauge x L_1, epsilon_n = (langle K rangle / 10) x L_2) using exactly the puncture loads L_1 = 0.22417 and L_2 = 0.13805 derived in Paper 21. The nineteen no-go results in Part II remain as documented research provenance constraining the search space; the L_1 and L_2 puncture-load derivations remain load-bearing inputs to Paper 22's rate-dressing construction. Observational denominators per IO Framework Observational Conventions v1 (https://dfife.github.io/data/observational_conventions_v1.md). Paper 21's distinctive results (operator algebra construction, nineteen killed P_resp routes, puncture load derivations L_1 and L_2) are unaffected by this correction.

v1.4 (April 2026): Appendix replaced with Paper 20 v1.5 clean + Paper 21 results. AC1 closed. Open/Closed tracking.

v1.3 (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). Paper 19 intermediate supersession notes updated. Bare branch (H₀ = 61.06) references in §§7, 13, 14 marked SUPERSEDED (Paper 29). Title page standardized. All body theorems (AC1 derivation, SU(2) geometric weight, sky-slot inheritance, optical filtration, F_abs) are branch-independent.

Version 1.2 includes cycloid parameterization correction, clean Appendix A catalog (Steps 1–207) with Papers 18–20 status updates applied, and Wolfram/Gemini hostile review passes.