The Interior Observer Cosmological Framework: Paper 20 - The Radiation Scope-Boundary Theorem, the Acoustic Theorems, and the BBN Radiation Algebra

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 addresses three foundation problems, diagnoses the assembly gap in the background equation, and conducts the deepest investigation of the BBN radiation sector yet attempted in the IO framework. Two new theorems are proved: the Acoustic History Reduction Theorem (Theorem 20. 1) and the Acoustic Phase-Calibration Theorem (Theorem 20. 2, conditional on premise AC1), predicting the CMB acoustic scale θ* to 0. 429% of Planck's measurement with no fitted parameters. The radiation-slot identity is closed as a scope-boundary result. The torsion-Λ bare branch is algebraically specified with H₀ = 61. 06 km/s/Mpc. The D/H discrepancy identifies a required excess ΔNₑff ≈ 0. 37 for future derivation; twelve candidate mechanisms are tested and ruled out at various levels of rigor. Three radiation-sector construction theorems are proved, the puncture-resolved isolated-horizon algebra is constructed, and the sharpest remaining construction route is identified. Developed through a multi-AI collaborative pipeline: Claude (Anthropic) as orchestrator, Codex/ChatGPT (OpenAI) for computation, Wolfram/ChatGPT (OpenAI) as primary validator, and Gemini (Google DeepMind) as adversarial reviewer. https: //dfife. github. io/index. html v2. 0 (May 2026): First publication-ready release. Major scope reduction and retitle: the paper is restructured around the three surviving theorem families that are not superseded by downstream papers — the Radiation Scope-Boundary Theorem (20. 3), the Acoustic Theorems (20. 1 and 20. 2), and the BBN Radiation Algebra Theorems (20. RAD1, 20. RAD2, 20. RAD3). Removed: the bare package reconstruction (former Part II) and assembly gap diagnostic (former Part IV), closed by Paper 29 as a normalization error; the ΔNₑff investigation and radiation target (former §13–§14), superseded by Paper 22 v1. 5/v1. 6’s rate-dressing resolution; and the reduced-to-full extension sketch (former Part VI), replaced by Paper 31’s coexact-vector channel uniqueness theorem and Paper 32’s fermionic/chiral bridge sector. The R4 optical readout normalization is FIRAS-fixed (R4FIRAS = 1. 0031 ± 0. 0096 via Paper 17 v1. 5 Theorem 17. 2) ; the observed CMB temperature is not counted as an independent IO prediction. The acoustic-phase-calibration premise AC1 is DERIVED/CONDITIONALVERIFIED through Paper 21 closure. Status labels follow the canonical Claims Discipline at https: //github. com/dfife/io-framework-public/tree/main. Section numbering compressed from sixteen to nine; Parts compressed from six to three. Acoustic residual alignment: the legacy 0. 429% percentage residual (computed under an earlier convention) is dropped; the current row is the 9. 2σ residual against Planck’s θ* = 0. 597° ± 0. 00026°. Reproducibility bundle: paper20-v2. 0 (release tarball SHA256 6e3d9a6cb002a68548bb71ed9615c0d900377724be261bc931589fd69f1ee091; validator 22/22 PASS). v1. 7 (May 2026): Cross-paper reference update to reflect current Paper 22 published state, plus Conventions v2. 0 citation upgrade. All references to "Paper 22 v1. 3" updated to "Paper 22 v1. 5" (nine total locations including two bold supersession callouts at Section 13 and Section 14) since Paper 22 has subsequently been corrected through v1. 4 (PRyMordial wrapper YPBBN -> YPCMB correction, May 2026) and v1. 5 (GMP/TBS premise-status corrections labeling Theorems 22. 23-22. 25 as DERIVED/CONDITIONAL on GMP + TBS, May 2026). The cited Paper 22 chi² (D/H + Yₚ) value is updated from 1. 50 (Paper 22 v1. 3 published, using YPBBN output) to 0. 80 (Paper 22 v1. 5 corrected, DERIVED/CONDITIONAL on GMP + TBS) at two locations. The Paper 20 v1. 6 corrected scorecard (Yₚ +0. 70 sigma, D/H -0. 55 sigma, chi² = 0. 80) is unchanged and now matches Paper 22 v1. 5 exactly, confirming cross-paper consistency. Bibliography conventions entry is updated to cite IO Framework Conventions v2. 0 (unified: observational, labeling, versioning, and cross-paper reference conventions; https: //dfife. github. io/data/conventionsᵥ2. md), the new canonical reference deployed in May 2026 that consolidates the prior Observational Conventions v1. 0 (now Section 1 of v2. 0) with formal labeling, versioning, and cross-paper reference conventions in Sections 2-4. The v1. 0 file remains live at its original URL for backward compatibility with already-published papers including Paper 20 v1. 6; in-text references to "Observational Conventions v1" remain accurate as a historical citation. Section 8 (Tiered Scorecard) classification is corrected: D/H at -0. 55 sigma is moved out of "Failures" into a new "Former failure resolved by v1. 6 correction" subsection, while Li-7 at +12. 20 sigma remains under "Remaining failure. " The previous classification contradicted the v1. 6 correction's own narrative (the abstract, version history, Section 9 update, and Sections 13-14 supersession notes all say D/H is largely resolved by the wrapper/amplitude correction). No Paper 20 numerical values, theorems, or no-go results change in v1. 7; this is a reference-hygiene plus internal-classification-consistency update only. The Master Mathematical Reference table source labels for D/H and Yₚ are also updated from plain 'Paper 12' to 'Paper 12 / Paper 20 v1. 7 corrected wrapper' to disambiguate that the displayed values are wrapper-corrected, not historical Paper 12 values (matching the Paper 21 v1. 6 convention). Paper 20's distinctive results (Acoustic Phase-Calibration Theorem 20. 2, twelve eliminated paths for theta*, BBN multi-channel incompatibility, Fₐbs target identification, abundance ratio measurement immunity) are unaffected by this update. v1. 6 (May 2026): PRyMordial output index correction (YPBBN -> YPCMB) and amplitude framework alignment to Paper 22 v1. 3 / Paper 24 v2. 2 standard (epsilonw = 0. 012301, epsilonₙ = 0. 023842). Paper 20 v1. 5 BBN scorecard reflected an older amplitude branch and read PRyMordial output index 4 (YPBBN) instead of index 3 (YPCMB). Corrected scorecard: Yₚ = 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), chi² (D/H + Yₚ) = 0. 80. Sections 13 (Twelve No-Go and Null Results for DeltaNₑff) and 14 (The Radiation Target) are superseded by Paper 22's rate-dressing paradigm: the v1. 5 D/H tension at -3. 9 sigma that motivated those sections shrinks to -0. 55 sigma under the corrected wrapper plus modern amplitudes, removing the phenomenological need for DeltaNₑff approximately 0. 37. Paper 22 v1. 3 derives the active resolution through the j=1/j=2 channel-resolved rate-dressing construction. The twelve no-go results in Section 13 remain as documented research provenance constraining the search space. Observational denominators per IO Framework Observational Conventions v1 (https: //dfife. github. io/data/observationalconventionsᵥ1. md). Paper 20's distinctive results (Acoustic Theorems 20. 1-20. 2, Scope-Boundary Theorem, BBN Radiation Algebra Theorems 20. RAD1/RAD2/RAD3, puncture-resolved isolated-horizon algebra construction) are unaffected by this correction. v1. 5 (April 2026): Appendix replaced. Open/Closed tracking. Schur labels corrected. v1. 4 (April 2026): Full Schur branch appendix correction. All inherited appendix steps (29, 58, 60, 107, 122) and open-problem Item 16 updated to Schur definitive branch (H₀ = 68. 91, Paper 29). H₀ summary line corrected. Numerical values line marked SUPERSEDED. Title page standardized. All body theorems (Acoustic Theorems 20. 1–20. 2, Scope-Boundary, twelve θ* eliminations) are branch-independent v1. 3 (April 2026): Paper 29 branch consistency audit. The torsion-Λ bare branch (H₀ = 61. 06) in §2 is retired. The assembly problem (§6) and five ruled-out assembly paths (§7) are closed by Paper 29 — the root cause was a normalization error, not missing physics. §8 scorecard is superseded by the Schur definitive branch (H₀ = 68. 91, Ωₘ = 0. 336, Ωₖ = −0. 006). All component theorems (Scope-Boundary Theorem §1, Acoustic Theorems 20. 1–20. 2, twelve eliminated θ* paths §5) are unaffected. v1. 2 (March 2026): Full Appendix A catalog inherited from Paper 19 (Steps 1–129) with Paper 20 results appended (Steps 130–166). Title page reformatted. All main body results are convention-independent. See Paper 21 v1. 1 for the full audit.