Big Bang Nucleosynthesis, the Unified Tension, and the c³ Hypothesis (Interior Observer Paper 7)

Paper 7 in the Interior Observer (IO) cosmological framework, which proposes the observable universe exists inside a Schwarzschild black hole. Big Bang Nucleosynthesis: Primordial element abundances are computed with IO parameters (H_IO/H_ΛCDM = 0.955, ω_b = 0.01694, η = 5.0×10⁻¹⁰). Helium-4 is consistent with observations (Y_p = 0.239, 1.5σ). The cosmological lithium problem is reduced by 42% compared to ΛCDM. Deuterium is overproduced by 38% (D/H = 3.5×10⁻⁵ vs observed 2.53×10⁻⁵), driven by the low baryon-to-photon ratio. All results independently verified by analytical computation (Wolfram/ChatGPT 5.3). Unified Tension Diagnosis: The deuterium excess, CMB first peak shift (ℓ₁ = 180, Paper 6), and H₀ gap (58.2 vs 67.4) trace to a single root cause: h = 0.582. A systematic investigation eliminates all candidate corrections: the FRW lapse is identically 1 (confirmed by Wolfram), Einstein-Cartan torsion-fermion coupling does not modify the metric (verified by three AI systems), holographic x^(1/3) scaling lacks a derivation, and Buchert backreaction is four orders of magnitude too small. Age Prediction: The IO Friedmann equation with reference parameters gives age = 19.2 Gyr — not 13.8 Gyr. This is consistent with all direct stellar age measurements (lower bounds ~12-13 Gyr) and provides the extended temporal runway needed to explain JWST observations of unexpectedly mature high-redshift galaxies. The derivation chain is self-consistent: M_U → r_s → Λ_IO → H(a) → age = 19.2 Gyr → R_U = 4.40×10²⁶ m. The c³ Hypothesis: In the Λ-dominated IO expansion (Ω_Λ = 0.933), the dark energy term provides 93.3% of H₀². The Hubble constant scales as H₀ ≈ c³√K_Λ/(2√3 × GM_U), an algebraic consequence of deriving Λ from the Schwarzschild horizon (Λ_IO = K_Λ/r_s²). The sensitivity d ln H₀/d ln c = 2.67 (→ 3.0 in the Λ-only limit). H₀ and T_IO move in opposite directions with M_U (d ln H₀/d ln M = −0.83, d ln T/d ln M = +0.41), proving the framework is structurally un-tunable. K_Λ Gap: The bare EC torsion formula gives K_Λ = 9π²/[4(1+γ_BI²)] = 21.02. The Friedmann closure requires K_Λ = 49.82 — a factor of 2.37, close to x² = (r_s/R_U)² = 2.31. Papers 1 and 4 used an x² correction, which this paper identifies as phenomenological, not derived. If the x² factor is physical, Λ ∝ 1/R_U² (epoch-dependent, w ≠ −1). This gap is identified as the framework's most critical open problem. The IO framework predicts H₀ = 58.2 km/s/Mpc and age = 19.2 Gyr — specific, falsifiable values derived from c³/(GM_U) with zero free parameters. Multi-AI research: Claude Code (Anthropic) for BBN computation, lapse investigation, speculative path analysis, and M_U sensitivity; Wolfram/ChatGPT 5.3 (OpenAI + Wolfram) for analytical verification of all results; Gemini 2.5 Pro (Google DeepMind) for unified tension diagnosis, torsion-fermion proposal, and adversarial review; Claude (Anthropic) for orchestration. Companion to Paper 1 (DOI: 10.5281/zenodo.18854813), Paper 2 (DOI: 10.5281/zenodo.18868612), Paper 3 (DOI: 10.5281/zenodo.18876346), Paper 4 (DOI: 10.5281/zenodo.18883069), Paper 5 (DOI: 10.5281/zenodo.18889865), and Paper 6 (DOI: 10.5281/zenodo.18891475).